The Pennsylvania State University

The Graduate School

ELECTRICAL CONDUCTION THROUGH POLYVINYLIDENE

FLUORIDE: EXPLOITING THE INTERFACE AS A BARRIER TO

CHARGE TRANSPORT

A Dissertation in

Materials Science and Engineering

by

Michael Anthony Vecchio

© 2019 Michael Anthony Vecchio

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

August 2019

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The dissertation of Michael Anthony Vecchio was reviewed and approved* by the following:

Zoubeida Ounaies

Professor of Mechanical and Nuclear Engineering

ALP Fellow, Big Ten Academic Alliance

The International Society for Optics and Electronics Senior Member

Dissertation Co-Advisor

Co-Chair of Committee

Michael T. Lanagan

Professor of Engineering Science and Mechanics

Dissertation Co-Advisor

Co-Chair of Committee

Michael Hickner

Professor of Materials Science and Engineering, Chemical Engineering

Corning Faculty Fellow

Ramakrishnan Rajagopalan

Assistant Professor of Engineering in Applied Materials

John Mauro

Professor of Materials Science and Engineering

Associate Head for Graduate Education

Chair, Intercollege Graduate Degree Program

*Signatures are on file in the Graduate School

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ABSTRACT

Polymer capacitors exhibit a combination of unique properties including high dielectric

breakdown strength, light weight, flexibility, and low-cost production that make them appealing

candidates for film capacitor technologies. For high power capacitor applications, biaxially

oriented polypropylene (BOPP) is considered state of the art and exhibiting breakdown strengths

as high as 850 MV/m, however its low permittivity (εr = 2.2) prevents its use in high-energy density

demanding applications. In this dissertation, high permittivity (8 < εr < 12) polar polymers

poly(vinylidene fluoride) (PVDF) and its copolymer poly(vinylidene fluoride trifluoroethylene)

(P(VDF-TrFE)) are used as model materials to investigate the role of interfaces on low frequency,

high temperature and high electric field charge transport. This work demonstrates 1) the

importance of electrode/dielectric interface chemistry in controlling charge injection and

conduction, and 2) how interfaces in layered dielectrics block transport of impurity ions ultimately

influence dielectric performance.

The high field performance of hot-pressed layered dielectrics in pure PVDF laminates was

explored first. The solution processing and hot-press lamination procedure produced films

containing both alpha and beta crystal phases throughout the bulk. Impedance spectroscopy at

70oC combined with equivalent circuit (EC) modeling demonstrated a blocking effect in PVDF

films containing 4 layers relative to the 1-layer control. Finally, dielectric breakdown experiments,

analyzed via Weibull statistics, reveal a statistically significant 16% increase in the breakdown

strength of 3-layer films (490 MV/m) relative to 1-layer (415 MV/m) analyzed using a 90%

confidence interval. These initial results imply that multilayer lamination low frequency charge

migration which leads to higher dielectric breakdown strength, however hot-pressing proved to be

a disadvantageous processing procedure: layer counts beyond 4 were not possible due poor

repeatability and individual layer thickness is ~10μm.

A spin cast process was developed as an alternative to hot pressing for creating

reproducible P(VDF-TrFE) thin films. (~1μm thick). Electrode/dielectric interfacial chemistry on

high-field conduction was studied by controlling P(VDF-TrFE) surface chemistry using a CF4/O2

reactive ion plasma treatment. It was found that oxygen based chemical moieties detected using

X-ray photoelectron spectroscopy (XPS) grafted to the film surface cause Schottky barrier height

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lowering by approximately 0.05 eV. This reduction accounted for an order of magnitude increase

in leakage current at high fields.

The effect of a pure oxygen plasma treatment was then assessed in 10μm thick polyimide

(PI) films. PI exhibits a non-polar chemical structure and surface chemistry modification after

plasma treatment had a different effect on high-field conduction relative to P(VDF-TrFE). A

combination of hopping, Poole-Frenkle, and Schottky theoretical frameworks were used to analyze

charging current as a function of voltage and temperature in untreated and oxygen plasma treated

PI. It was found that oxygen moieties introduced via plasma treatment caused both decrease in the

leakage current of PI films at high temperature and delayed transition from bulk dominated

conduction (hopping) to interface dominated conduction (Schottky) by 50oC relative to untreated

PI. It is posited that the presence of electronic trapping centers introduced by chemical

modification at the electrode/dielectric interface are responsible for electronic charge scattering

and trapping at high temperatures.

The influence of interfaces on ionic transport in P(VDF-TrFE) multilayer films was

explored. Lithium perchlorate (LiClO4) is first doped into 1-layer P(VDF-TrFE), creating

dielectrics in which the impurity ion species is controlled and well known. Differential scanning

calorimetry (DSC) revealed a correlation between curie transition temperature of copolymer’s beta

phase and LiClO4 concentration added into the material. EC modeling of impedance spectra as a

function of temperature captured Li+ ion interaction with crystalline phases distributed throughout

the bulk as well as the electrode dielectric interface at low frequency and high temperature. It was

found that the impedance of crystalline interfaces and the electrode/dielectric interface is a major

contributor to the overall electrical response of the film, indicating that ions are blocked at

interfaces.

Finally, multilayered composites were created with alternating doped P(VDF-TrFE) and

thin (500nm) poly(vinyl alcohol) (PVA) layers used to develop an ion depleted interface. The EC

model used to describe 1-layer films of P(VDF-TrFE) was used to develop a model that predicts

the impedance behavior of doped layered composites. Impedance spectroscopy, EC modeling, and

TSDC are used to prove the occurrence of impurity ion blocking at the interface leading to

substantial space charge distribution through the bulk of the composites at low frequencies and

high fields. Finally, high voltage dielectric breakdown experiments were performed, and the defect

v

dominated breakdown mechanism showed most significant effect due to layering and is described

well using Weibull statistics.

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TABLE OF CONTENTS

LIST OF FIGURES ………………………………………………………………………………x

LIST OF TABLES ………………………………………………………………………………xv

ACKNOWLEDGEMENTS …………………………………………………………………….xvi

CHAPTER 1: INTRODUCTION ………………………………………………………………..1

1.1 HISTORY OF CAPACITORS ………….………………………………………………...1

1.2 CAPACITORS AND DIELECTRIC MATERIALS ……………………………………..2

1.2.1 Electrochemical Capacitors ……………………………………………….………...3

1.2.2 Ceramic Dielectrics …………………………………………………………………5

1.2.3 Polymer Dielectrics …………………………………………………………………7

1.3 PVDF AS A DIELECTRIC MATERIAL ……………………………………….………10

1.3.1 Material Structure ………………………………………………………….………10

1.3.2 Limitations of PVDF for Energy Storage ………………………………….………11

1.4 INTERFACES FOR IMPROVED DIELECTRIC PERFORMANCE ………………….15

1.4.1 The Electrode/Dielectric Interface ………………………………………………...15

1.4.2 The Bulk Distributed Interface ……………………………………………….……16

1.5 PROBLEM STATEMENT AND RESEARCH GOAL ………………………….……...19

1.6 ORGANIZATION OF DISSERTATION ……………………………………….………21

CHAPTER 2: MATERIAL PROCESSING, CHARACTERIZATION AND DATA

PROCESSING TECHNIQUES …………………………………………………………………23

2.1 INTRODUCTION ………………………………………………………………….……23

2.2 PVDF PROCESSING AND SAMPLE PREPERATION ………………………….……24

2.2.1 PVDF Casting and Hot-Press Lamination …………………………………….…...24

2.2.2 P(VDF-TrFE) Spin Casting …………………………………………………….….26

2.2.3 Electrode Deposition ………………………………………………………………27

2.2.4 Plasma Treatment ………………………………………………………………….29

2.3 MATERIAL CHARACTERIZATION EQUIPMENT AND METHODS ……………...32

2.3.1 Bulk Chemical Characterization …………………………………………………...32

2.3.1.1 Differential Scanning Calorimetry (DSC) …………………………….…32

2.3.1.2 Fourier Transform Infrared Spectroscopy (FTIR) …………………….....33

2.3.2 Surface Chemical Characterization …………………………………………….…..36

2.3.2.1 Optical Profilometry ………………………………………………….….36

2.3.2.2 H2O Contact Angle ……………………………………………………....36

2.3.2.3 X-ray Photoelectron Spectroscopy (XPS) ………………………………..38

2.3.2.4 Time of Flight Secondary Ion Mass Spectrometry (ToF-SIMS) ………....40

2.3.3 Electrical Characterization ………………………………………………………...41

2.3.3.2 Impedance Spectroscopy and Equivalent Circuit Modeling …………….41

2.3.3.2 Current Voltage (I(V)) Charging Experiments ……………………….….44

2.3.3.3 Thermally Stimulated Depolarization Current Measurement (TSDC) …..49

2.3.3.4 High Voltage Dielectric Breakdown Measurements and Weibull

Statistics………………………………………………………………………….52

2.4 SPECIAL ANALYTICAL TECHNIQUES ………………………………………….….54

2.4.1 Bootstrap Statistics Applied to I(V) Data …………………………………….……54

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2.4.2 Equivalent Circuit (EC) Modeling …………………………………………….…...57

2.4.2.1 Equivalent Circuit Theory ……………………………………………….58

2.4.2.2 Statistical Interpretation of Fit Parameters ………………………….…..61

2.4.3 TSDC Peak Deconvolution ………………………………………………………...62

CHAPTER 3: HOT-PRESSED PVDF LAMINATES ………………………………….………64

3.1 INTRODUCTION ………………………………………………………………….……64

3.2 MATERIALS AND METHODS ………………………………………………………..65

3.2.1 Materials Selection ………………………………………………………………...65

3.2.2 Multilayer Laminate Fabrication ……………………………………………….….65

3.2.3 Structural Characterization …………………………………………………….......66

3.2.4 Dielectric Measurement …………………………………………………………....66

3.3 RESULTS …………………………………………………………………………….….67

3.3.1 SEM Imaging the Interface …………………………………………………….…..67

3.3.2 DSC PVDF Thermal Analysis ………………………………………………….….67

3.3.3 FTIR PVDF Crystal Structure Analysis ……………………………………….…..68

3.3.4 Dielectric Breakdown ………………………………………………………….…..69

3.3.5 Impedance Spectroscopy …………………………………………………………..71

3.4 CONCLUSIONS …………………………………………………………………….…..73

CHAPTER 4: PLASMA SURFACE MODIFICATION OF P(VDF-TrFE): INFLUENCE OF

SURFACE CHEMISTRY AND STRUCTURE ON ELECTRONIC CHARGE INJECTION ...75

4.1 INTRODUCTION ...………………………………………………………………….….76

4.2 EXPERIMENTAL SECTION ……………………………………………………….…..78

4.2.1 Materials …………………………………………………………………………...78

4.2.2 Thin Film Fabrication ……………………………………………………………...78

4.2.3 Plasma Surface Modification ……………………………………………………....78

4.2.4 Investigated Processing Conditions ………………………………………………..79

4.2.5 Characterization Techniques ………………………………………………………79

4.2.5.1 Chemical and Structural ………………………………………………....79

4.2.5.2 Electrical ………………………………………………………………...80

4.3 RESULTS AND DISCUSSION ………………………………………………………....81

4.3.1 Differential Scanning Calorimetry ………………………………………………...81

4.3.2 X-ray Photoelectron Spectroscopy: Surface Chemistry and Structure Analysis …..82

4.3.3 ToF-SIMS Depth Profiling ………………………………………………………...84

4.3.4 Surface Roughness and Contact Angle Analysis …………………………………..85

4.3.5 Low Field Measurements ………………………………………………………......88

4.3.5.1 Dielectric Spectroscopy …………………………………………….……88

4.3.5.2 Ohmic Current – Voltage (I-V) Experiments ……………………….……90

4.3.6 High Field Current Density – Electric Field (J-E) Measurements …………………91

4.3.6.1 Conduction Mechanism Identification: Schottky and Poole-Frenkel

Modeling ………………………………………………………………………....91

4.3.6.1 Quantifying the Change in Barrier Height ………………………………94

4.4 CONCLUSIONS …………………………………………………………………….…..97

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CHAPTER 5: CONFUCTION THROUGH PLASMA TREATED POLYIMIDE: ANALYSIS

OF HIGH FIELD CONDUCTION BY HOPPING AND SCHOTTKY THEORY ………….....99

5.1 INTRODUCTION ……………………………………………………………………...100

5.2 ANALYTICAL METHODS …………………………………………………………...102

5.2.1 Bulk Dominated Conduction ………………………………………………….….103

5.2.2 Interface Dominated Conduction ………………………………………….……...104

5.3 RESULTS AND DISCUSSION ………………………………………………….…….104

5.3.1 Leakage Current Results …………………………………………………….……104

5.3.2 Data Analysis ……………………………………………………………….…….106

5.3.2.1 Modeling Bulk Conduction ………………………………….………….106

5.3.2.2 Interface Dominated Conduction ………………………………………112

5.4 DISCUSSION AND CONCLUSIONS ………………………………………….……..115

CHAPTER 6I: ANALYSIS OF LOW FIELD IMPURITY ION MIGRATION IN LiClO4

DOPED P(VDF-TrFE) THIN FILMS ………………………………….………………………117

6I.1 INTRODUCTION …………………………………………………………………….119

6I.2 MATERIALS AND METHODS …………………………………………….………..120

6I.2.1 Materials ………………………………………………………………….……...120

6I.2.2 Thin Film Fabrication …………………………………………………….……...121

6I.2.3 Structural Characterization ……………………………………………….……...121

6I.2.4 Electrical Measurements ………………………………………………………...121

6I.3 RESULTS AND DISCUSSION ………………………………………………………122

6I.3.1 Differential Scanning Calorimetry (DSC) ………………………………………122

6I.3.2 Dielectric Spectroscopy …………………………………………………………123

6I.3.3 AC Conductivity ………………………………………………………………...125

6I.3.4 Impedance Spectroscopy ………………………………………………….……..126

6I.4 EQUIVALENT CIRCUIT MODELING …………………………………….………..130

6I.4.1 Modeling the Capacitive Response …………………………………….………..132

6I.4.1.1 Electronic Polarization ………………………………………………..132

6I.4.1.2 Permanent Dipole Orientational Polarization ………….……………..132

6I.4.1.3 Ionic / Space Charge Conduction ………………………….…………..134

6I.4.1.4 Blocking Polarization ……………………………….…………………135

6I.4.2 Modeling the Resistive Response ……………………………………….……….137

6I.5 CONCLUSIONS …………………………………………………………….………...139

CHAPTER 6II: CONDUCTION IN MULTILAYERED LAMINATES: EXPLOITING THE

INTERFACE AS A BARRIER TO CHARGE TRANSPORT ………………….……………..141

6II.1 INTRODUCTION ……………………………………………………………………141

6II.2 MATERIALS AND METHODS ………………………………………….………….142

6II.2.1 Materials ………………………………………………………………………..142

6II.2.2 Multilayer Processing …………………………………………………………..143

6II.3 RESUTS AND DISCUSSION ………………………………………….…………….144

6II.3.1 Differential Scanning Calorimetry …………………………………….………..144

6II.3.2 Dielectric and Impedance Spectroscopy ……………………………….……….145

6II.3.3 Equivalent Circuit Modeling ………………………………………….………...148

6II.3.4 Thermally Stimulated Depolarization Current Measurements (TSDC) .………..151

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6II.3.4.1 TSDC on 1-layer P(VDF-TrFE) ……………………………………...151

6II.3.4.2 TSDC on 4-layer P(VDF-TrFE) ……………………………………...155

6II.3.5 High Voltage Dielectric Breakdown ………………………….………………...158

6II.4 CONCLUSIONS ……………………………………………………………………..160

CHAPTER 7: CONCLUSIONS AND FUTURE WORK …………………………….………162

7.1 CONCLUSIONS ……………………………………………………………….………162

7.2 SIGNIFICANT CONTRIBUTIONS …………………………………….……………..166

7.3 FUTURE WORK ………………………………………………………………………169

7.3.1 Tailoring the Electrode/Dielectric Interface for Controlled Current Injection …...169

7.3.2 Multilayer Dielectric Processing ………………………………………….………169

7.3.3 Composite Characterization Using High Voltage Techniques ………….………..171

APPENDIX A: Annotated Code for I(V) Nonlinear Regression ……………..……….………174

APPENDIX B: Annotated Code for TSDC Peak Fitting ………………………………………177

APPENDIX C: P(VDF-TrFE) Poole-Frenkel Analysis …………….…………………………180

APPENDIX D: Polyimide I(V) Nonlinear Regression Parameter Estimates ……………….…182

APPENDIX E: Equivalent Circuit Estimate Error Reports ……………………………………185

Bibliography…………………………………………………………………………………...187

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LIST OF FIGURES

Figure 1-1: Ragone plot comparing the specific power and energy in common types of energy and

power storage devices. (figure credit [1]).

Figure 1-2: The charging and discharge cycle depicted for a typical electrochemical capacitor

(image credit [2]).

Figure 1-3: The dielectric constant of BaTiO3 as a function of temperature. Crystal phase

transitions are shown as a function of temperature above, corresponding to maxima in the

material’s dielectric constant (image credit [3]).

Figure 1-4: Breakdown strength of polymers, composites (nanodielectrics) and ceramics

organized by their dielectric constant (credit Tan et al. MatSc&App 2013).

Figure 1-5: a) impact of BaTiO3 nanoparticle inclusion and nanoparticle chain alignment on Ebd

in silicone composites [4] and b) impact of Al nanoparticle inclusion on Ebd in PP [5]. DC dielectric

breakdown data analyzed via 2 parameter Weibull statistics.

Figure 1-6: a) polymer chains of PVDF showing TTTT and TGTG¯ conformations associated

with the β- and α-phases respectively (image credit [6]), b) α-phase crystal structure and c) β-phase

crystal structure (image credit [7]).

Figure 1-7: Ragone plot for an ideal battery depicting the energy/power relation with and without

contributions from leakage RL (image credit [8]).

Figure 1-8: a) displacement current D vs electric field E loop depicting normal ferroelectric

behavior with purple shaded region representing recoverable energy density (image credit [9]) and

b) D-E behavior of biaxially oriented PVDF at 10Hz showing strong ferroelectricity (imag credit

[10]).

Figure 1-9: a) dielectric breakdown strength of P(VDF-TrFE-CTFE) as a function of electrode

material and b) high field leakage current as a function of electrode material. Major differences

are observed for Ag vs Al, reflecting significance of electrode/dielectric interface on controlling

high field conduction [11].

Figure 1-10: BOPVDF TSDC for a) Ag electrodes and b) Al electrodes. Both samples are

measured under the same conditions: Ep = 10 MV/m, Tp =50oC, heating rate = 5oC/min, and tp

ranges from 10 min – 50 min [12].

Figure 1-11: Leakage current as a function of electric field for untreated and plasma treated PI at

150oC. Both reduction of data scatter and magnitude of leakage current occurs after plasma

treatment [13].

Figure 1-12: a) SEM images of 32-layer and 256-layer P(VDF-HFP) / PC microlayer coextruded

multilayer laminate along with b) effect of composite structure on breakdown strength. The 32-

layer laminate from a) results in a composite dielectric breakdown strength surpassing P(VDF-

HFP) and PC alone [14].

Figure 1-13: a) schematic showing PC / P(VDF-HFP) coextruded composite (similar to Mackey

et al.) with PMMA tie layer incorporated. b) dielectric breakdown strength of multilayer composite

using multiple tie layer materials and c) dielectric loss tangent showing frequency reduction in

ionic relaxation for the PC / PMMA tie layer / P(VDF-HFP). Decrease in relaxation frequency is

related to decreased ionic mobility in the PMMA/P(VDF-HFP) interphase shown in a) [15].

Figure 1-14: Schematic of the proposed multilayer dielectric model system. The

electrode/dielectric interface is tailored by plasma treatment. Under electric field, Li+ cations

behave as a probe to target interfaces introduced via spin casting.

xi

Figure 2-1: PVDF processing procedure showing a) magnetic stirring (10-15% solid wt), b)

solution degassing, c) solution casting using Dr. Blade, d) film drying under vacuum 180oC for 1

hr stepped down to 60oC for 3 hrs with final 1-layer film, e) stacked multilayer sandwiched

between Kapton protective sheets and f) hot-pressing at 18-24 MPa at 150oC for 30 min.

Figure 2-2: Spin cast procedure depicting a) 3 – 15 wt% P(VDF-TrFE) solution deposition, wet

film drying at 100oC for 15 min and c) schematic of dried film with 10 scratched in profilometer

scan areas.

Figure 2-3: Spin cast parameter study varying spin speed (rpm) and solution solid wt%. a) contains

data for 15 and 7.5% wt films while b) shows thicknesses measured for 3% wt thin films.

Figure 2-4: Schematic showing stepwise process of determining plasma process etch rate. a) film

deposition onto square silicon substrate, b) scratched groove spanning substrate, c) profilometry

over step edge (5 scans total) d) application of 30s plasma treatment (see Table III for parameters),

and e) profilometry on treated film. Steps e – d are repeated 3 times.

Figure 2-5: Copolymer film thickness as a function of plasma treatment exposure time. A

calculated R2=9.97 indicates a linear relation between film thickness and exposure time where an

etch rate of 0.74 nm/s can is extracted.

Figure 2-6: Simplified model for a dielectric material under impedance spectroscopy test,

incorporating ideal capacitive and resistive components to describe electronic, orientational, and

ionic polarizations. The EC used in this dissertation is leveraged from this and discussed in section

2.4.2.

Figure 2-7: J(E) behavior of a) PI sample set displaying 45 data points taken at 25oC and b) the

bootstrapped sample set PI* containing 45 data points resampled with replacement from PI. The

outcome of resampling with replacement can be seen by gaps in data due to duplicate sampling.

Figure 2-8: EC model depicting polarization mechanisms associated with P(VDF-TrFE)

polycrystalline structure at frequencies spanning 10-1-105 Hz. Nested CPE3/R4 and CPE4

distributed circuit elements are incorporated to describe low frequency ion interaction with crystals

and the electrode/dielectric interface respectively.

Figure 2-9: Schematic of TSDC peak deconvolution procedure depicting a) fitting of strongest

signal in convoluted spectrum, b) subtraction of fit function from raw data over temperature range

and c) fitting deconvoluted low temperature peak.

Figure 3-1: a) SEM image of 2-layer cross section (displaying developed interface) and b) DSC

thermogram of un-pressed, 1-layer hot-pressed, and 4-layer laminate.

Figure 3-2: ATR-FTIR morphological characterization of hot-pressed laminates. Absorbance

spectra of PVDF films from top to bottom A) 1-layer, B) 1-layer hot-pressed, C) 2-layer D) 3-layer

and E) 4-layer laminates. Salient spectral features are discussed in this section. All PVDF

vibrational modes are presented in Chapter 2 section 2.3.1.2 Table 2-IV.

Figure 3-3: a) dielectric breakdown strength shown for 1-layer films, 1-layer hot pressed, 2- and

3-layer films and b) dielectric breakdown strength plotted as a function of t for 1-layer hot pressed,

2- and 3-layer films.

Figure 3-4: Dielectric permittivity and loss tangent calculated from impedance spectroscopy

measurements between 10-2 Hz – 105 Hz for 1-layer and 4-layer PVDF laminates. EC modeling

performed using the shown circuits for each sample set (bottom left) with parameter estimates

(bottom right).

xii

Figure 4-1: C1s and O1s spectra for as-spun control as well as post-anneal samples. Line shape

does not vary between 45s – 180s treatment times for all sample sets. Intensity axis heights share

the same scaling for easy comparison in each C1s and O1s group respectively.

Figure 4-2: ToF-SIMS depth profiles for CFO+ and CO+ ions in a plasma-treated film. This plot

was generated by taking the ratio of the corresponding profiles of the treated film to those of the

untreated control film (plasma treated signal/untreated signal).

Figure 4-3: a) Copolymer surface roughness (Sq) as a function of plasma exposure time for the

as-spun control and post-anneal sample sets. Data is averaged from 8 separate 87μm x 87 μm scans

per sample. b) Images of film surface topology for each treatment condition taken by optical

profilometry. Each image corresponds to the average Sq in a.

Figure 4-4: a) Contact angle measured as a function of treatment time as-spin and post-anneal

conditions. b) Images of H2O sessile drops at first impact on copolymer surface for each treatment

time.

Figure 4-5: Dielectric response under 1V rms AC electrical signal for the post-anneal processing

condition. Untreated, 45s, and 180s treated samples were tested.

Figure 4-6: Low field I(V) measurements for the post anneal sample set. The untreated control,

45s treated, and 180s treatment times are shown.

Figure 4-7: High field J(E) measurements for the post-anneal processing condition. Again, the

untreated control, 45s and 180s treatment times are shown.

Figure 4-8: Both Schottky and Poole-Frenkel plots for untreated and plasma treated P(VDF-TrFE)

J(E) data are displayed. The linear fit equation used to calculate permittivity from equations (4-5)

and (4-6) for each set of data are labeled and displayed next to the corresponding curve.

Figure 4-9: Parametric study of current generation during a Schottky emission process. Graph a,

b, and c demonstrate the impact of ranging A*, εr, and ϕS, respectively. Variables held constant and

their respective values are shown above each plot, while the upper and lower limits of the

parameter ranged is indicated within the plot.

Figure 5-1: Charging current measured for PI as a function of charge time at room temperature.

Figure 5-2: J(E) data for untreated and O2 plasma surface treated PI at a) 25oC, b) 100oC, and c)

150oC. Applied voltage is held for 20s (time required to obtain steady state conduction) before

current measurement at each field

Figure 5-3. Arrhenius plot for Pure P1 over the temperature range 25oC – 150oC. Activation

energy is extracted from linearization of equation (5-6) and the slope of the linear fit function

Figure 5-4 Hopping parameters Jo and d estimated using the bootstrapping statistical approach

Figure 5-5 J(E) data from Figure 5-2 transformed into Schottky plot format. Again, measurements

were taken at a) 25 oC, b) 100 oC and c) 150 oC. Here slope of linear fit corresponds to βs/kT in

equation (5-7)

Figure 5-6 Permittivity values calculated from linear fits from Schottky plots between 25oC –

175oC. A shaded region is marked indicating the range between high frequency permittivity (n2)

and permittivity measured between 100Hz – 100kHz.

Figure 6I-1: a) real part of the permittivity and b) loss tangent measured at 25oC as a function of

frequency for ionic content up to 1.0 wt%.

Figure 6I-2: a) real part of the permittivity and b) loss tangent measured at 100oC as a function of

frequency for salt wt %’s 0 – 1.0%.

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Figure 6I-3: AC conductivity calculated using equation 1 calculated at 100 kHz – 0.1 Hz for each

of the measured LiClO4 wt %. Temperatures measured are a) 40oC, b) 80oC, and c) 100oC.

Figure 6I-4: Cole-Cole plot of impedance for 0 – 1.0% doped samples at 25oC. The material’s

bulk response cannot be fully resolved however a general trend between LiClO4 addition and

conductivity is observed.

Figure 6I-5: Complex impedance Cole-Cole plots at 100oC for a) all tested samples, b) 0.1% –

1.0% samples and c) 0.25 – 1.0% samples.

Figure 6I-6: Arrhenius plot of σb for LiClO4 range of 0.25% – 1.0%. Extracted activation energies

from linear fits are shown in the embedded table

Figure 6I-7: a) physical model of doped P(VDF-TrFE) with equivalent circuit (EC) model used

in fitting impedance spectra, b) raw impedance data (open symbols) with EC fit (solid lines) at

25oC and c) 100oC.

Figure 6I-8: Estimated parameter values for a) Q2 from CPE2 as a function of salt wt % and b)

approximated material permittivity. Each film tested is of equivalent thickness. Units for Q are

written in terms of conductivity as S sn given equation 61-5.

Figure 6I-9: The behavior of CPE3 as a function of LiClO4 wt % for the temperatures 25 oC – 100 oC. the standard deviation of parameter estimates in the sample set are reflected by error bars.

Fitting between 100oC – 110oC produces large standard deviations in n3 as well as erratic parameter

estimates for n3 and Q3.

Figure 6I-10: Fit results for CPE4 and n4 as a function of salt wt % at temperatures 25 oC – 110 oC. Q4 reflects ionic charge interaction associated with Li+ and the electrode where 0.5 < n4 < 1.0

estimates indicate electrode/polymer interfacial roughness and heterogeneous charge distribution

at the interfce.

Figure 6I-11: Fit results for resistive EC elements a) R3 associated with amorphous regions of the

bulk and b) R4 associate with the crystalline/amorphous interface plotted as a function of LiClO4

solid wt %. R4 is shown to dominate resistive response at low temperature and LiClO4 wt%.

Figure 6II-1: schematic of multilayer material system depicting material components and the

anticipated results.

Figure 6II-2: SEM image of 5-layer sample depicting PVA interfaces and P(VDF-TrFE)

copolymer layers.

Figure 6II-3: permittivity and loss tangent for pure 10μm copolymer cast from MEK. A strong

relaxation peak in the loss tangent is observed between 1-30 Hz in the vicinity of Tc.

Figure 6II-4: a) permittivity and loss tangent for a 0.25% doped 1-layer, b) permittivity and los

tangent for 0.25% 4-layer. Integration of interfaces reduces low frequency polarization as well as

lowers relaxation frequency and tan(δ) peak magnitude. c) M’’ relaxation of doped P(VDF-TrFE)

compared with pure PVA.

Figure 6II-5: AC conductivity at 100oC calculated using equation 6I-1 for a doped 1-layer, PVA

film, and doped 4-layer. Conductivity is reduced by two orders of magnitude at low frequency in

the layered film relative to the 1-layer control.

Figure 6II-6: a) EC used in fitting the composite impedance data. The model takes into account

bulk responses from doped P(VDF-TrFE), pure PVA and electrode/dielectric blocking

polarization. b) EC fits to 4-layer M’ data at 40oC, 80oC, and 110oC. Good qualitative fits enforce

model accuracy.

xiv

Figure 6II-7: a) CPE2 and CPE5 EC outputs corresponding to P(VDF-TrFE) and PVA bulk

capacitances as a function of temperature are shown (left) and converted to permittivity (right). b)

1-layer blocking CPE estimations (left) and 4-layer blocking CPE estimations (right).

Figure 6II-8: Depolarization current density for pure 1-layer 10μm films at a) Ep=10MV/m, b)

Ep=20MV/m, and c) Ep=30MV/m. All measurements were performed using tp=15min, Tp=50oC

and heating rate 5oC/min.

Figure 6II-9: fit TSDC spectrum using Bucci-Fieschi equation along with parameter estimates for

entire 1-layer sample set undergoing TSDC with the following parameters: Ep=20MV/m,

Tp=50oC, tp=15min, and scan rate 2.5oC/min. Individual fit components along with total synthetic

spectrum are shown.

Figure 6II-10: Depolarization current density for 0.25% doped 1-layer 10μm films at heating rates

a) 5oC/min, b) 2.5oC/min, and c) 1oC/min. All measurements were performed using tp=15min,

Tp=50oC and Ep=20MV/m.

Figure 6II-11: Depolarization currents for a) pure 1-layer sample set and b) pure 4-layer sample

set. Experimental TSDC conditions are Ep=20MV/m, Tp=50oC, tp=15min and a heating rate of

2.5oC/min for both sets.

Figure 6II-12: Depolarization currents for a) 1-layer doped sample set compared to 4-layered

doped sample set and b) 1-layer pure sample compared with 4-layer doped sample. Experimental

TSDC conditions are Ep=20MV/m, Tp=50oC, tp=15min and a heating rate of 2.5oC/min for both

sets.

Figure 6II-13: High voltage dielectric breakdown Weibull analysis for a) all breakdown fields

exhibiting bi-modal Weibull distributions separating defect and intrinsic type breakdown

mechanisms and b) 7 lowest Ebd events analyzed under IEEE standards for small sample sizes.

Figure 7-1: Space charge distribution between cathode and anode of INS3-SC1 cable insulation

under 60kV/mm stress as a function of measurement time. Packets of positive and negative charge

are clearly resolved [16]. Figure C-1: Linearized J(E) data into Poole-Frenkel plots for PI and PPIDS. Data is shown for

measurements at a) 25oC, b) 100oC, and c) 150oC.

Fig C-2: Permittivity values calculated from linear fits in PF plots. A shaded region is marked in

both plots that indicates the range between high frequency permittivity defined by polyimide’s

refractive index squared (n2) and permittivity measured at 1kHz.

Figure D-1: Histograms of parameter estimates from PI* after 10,000 iterations for Jo and d at

25oC, 75oC, and 100oC.

Figure D-2: Histograms of parameter estimates from PPIDS* after 10,000 iterations for Jo and d

at 25oC, 75oC, 100oC, 125oC, and 150oC.

Figure D-3. raw data from the PI data set (black points) displaying the converged fit result using

nonlinear regression (blue solid line) superimposed.

Figure D-4. Raw data from the PPIDS data set (red points) displaying the converged fit result

using nonlinear regression (blue solid line) superimposed

xv

LIST OF TABLES

Table 1-I: Dielectric breakdown strength of PVDF in relation to CF4/O2 plasma treatment time

and power [17].

Table 1-II: Dielectric breakdown strength of untreated, single side treated, and double side O2

plasma treated PI [13].

Table 1-III: A brief review of literature that investigates the impact of ionic conduction through a

variety of polymer dielectrics [18] [12] [19] [20] [21] [16] [22] [23] [24]. The fact that contributing

ionic species is frequently poorly defined or unknown is highlighted.

Table 2-I: calculated average film thickness, standard deviation and thickness variation in hot

pressed multilayers. 1-, 3- and 4- layer stacks consisted of ~8 micron thick single layer films, while

the 2-layer stack contained two ~13 micron films.

Table 2-II: Profilometer scan thicknesses t for two films processed at 3% solid wt., 1,000 rpm

measured as described in Figure 2-2.

Table 2-III: Plasma treatment parameters used on P(VDF-TrFE) and PI in this work.

Table 2-IV: Characteristic features of PVDF FTIR spectra by wave number, adopted from

Lanceros-Mendez et al. and other contributing authors [25, 26, 27, 28, 29, 30, 31].

Table 2-V: Surface polarity calculated for a number of common polymers using contact angle

experiments, depicting influence of plasma treatment on surface properties [32, 33, 34, 35, 36, 37,

38].

Table 4-I: Elements detected by XPS in atomic percentage

Table 4-II: Chemical species determined by XPS in atomic percentage

Table 5-I: parameter fit values and confidence intervals at each temperature for untreated PI

sample set. No values for Jo or d are provided because of the program’s inability to fit the data

using equation (5-2).

Table 5-II: parameter fit values and confidence intervals at each temperature for the plasma treated

PPIDS sample set

Table 6I-I: DSC results as a function of LiClO4 solid wt% for the first heating cycle. Endothermic

peak temperatures along with integration results are shown and the range in standard deviations of

the sample sets are given in italics.

Table 6I-II: Error % for CPE4 extracted from Q4 and n4 parameter estimates in 1 μm and 10 μm

samples.

Table 6II-I: DSC results for the first heating of 10 micron P(VDF-TrFE) without (pure) and with

0.25% LiCLO4 included. The solvent used was MEK, dried for 15 min at 100oC and annealed for

24 hrs at 142oC under vacuum.

Table E-I: Error percent associated with CPE2 parameter estimates out-put from the model

Table E-2: Error percent associated with CPE3 parameter estimates out-put from the model

Table E-3: Error percent associated with CPE3 parameter estimates out-put from the model

Table E-IV: Error percent associated with R3 and R4 parameter estimates out-put from the model

xvi

ACKNOWLEDGEMENTS

I would first like to acknowledge my two advisors, Dr. Zoubeida Ounaies and Dr. Michael

T. Lanagan, as well as colleague Dr. Amira Meddeb and former colleague Rudeger Wilke. These

individuals have provided unwavering support and guidance from the beginning of my career as a

graduate student, through a full repertoire of Materials Science coursework, departmental

candidacy and comprehensive exams and final defense of a 5 year long Ph.D. Simply put, it would

have been impossible to become the scientist I am today without their knowledge and willingness

to support my growth as a professional, teammate and individual. I hope they continue to impact

the lives of future students the same way they have done for me.

I am also grateful for support received from my committee members Dr. Ramakrishnan

Rajagopalan and Dr. Michael Hickner. Having well thought out critique early in the formulation

of this dissertation improved the rout my research took, teaching me the value of approaching

science from many different angles. My experience with them was positive, and I will continue to

seek input from experts in similar fields as mine to enhance my future work, whatever it may be.

My thanks go out to the individuals I have met along the way. EMCLab mates Hassene,

Nirmal, Saad, Masud, The Duke of Harrisburg Albert Forster III, Wei, John, Travis, Jess, Nick,

Lydia, Tahzib, new students Dash, Jai, and Xiaoue as well as High Energy Capacitor Group mates

Mengxue, Wutti, Maryam, Amir, Jiasheng, Rodger, Cesar, and Hossein have all made my graduate

school experience exceptional, as well as enabled me to add a particularly impressive run on

sentence in an otherwise well written document. In addition, Jeff Long, Steve Perini, Josh

Stapleton, Max Wetherington, and Jeff Shallenberger all played integral parts in my research and

were indispensable teammates during experimental planning and execution.

I am grateful for the National Science Foundation as part of the Center for Dielectrics and

Piezoelectrics under grant Nos. IIP-1361571 and IIP-1361503 for providing financial support.

Without this grant, research would have been impossible and this dissertation nonexistent.

Finally, my love and thanks go out to my mother Carmen Vecchio for her unyielding

strength, love, and encouragement for me to achieve the best in all aspects of my life and become

the best version of myself. She should know that distance will never lessen her presence in my life.

xvii

This chapter of my life is dedicated to my mother Carmen Vecchio and father Vincent Vecchio,

who I love very much

1

CHAPTER 1

INTRODCTION

1.1 HISTORY OF CAPACITORS

In the year 1745, German scientist Ewald Georg von Kleist developed the first known

capacitor technology which was then independently discovered at the University of Leyden,

Holland, by Dutch physicist Pieter van Musschenbroak. The technology was named the Leyden

jar, however both Ewald Georg von Kleist and Pieter van Musschenbroak are given credit for its

development [39] [40]. The capacitor consisted of a glass jar wrapped with metal foil inside and

out, where an electrostatic generator was used to deliver electrical charge to the inner foil while

holding the outer foil grounded causing a maintained state of charge which could be dissipated.

Although the current state of technology at the time did not allow for the capacitor as an electrical

component, its creation marked a turning point in the field of science concerning electricity and

energy storage.

As time and the field of electronics progressed, so did the complexity of capacitors and

their potential applications. Over one century after the Leyden jar’s development came the wax-

impregnated dielectric capacitor invented by Fitzgerald in 1876 [41]. Early capacitors used in radio

receivers typically employed the foil-wax paper capacitor as a power supply filter used for ripple

current reduction [39]. In 1909, William Dubliner invented the first capacitor employing mica as

the dielectric which was predominantly used in radio transmission applications, which was then

shortly followed by the aqueous electrolytic capacitor (first appearing in radio technology in the

late 1920s) [39].

As stated before, mica became a widely used ceramic for capacitors until the discovery of

barium titanate in 1941 [42]. The high permittivity of barium titanate in the range of 1,000 – 10,000

out matched the available repertoire of dielectrics of that time, catalyzing efforts to understand the

material’s crystal structure in relation to dielectric performance and optimize its family of materials

[43]. Around the same time frame (early 1950s) paper capacitors with vacuum deposited electrodes

entered the scene, making a debut in the telephone industry [39]. The process of vacuum metal

deposition termed “metallization” onto paper produced reliable electronic devices. Design

incorporating metalized paper dielectrics is believed by experts in the field of polymer dielectric

2

science including Janet Ho, T. Richard Jow and Steven Boggs to have paved the way for the

creation of initial polymer film capacitor concepts [39]. As mentioned in Ho et al. [39] and

reinforced by claims made from Tran Doan Huan et al. [44] research done through Bell Labs in

1954 on lacquer separation from paper dielectrics lead to the creation of the metalized lacquer film

capacitor [45], suggested to be the first metalized polymer film capacitor technology ever created.

Since work done by McLean and Wehe [45], metalized polymer film capacitors have become the

present-day cornerstone for high power static electrical storage and dissipation technology. A

significant amount of effort from the dielectric community is focused on improving polymer film

capacitor characteristics such as dielectric breakdown, leakage current, AC dielectric loss tangent

and permittivity, and degradation at high temperatures.

In the remainder of this chapter, a brief survey of current materials implemented in

capacitor design is presented along with their use in modern day applications. This is followed by

an in-depth overview of materials used in this dissertatio. The chapter concludes with outlining

the problem and motivation behind this research, as well as this work’s goal.

1.2 CAPACITORS AND DIELECTRIC MATERIALS

Since the invention of the Leyden jar, materials used in capacitor technologies have

expanded to include multiple types of materials depending on the desired applications. In this

section, three types of capacitors and their associated dielectric materials are reviewed:

electrochemical capacitors, ceramic capacitors and polymer capacitors. Each type exhibits unique

characteristics based on the underlying mechanisms for charge storage, which is portrayed in a

Ragone plot depicting specific power as a function of specific energy in Figure 1-1. It is seen that

polymer and ceramic based capacitors perform quite differently than electrochemical capacitors,

enabling higher power densities rather than energies. An even greater disparity is seen relative to

batteries and fuel cells which show the highest specific energy of all charge storage devices. In the

following sections, the mechanisms that drive capacitor performance will be reviewed from a

material’s perspective. Discussion will begin with a brief review of electrochemical capacitor

technology and end with polymer dielectrics.

3

Figure 1-1: Ragone plot comparing the specific power and energy in common types of energy and power storage

devices. (figure credit [1]).

1.2.1 Electrochemical Capacitors

Electrochemical Capacitor’s (EC) mechanism of energy storage involves charge separation

between the interface of an electrolyte and a solid electrode. A basic schematic of a typical EC is

presented in Figure 1-2 which depicts the components of the EC, the charging, and discharging

states of the device. The anode and cathode contain an electrolytic solution that provides the

available anionic and cationic charges distributed through the bulk of the device. In the charged

state, anion interaction with the anode and cation interaction with the cathode create charge

separation at the electrode/electrolyte interface termed double layer capacitance. EC’s exhibit

characteristically large capacitances which can be understood by considering the fundamental

equation for capacitance:

𝐶 =휀𝑟휀𝑜𝐴

𝑑 (1 − 1)

where εr is relative dielectric permittivity, εo is the dielectric permittivity of vacuum (=8.85.10-12

F/m), A is effective surface area and d is thickness. Small d associated with the electrical double

layer as well as large A values resulting from electrode texturing enable these devices to store large

amounts of charge.

Electrode materials can consist of carbon, metal-oxides, and conductive polymers. Each

electrode material influences capacitor performance. For example, the use of carbon-based

4

Figure 1-2: The charging and discharge cycle depicted for a typical electrochemical capacitor (image credit [2]).

electrode materials provide a high surface area which is controlled by the electrode porosity and

can be tuned to achieve optimal performance based on cation and anion size [46]. Metal-oxides

provide their own advantages including low electrical resistance and high specific capacitance.

Research done by the US Army Research Laboratory suggests both ruthenium-oxide and

manganese-oxide show promise in the development of high energy double layer capacitors based

on energy densities and power densities of 8.5 Wh/kg and 6 kW/kg (ruthenium-oxide) and

potential for low cost (manganese-oxide). A porous separator material is placed between anode

and cathode, allowing ionic passage through its thickness however preventing electrical interaction

between the anode and cathode.

Electrode material influences the choice of electrolyte used in the EC’s design. Electrolytes

used in EC’s fall under either organic or aqueous electrolytes. Aqueous electrolytes enable high

power operation of the EC due to a high concentration and conductivity of ionic carriers [47] [1].

Simple salts such as ACl, A2SO4, ANO, ALi, Na, and K eliminate the need for purification and

handling under controlled atmospheres, allowing for simple fabrication. Organic electrolytes

typically exhibit high breakdown voltages in comparison to aqueous, which increases the

attainable cell voltage of the EC (2-2.5V) and directly relates to the possible energy density

achievable by the capacitor [47]. Separator materials used in EC design are dependent on

characteristics of the electrolyte: organic electrolytes typically requiring polymer or paper

separators while aqueous electrolytes are usually coupled with either ceramic or glass fiber

5

separators. Regardless of material selection, high ionic conductance, high electrical resistance and

low thickness are required [47].

EC’s are typically used to “fill the gap” between capacitors and battery technology (see

Figure 1-1). Applications demanding energy within the time span of 10-2 s ≤102 s are ideal for

EC’s due to the ratio of stored energy to available power inherent of the device that prevents the

need to use oversized capacitor and battery components [48]. Another favorable attribute to EC’s

is a lack of toxic materials typically found in battery technologies and ability to withstand large

quantities of charge-discharge cycles without servicing [48, 49, 50]. Despite their benefits, EC’s

cannot support applications which require AC conditions or high ripple currents because high

internal resistance put the device at risk for thermal degradation [48]. By the same mechanism,

large internal resistances limit the device’s achievable peak power in comparison to conventional

capacitors, making them less desirable for pulse power applications.

1.2.2 Ceramic Dielectrics

Ceramic capacitors have become integral components of modern-day electronics such as

cell phones and computers, in which hundreds to thousands are present. In application,

multilayered ceramic capacitors (MLCC) are typically employed due to their compactness and

high capacitance [51]. MLCCs are predominantly used in resonant circuits and filters (requiring

low dielectric loss and high stability) and power supply bypass and decoupling (requiring high

capacitance but allowing for moderate dielectric loss) [51]. Ceramic dielectrics fall into three

classes: 1) low permittivity dielectrics offering superior temperature and voltage stability and low

losses for resonant circuit applications, 2) high permittivity dielectrics offering superior volumetric

efficiency, however nonlinear capacitance change over broad temperature and frequency ranges,

and 3) barrier layer dielectrics offering very high capacitance with limited operating voltage

(<25V). Since class 3 dielectrics operate based on different fundamental principles than the

materials used in this dissertation, the following will focus on dielectric classes 1 and 2.

Class 1 ceramic dielectric materials are characterized by their low relative dielectric

permittivity εr in the range of 5 to 100’s, and a low dissipation factor less than 0.01 [51]. Early

dielectric materials used to manufacture class 1 dielectrics have consisted of porcelain, steatite,

and mica. Modern day low permittivity ceramic dielectrics are based on simple oxides such as

TiO2 (rutile) as well as perovskite titanates such as CaTiO3 as well as modified (Ca,Sr) (Zr,Ti)O3.

6

Dopant elements may also be added during the dielectric fabrication process as needed to achieve

optimal dielectric performance. The influence of Nb, Ta, Al, Ca, Y, Ba, and Mn on TiO2’s optimal

processing conditions, microstructure, and electrical properties have all been extensively

investigated in past work [52, 53, 54, 55, 56, 57]. For example, work done by Chao and Dogan

[57] showed that 0.05 mol% Mn doped into TiO2 results in reduced conductivity and dielectric

loss, while increasing dielectric breakdown strength by 25% and energy storage efficiency from

93% - 98%. This was achieved in TiO2 dielectrics with low concentrations of dopant Mn that

maintain a linear permittivity – temperature relationship between 25oC – 200oC, which is a

characteristic of class 1 ceramic dielectrics [51].

Class 2 ceramic dielectrics exhibit characteristically high εr >1000 and thus higher

volumetric efficiency than class 1, however εr’s nonlinear temperature dependence as well as

voltage dependent capacitance make these materials suitable in applications where low loss and

high stability are not necessary. Unlike paraelectric class 1 dielectrics, class 2 dielectrics are

ferroelectric ceramics in which the material’s crystal symmetry allows for crystal domains

exhibiting spontaneous polarization to exist within the material’s bulk. Perhaps the most famous

ceramic, barium titanate (BaTiO3) exhibits an εr as high as 10,000 arising from ferroelectric

domain configurational entropy associated with the tetragonal – cubic phase transition portrayed

in Figure 1-3. Another characteristic of BaTiO3 is the material’s charge state dependence on strain

called piezoelectricity. This phenomenon arises from strain dependent displacement of Ti in the

tetragonal phase of the material. The piezoelectric nature of BaTiO3 as well as other class 2

ceramics such as lead zirconate titanate (Pb[ZrxTi1-x]O3 or “PZT”) extends their application

beyond power supply bypass and decoupling and into sensing and actuation. Previous work

demonstrates successful PZT based device development including cantilever actuators, atomic

force microscopy probes, micro pumps, and ultrasonic micromotors/transducers [58, 59, 60, 61,

62]. In recent years, concerns involving the toxicity of lead have catalyzed the development of

lead free piezoelectric ceramic materials such as sodium niobate [(K0.5Na0.5)NbO3 or “KNN”] [63],

and SrZrO3 modified sodium bismuth titanate [(Bi0.5Na0.5)TiO3-SrZrO3 or “BNT-SrZrO3”] [64].

Despite the development of lead-free high permittivity ceramics, their inherent mechanical

properties such as high stiffness as well as required high temperature processing conditions limit

their use in practical applications in which high strain and compatibility with polymers is required.

7

Figure 1-3: The dielectric constant of BaTiO3 as a function of temperature. Crystal phase transitions are shown as a

function of temperature above, corresponding to maxima in the material’s dielectric constant (image credit [3]).

1.2.3 Polymer Dielectrics

Polymer dielectrics are typically sought after in energy storage technologies for

applications requiring high breakdown strength. Unlike ceramic capacitors, polymers exhibit low

dielectric permittivities and high breakdown strengths, enabling them to achieve large energy

densities given equation 1-2 below:

𝐸𝑠𝑡𝑜𝑟𝑒𝑑 =1

2휀𝑟휀𝑜𝐸𝑏𝑑

2 (1 − 2)

where εr and εo are the material’s relative permittivity and permittivity of vacuum respectfully, and

Ebd is the dielectric breakdown field of the material. Another quality of polymer dielectrics is their

ability to undergo self-clearing defined as the electrical isolation of defect driven breakdown

events through excessive evaporation of the electrode. Self-clearing electrodes enable continued

device use after localized breakdowns and enhance the reliability of the overall device. Currently

the demand for improved polymer capacitor technologies comes from consumer-based markets

such as general consumer electronics and hybrid/electric vehicles, industrial markets requiring

improved power conversion electronics, and also military applications. The drive for improved

polymer dielectrics is centered on the following requirements: 1) improvement of high temperature

performance and thermal management in power electronics with emphasis on efficient thermal

regulation, and 2) increased achievable electrostatic energy density without increasing dielectric

losses or reducing operating field. This objective is focused around improvement of the dielectric

constant of the material as well as dielectric breakdown strength [44]. The following discussion in

8

this section is focused on requirement 2, improvement of electrostatic energy density in polymer

dielectric materials for power and energy density applications.

Initial dielectric development was centered around the consumer radio electronic market,

however a demand for improved high temperature performance and increased energy density while

maintaining low cost of production motivated development of polymer dielectrics. Since the Bell

Labs discovery of the metalized lacquer film capacitor [39] [44] [45], dielectrics manufactured for

polymer film capacitor applications expanded to include polyethylene (PE), polystyrene (PS used

as the main ingredient in Styrofoam), polytetrofluoroethylene (PTFE known as Teflon™),

polyimide (PI) and polypropylene (PP). The modern state of the art dielectric material for high

energy density applications is currently biaxially oriented polypropylene (BOPP). The maximum

achievable stored electrostatic energy density of a linear dielectric material is governed by the

following equation 1-2. Estored’s dependence on the square of Ebd make dielectric breakdown

strength the dominating parameter for determining a dielectric’s potential to succeed in energy

density applications. In this regard, the high dielectric breakdown field of BOPP measured as high

as 850 MV/m [65] makes BOPP a dominating material for energy density applications despite its

low permittivity of 2.2. High dielectric breakdown strength is an inherent quality of polymer film

dielectrics, surpassing that of their ceramic counterparts exemplified by Figure 1-4.

Figure 1-4: Breakdown strength of polymers, composites (nanodielectrics) and ceramics organized by their dielectric

constant (image credit [66]).

9

Although BOPP exhibits one of the highest breakdown strengths and thus achievable

energy densities of ceramics, nanodielectric composites and polymers, the material undergoes

considerable de rating at elevated temperatures due to its relatively low melting temperature of

80oC [44]. Other materials such as PI are being considered due to their high glass transition

temperatures in the range of 370 – 400oC [67] [68] (depending on chemical structure and

processing) as well as their considerably high dielectric breakdown strength reported as high as

615 MV/m [13].

Both BOPP and PI are non-polar polymers and exhibit low permittivities (2.2 and 3.2

respectively). In order to improve energy density in organic dielectric films, recent attention has

been placed on increasing the permittivity of materials used in high field applications. One

example of this is the introduction of high permittivity nanofillers embedded into a polymer matrix

to improve composite permittivity. Work done by Tomer and Randall [4] report increased

dielectric permittivity in silicone composites containing BaTiO3 nanoparticles in the range of 15 –

25% volume fraction, however reduction in Ebd of the composite (Figure 1-5a) detrimentally

impacts the maximum achievable electrostatic energy density by equation 1-2. Trends in reduced

dielectric breakdown strength in nano-composite polymer dielectrics is observed in other systems

as well including PP where increased Al nanofiller presence in the PP matrix cause reduction in

dielectric breakdown strength [5]. Another approach is to improve energy density capabilities of

polymer film by using high permittivity polar polymers as the main dielectric material to improve

Figure 1-5: a) impact of BaTiO3 nanoparticle inclusion and nanoparticle chain alignment on Ebd in silicone composites

[4] and b) impact of Al nanoparticle inclusion on Ebd in PP [5]. DC dielectric breakdown data analyzed via 2 parameter

Weibull statistics.

10

permittivity without detrimentally impacting Ebd by the inclusion of high εr particles. Examples of

recent work focusing on high field performance of organic dielectrics in the absence of nanofillers

implement poly(vinylidene fluoride) (PVDF) as the high εr material. PVDF along with recent

advances in dielectric material development incorporating PVDF is reviewed in the following

section.

1.3 PVDF AS A DIELECTRIC MATERIAL

1.3.1 Material Structure

PVDF is characterized by a chemical formula linking PE with PTFE in the following

sequence –(CH2–CF2)n–. The flexibility afforded by its structure along with stereochemical

constraint afforded by PTFE groups enable the formation of multiple molecular structures [69].

PVDF can crystallize into four main phases labeled α, β, γ, and δ (referred to as forms II, I, III,

and IV respectively) depending on the conditions the material is exposed to during processing and

fabrication [70] [71]. The α-phase (form I) shown in Figure 1-6 is a non-polar crystal phase of the

material in which the molecular chain assumes a trans-gauche (TGTG¯) configuration. Unlike α,

β-phase crystals (Figure 1-6) exhibit an all trans configuration (TTTT), resulting in a polar phase

arising from aligned CF dipoles along the crystal’s c axis. The α-phase is typically converted to β-

phase through mechanical deformation of the material’s α-phase via stretching uniaxially or

biaxially [72] [73] [74]. Other methods have also been reported to result in the formation of β-

phase during film processing including quenching from the melt [75], controlling pressure and

temperature, and choice of solvent/solvent drying protocol required during solution processing

[76] [69]. The γ and δ phases are quite similar, both exhibiting a weakly polar crystal structure in

comparison to the β-phase, in which the TGTG¯ chain propagation is in the c direction (γ-phase).

The differentiation between γ-phase and δ-phase is a…TTTTTGTG¯TTTT… chain conformation

Figure 1-6: a) polymer chains of PVDF showing TTTT and TGTG¯ conformations associated with the β- and α-

phases respectively (image credit [6]), b) α-phase crystal structure and c) β-phase crystal structure (image credit [7]).

11

exhibited by δ, where the transgauche kinks in the polymer chain along the crystal’s c direction

disrupts long range TTTT configuration characteristic of β-phase. The γ-phase can be attained by

annealing near the melt and through solvent choice while δ-phase has been reported to arise from

poling α-crystals under strong electric fields [76, 77, 78, 79]. Regardless, the weak polarity of the

γ- and δ-phases in comparison to β-phase makes them unfit for practical applications requiring a

polar crystal structure.

PVDF’s electrical properties are controlled by the type and quantity of crystal phases

present in the material. For example, β-phase development within the bulk of the material results

in a ferroelectric PVDF due to permanent dipole orientation and upon poling using an external

electric field. Outside of the material’s ability to be processed into a ferroelectric film, the presence

of CF dipoles within the material also cause PVDF to have a high dielectric constant in the range

of 8-12 which makes it appealing as a material for energy storage applications. Additionally,

ferroelectric polymers including PVDF exhibit a nonconjugated polymer backbone structure,

making them highly insulating materials [69]. Good insulating properties combined with a melting

temperature Tm = 160oC enables PVDF to exhibit DC dielectric breakdown strength comparable

BOPP [44] (reported in the range of 720 – 770 MV/m [80]).

1.3.2 Limitations of PVDF for Energy Storage

Despite the material’s favorable properties such as high breakdown strength and dielectric

permittivity, large dielectric losses in the range of 0.5 – 1.0% as well as high leakage currents in

the range of 10-3 – 10-2 A/m2 at electric fields exceeding 20 MV/m limit its use in practical

applications [71] [44]. This point can be further understood by considering a Ragone plot for

power electronics where the boundaries of material performance are established by power and

energy density, which are controlled by material internal losses or leakage [8]. An example of this

is the Ragone plot for an ideal battery where the energy/power relation is theoretically derived

with and without leakage contributions (denoted by RL) in Figure 1-7. Other limitations damaging

unmodified PVDF as a viable material for high energy density are linked to its β-phase: there is a

strong ferroelectric hysteresis associated with polar domain switching leading to energy dissipation

and low recoverable energy densities especially in AC conditions (exemplified by Figure 1-8)

[81]. Recent work has targeted ferroelectric P(VDF-TrFE) and the relaxor ferroelectric

12

Figure 1-7: Ragone plot for an ideal battery depicting the energy/power relation with and without contributions from

leakage RL (image credit [8]).

Figure 1-8: a) displacement current D vs electric field E loop depicting normal ferroelectric behavior with purple

shaded region representing recoverable energy density (image credit [9]) and b) D-E behavior of biaxially oriented

PVDF at 10Hz showing strong ferroelectricity (imag credit [10]).

13

poly(vinylidenefluoride-trifluoroethylene-chlorofluoroethylene) [P(VDF-TrFE-CTFE)], with

promise of a reduced ferroelectric hysteresis above the coercive field [9]. Research on P(VDF-

TrFE) demonstrates electron beam irradiation and γ-irradiation result in narrower hysteresis loops

[82], however the high cost of (VDF-TrFE) based materials coupled with degraded mechanical

properties prevent large scale applications [12]. P(VDF-TrFE-CTFE), hereby referred to as

terpolymer, has uniquely high dielectric constant of 50 achieved by using defect modification via

introduction of Cl side groups to disrupt ferroelectric domains and reduce remnant polarization

[83] [84]. Despite chemical modifications, terpolymers exhibit limited energy density of ~10 J/cm3

linked to early saturation of polarization at elevated fields [83] [11].

Finally, work done by Chen et al. [11] and Yang et al. [12] highlight the significance of

electrode/dielectric interface in the high field performance of PVDF and its derivatives. The high

field performance of P(VDF-TrFE-CTFE) was analyzed by high voltage dielectric breakdown and

current vs. voltage measurements by Chen et al. [11]. Electrode material as well as electrode

deposition technique was varied to change contact properties between the electrode and the

polymer. It was found that dielectric breakdown strength ranged from 245 MV/m to 380 MV/m in

films with Ag and Al electrodes deposited via thermal evaporation respectively (Figure 1-9). The

leakage current during charging was also electrode material dependent with high dielectric strength

Al and Cr producing the lowest high field leakage currents relative to low dielectric strength Ag.

Yang et al. [12] reports on the high field performance of biaxially oriented PVDF. Thermally

stimulated depolarization current (TSDC) measurements performed with different electrode

materials indicate that both electronic injection (similar to reports by Chen et al. [11]) as well as

impurity ion concentration associated with ionic polarization in the samples depend on the nature

of electrode/dielectric contact (Figure 1-10). It was postulated based off research done by Eberle,

et al. [85] that HF gas emitted at high electric fields reacts with Al and Ag electrode metals to

produce Ag+ and Al3+ cations, as well as F- anions which contribute to the large ionic

depolarization peak in TSDC. The exact nature of these ionic species in PVDF are not well

understood, however their presence induces space charge accumulations that create high field

concentrations distributed heterogeneously throughout the material. Not only does this

demonstrate the electrode/dielectric’s dominating role on high field conduction in PVDF based

dielectrics, but also the prevalence of both electronic and ionic space charge that contribute to

conduction in the material. Although space charge migration and distribution at high fields has not

14

been extensively studied in PVDF, research on PE and crosslinked PE suggests space charges at

high fields significantly impact both conduction properties as well as field distribution through the

material [86, 87, 88]. Due to PVDF’s susceptibility to impurity ion and injected space charges at

fields required to achieve high energy densities, material development aimed at improving

dielectric breakdown as well as mitigating low frequency charge migration and space charge

concentrations under high fields is necessary prior to using PVDF in practical applications.

Figure 1-9: a) dielectric breakdown strength of P(VDF-TrFE-CTFE) as a function of electrode material and b) high

field leakage current as a function of electrode material. Major differences are observed for Ag vs Al, reflecting

significance of electrode/dielectric interface on controlling high field conduction [11].

Figure 1-10: BOPVDF TSDC for a) Ag electrodes and b) Al electrodes. Both samples are measured under the same

conditions: Ep = 10 MV/m, Tp =50oC, heating rate = 5oC/min, and tp ranges from 10 min – 50 min [12].

15

1.4 INTERFACES FOR IMPROVED DIELECTRIC PERFORMANCE

1.4.1 The Electrode/Dielectric Interface

Recent work done by Chen et al. [11] (Figure 1-9) and Yang et al. [12] (Figure 1-10)

highlights the dominant role of the electrode/dielectric interface in controlling electric conduction

through PVDF, however the concept of tailoring the material interface for improved high field

performance has existed for quite some time. Electron/proton irradiation and reactive plasma

treatments have proven effective in chemically tailoring polymer surfaces prior to electrode

deposition. A study done by Mammone et al. [17] in 1992 analyzes the effect of CF4/O2 gas plasma

on dielectric breakdown strength in PVDF films with results summarized in Table 1-I. Plasma

surface modification resulted in an 11% increase in the breakdown strength of treated films relative

to untreated control samples. Although the evolution of material structure as a result of plasma

treatment was not the focus, more recent reports by Adem et al. [89] indicate the formation of -

C=O and -COOH after electron and proton irradiation of PVDF. These results suggest that

improved dielectric breakdown strength reported by Mammone et al. [17] could be related to

surface chemical effects at the electrode/dielectric contact. In fact, evolved electrode/dielectric

interfacial chemistry as a result of plasma treatment is found to influence high field conduction

properties in other polymer dielectrics. Recent work by Meddeb et al. [13] correlates increased

oxygen at the electrode/dielectric interface after oxygen plasma treatment in PI with increased

dielectric breakdown (reported in Table 1-II) and reduced leakage current at high fields and

Table 1-I: Dielectric breakdown strength of PVDF in relation to CF4/O2 plasma treatment time and power [17].

16

temperatures, as shown in Figure 1-11. In this regard, turning surface chemistry of dielectric films

is considered an effective way to control electrical properties for high field applications,

warranting greater attention in polar materials considered for high energy density applications.

Table 1-II: Dielectric breakdown strength of untreated, single side treated, and double side O2 plasma treated PI

[13].

Figure 1-11: Leakage current as a function of electric field for untreated and plasma treated PI at 150oC. Both

reduction of data scatter and magnitude of leakage current occurs after plasma treatment [13].

1.4.2 The Bulk Distributed Interface

Recent work intended to advance organic capacitor technology for high energy density

applications not only use PVDF and its associated co- and ter-polymers for their unique properties,

but also take advantage of interfaces distributed throughout the dielectric’s bulk to mitigate the

effect of limitations discussed in section 1.3.2. Work done by Zhang et al. [83] shows that PVDF

blended with its relaxor ferroelectric counterpart P(VDF-TrFE-CTFE) produces a composite

dielectric exhibiting energy densities as high as 19.6 J/cm3 at 640MV/m which surpasses

performances reported for BOPP (1.2 J/cm3 at 640 MV/m). It was demonstrated by phase-field

17

simulation that interfaces between pure PVDF and P(VDF-TrFE-CTFE) domains play a role in

preventing low field polarization saturation and add interfacial polarization which both enhance

the achievable energy density of the composite [83]. Other efforts to improve high field dielectric

performance that involve bulk distributed interfaces are accomplished by combining low εr

polycarbonate (PC) with poly(vinylidenefluoride-co-hexafluoropropylene) (P(VDF-HFP)). In

work done by Mackey et al. [14], multilayer co-extruded PC/P(VDF-HFP) laminate dielectrics are

fabricated where the planar connectivity between PC and P(VDF-HFP) layers results in enhanced

dielectric breakdown strength as high as ~950 MV/m, surpassing either constituent material alone

(Figure 1-12). Due to the nature of breakdown initiation (electrical treeing) it was suggested that

the layered microstructure enables defect channel deflection and thus a greater time and electric

field required to achieve dielectric breakdown. This work was then followed up by Zhou et al. [15]

Figure 1-12: a) schematic showing PC / P(VDF-HFP) coextruded composite (similar to Mackey et al.) with PMMA

tie layer incorporated. b) dielectric breakdown strength of multilayer composite using multiple tie layer materials and

c) dielectric loss tangent showing frequency reduction in ionic relaxation for the PC / PMMA tie layer / P(VDF-HFP).

Decrease in relaxation frequency is related to decreased ionic mobility in the PMMA/P(VDF-HFP) interphase shown

in a) [15].

18

with work that assessed a PC/tie-material/P(VDF-HFP) laminate composite as a function of tie-

material. Use of PMMA as the tie material between PC/P(VDF-HFP) layers resulted in 25%

increased breakdown strength, 50% higher energy density and reduced hysteresis loop areas than

a 33-layer PC/P(VDF-HFP) control film. Enhanced dielectric breakdown strength was attributed

to a smoothing of the dielectric constant distribution along the thickness direction of the film due

to PMMA interdiffusion into adjacent PC and P(VDF-HFP) layers. These outcomes were also

coupled with slower ion migration through the film relative to the control sample, determined by

tracking the ionic relaxation peak in the loss tangent of dielectric spectroscopy measurements in

the range of 1 Hz – 50 Hz (Figure 1-13). It is postulated that PMMA/P(VDF-HFP) interphase

regions restrict ionic motion under the application of electric field. These advancements in

laminated polymer film technologies motivates continued research that targets the potential to

incorporate PVDF into all organic dielectric materials for energy storage. Similarly, the

dependence on composite structure highlights the impact interfaces have on high field performance

in layered dielectrics, however up to this point a controlled, systematic study that targets how

interfaces impact impurity ion and electronic charge transport in layered all organic dielectric

materials is absent in the current body of literature.

Figure 1-13: a) SEM images of 32-layer and 256-layer P(VDF-HFP) / PC microlayer coextruded multilayer laminate

along with b) effect of composite structure on breakdown strength. The 32-layer laminate from a) results in a

composite dielectric breakdown strength surpassing P(VDF-HFP) and PC alone [14].

19

1.5 PROBLEM STATEMENT AND RESEARCH GOAL

The proposed research is to study the influence of interfaces on degradation and dielectric

breakdown of multilayer dielectrics at high electric fields. We propose a model multilayer

dielectric system depicted in Figure 1-14 using P(VDF-TrFE) in which the effect of the interface

is enhanced via controllable ionic conductivity. The addition of ionic content into the multilayer

matrix is meant to create a system in which ionic transport at the interface can be separated from

transport through the bulk. Accomplishment of this objective will be done by accomplishing the

following tasks: 1) incorporation of a reactive plasma surface treatment to tailor film surface

chemistry and explore how electronic charge injection can be controlled by tailoring the

electrode/dielectric interface, 2) developing an additive spin-casting procedure which enables the

fabrication of thin (micron – submicron) layers, maximizing the ratio of interface to bulk present

within the structure. In this step, polyvinyl alcohol (PVA) is used as a sub-micron barrier layer to

construct P(VDF-TrFE)/PVA multilayered laminates. Finally, 3) doping individual layers in

multilayered dielectrics with ionic complex to increase conduction and accentuate the interface’s

influence on ionic transport through the material. Accomplishment of task 3 will address two

aspects of ionic conduction that are poorly understood in the current standing body of literature on

polymer dielectric performance. Although ionic charge migration in dielectrics is a well

documented phenomenon, the concentration of impurity species within dielectric films such as

PVDF are at or below the ppm level [90] [91]. Doping the model multilayer film in this dissertation

serves to increase the quantity of species contributing to ionic conduction, making their electrical

response highly recognizable during experimentation. The second aspect of ionic conduction

Figure 1-14: Schematic of the proposed multilayer dielectric model system. The electrode/dielectric interface is

tailored by plasma treatment. Under electric field, Li+ cations behave as a probe to target interfaces introduced via

spin casting.

20

through polymer dielectrics that doping will address is the wide-spread ambiguity surrounding the

actual chemistry of the impurity species contributing to ionic conduction. Impurity ions in the

dielectric will result from the process of suspension polymerization used by the polymer

manufacturing industry [92]. In the case of PVDF polymerization, chain transfer agents, H2O

soluble initiators such as persulfate salts, disuccinic acid peroxide, and β-hydroxyalkylperoxide or

alkylperoxybutyric acid are used [93] [94] [95] [96]. This is then compounded with additional

factors such as polymerization procedure temperature, pressure, ingredients, and post

polymerization processing steps that all influence final polymer chain characteristics and defect

species within the material. Because of the sub ppm levels of these impurities within the material,

their exact chemical nature is not possible to definitively measure which leads to either ambiguity

or complete disregard to the nature of impurities participating in ionic conduction in the literature.

This claim is exemplified by Table 1-III sampling literature that studies ionic conduction in a

variety of polymer materials where the contributing ionic species is not well defined or

unaddressed. This dissertation provides an avenue through doping by which the chemical species

of ionic impurity within the material is well defined and controlled to behave like space charge,

avoiding the ambiguity highlighted in Table 1-III.

Table 1-III: A brief review of literature that investigates the impact of ionic conduction through a variety of polymer

dielectrics [18] [12] [19] [20] [21] [16] [22] [23] [24]. The fact that contributing ionic species is frequently poorly

defined or unknown is highlighted.

21

1.6 ORGANIZATION OF DISSERTATION

Chapter 2 discusses polymer processing techniques implemented to create single layer,

plasma treated, and multilayered PVDF based dielectrics used in this work. An overview of

material characterization equipment used in this dissertation is then provided and broken into two

sections: structural/morphological characterization techniques (including microscopy,

profilometry, contact angle, differential scanning calorimetry, Fourier transform infrared

spectroscopy and X-ray photoelectron spectroscopy) and electrical characterization techniques

(including dielectric/impedance spectroscopy, thermally stimulated depolarization current

measurements, current voltage measurements, and high voltage dielectric breakdown). This

chapter is concluded with an overview of analytical techniques used to handle data.

Chapter 3 focuses on preliminary work done to determine the effect of the interface on

high voltage dielectric breakdown and ionic transport in pure PVDF hot pressed multilayer

laminates. The effect of multilayer lamination on PVDF crystal phase is addressed first. Dielectric

breakdown experiments at room temperature are then performed on 1- and 3- layer laminates.

Finally, an equivalent circuit model is developed to describe permittivity and loss tangent data at

70oC over a broad frequency range in 1- and 4-layer laminates.

Chapter 4 addresses the impact of surface chemical modification in P(VDF-TrFE). The

result of plasma treatment on P(VDF-TrFE) surface chemistry and morphology is analyzed as a

function of plasma treatment exposure time. Low and high field electrical properties are then

probed using dielectric spectroscopy, and current v voltage charging measurements. An analysis

by Poole-Frenkel and Schottky conduction theories inform on the mechanism of charge transport

through plasma modified P(VDF-TrFE). Finally, the Schottky equation is parametrically explored

where it is determined the Schottky barrier height dominates changes in conduction. Assumptions

involving measured plasma modified layer thickness as well as dielectric permittivity as a function

of plasma treatment conditions are used to simplify the Schottky equation and calculate the change

in barrier height caused by plasma treatment.

Chapter 5 focuses on the analysis of high field current voltage data in plasma treated PI.

Analysis is leveraged from results in Chapter 4 which demonstrate the interface’s importance on

limiting conduction. Current-voltage data analysis is performed by implementing hopping, Poole-

Frenkel, and Schottky conduction theories. Standard non-linear regression techniques combined

with bootstrap statistics are proposed as a method to extract the statistical significance of parameter

22

estimates during fitting, as well as identify breaks in the model’s ability to describe the data’s

behavior.

Chapter 6 is broken into two sections. Section 1 provides an in-depth analysis of how

material structure impacts impurity ion conduction of low quantities of Li+ through single layer

P(VDF-TrFE) films. Behavior of the materials curie transition temperature as a function of LiClO4

content in doped films is correlated to impedance, permittivity, and loss tangent over a broad

frequency range (105 Hz – 10-1 Hz) and temperature range (25oC – 110oC). Observations in data

are complemented by parameter estimates extracted from an equivalent circuit (EC) model that

describes polarization mechanisms associated with the material. Section 2 incorporates results

from chapter 5 to create a multilayered P(VDF-TrFE)/PVA laminate system exhibiting controlled

ionic conductivity. Concepts from impedance spectroscopy and EC modeling of doped 1-layer

films are applied to multilayered films to model the low field conduction behavior of multilayer

composites. Thermally stimulated depolarization current (TSDC) measurements focus analysis on

quasi DC ionic conduction in multilayered and single layered films. Depolarization mechanisms

are quantified using Bucci-Fieschi theory, providing a frame work for the mechanism responsible

for charge deflection in layered dielectrics. The section is concluded with high voltage dielectric

breakdown experiments to compare between 1-layer and 4-layer dielectrics of pure copolymer.

Chapter 7 outlines important conclusions and scientific contributions of this dissertation.

The section is concluded with suggestions for potential future work.

23

CHAPTER 2

MATERIAL PROCESSING, CHARACTERIZATION, AND DATA ANALYSIS

TECHNIQUES

2.1 INTRODUCTION

The contents of this chapter offer insight into processing procedures, characterization

techniques, and analytical techniques, however its contents are not imperative to understanding

subsequent chapters. The informed reader may skip this section and proceed with Chapter 3.

Contents of Chapter 2 address the following subject areas:

Processing Procedure Development – The processing procedures implemented in the

fabrication of hot pressed and spin casted samples in this dissertation are reviewed. An analysis to

determine quality of film produced as well as its repeatability is detailed in sections 2.2.1 and

2.2.2. Sections 2.2.3 explains the choice of electron beam evaporation as the electrode deposition

technique over sputtering and 2.3.4 details the specifics regarding plasma surface modification of

PI and P(VDF-TrFE).

Materials Characterization Equipment and Measurements – In this section, equipment and

the associated methods involved in data acquisition and analysis are reviewed. Section 2.3.1

presents characterization techniques used to analyze PVDF dielectric film bulk structure while

2.3.2 focuses on characterization techniques implemented to analyze film surfaces. The last section

2.3.3 gives a more detailed description of electrical characterization techniques and understanding

the electrical properties of PVDF and PI films at different frequencies and temperatures. Each

section includes a brief introduction to experimental and equipment set up involved in successful

implementation of the technique. From there, theory developed to describe data acquired using the

technique is discussed. Each technique has many different theories surrounding the production of

data and its interpretation, however only those theories implemented in this dissertation are

selected for discussion.

Special Data Analysis Techniques – Data interpretation required the use of advanced

analytical techniques to describe the behavior of electrical data. Section 2.4.1 reviews the

essentials of bootstrap statistics used to quantify parameter estimate significance during hopping

theory analysis of PI conduction in Chapter 5. In section 2.4.2, theoretical derivation of EC

24

impedance used to describe impedance spectroscopy data is reviewed, along with brief explanation

of the software used in complex nonlinear regression. Finally, section 2.4.3 reviews the concept

of peak deconvolution used to fit coalescing TSDC current peaks in P(VDF-TrFE) samples. Fitting

scripts were written in R-Studio and codes used in the analysis of data are annotated and presented

in their respective sections.

2.2 PVDF PROCESSING AND SAMPLE PREPARATION

The methods used to fabricate dielectric films are centered around solution casting

techniques. The following sections provide the specifics associated with solution casting and hot-

pressing PVDF films in greater detail than what is included in subsequent chapters.

2.2.1 PVDF Casting and Hot-Press Lamination

Single layer films of PVDF are fabricated by using a Doctor Blade casting tool depicted in

Figure 2-1. PVDF powder provided by Arkema is dissolved in anhydrous N,N

Dimethylformamide purchased from DrySolv and magnetically stirred for 2 hours. The solution is

then poured onto a glass plate previously cleaned using first IPA then Acetone. A Doctor Blade is

then used to spread the solution into a thin film which is then dried under vacuum for 1 hr, resulting

in a free-standing film. Thickness uniformity of the free-standing film is assessed by using a

Heidenhain Dial Gauge with 10-7m precision. Measurements were taken across the surface of an

approximately 5in x 7in casted film with approximately 1-2 cm between measured spots. Although

the average thickness of the film varied depending on solid wt% and blade height, each film

demonstrated reasonable uniformity in its thickness: standard deviations in film thickness fell

within the range of 3.9μm – 0.5μm for a film with average thickness of 79.3μm and 14.0μm

respectively. Thus the standard deviation in thickness of the entire film never surpasses 7% of the

average film thickness. Additionally, electrical measurements are taken using circular electrode

diameters of 1cm which is too small to capture local deviations in film thickness; therefore

thickness fluctuations were not though to be a significant contributor to electrical measurement

error in 1-layer casted films.

Hot pressed laminates were then constructed by stacking individual layers into multilayer

stacks ranging from 2 – 4 total layers. Two pieces of extruded polyimide Kapton films provided

25

Figure 2-1: PVDF processing procedure showing a) magnetic stirring (10-15% solid wt), b) solution degassing, c)

solution casting using Dr. Blade, d) film drying under vacuum 180oC for 1 hr stepped down to 60oC for 3 hrs with

final 1-layer film, e) stacked multilayer sandwiched between Kapton protective sheets and f) hot-pressing at 18-24

MPa at 150oC for 30 min.

Table 2-I: calculated average film thickness, standard deviation and thickness variation in hot pressed multilayers. 1-

, 3- and 4- layer stacks consisted of ~8 micron thick single layer films, while the 2-layer stack contained two ~13

micron films.

by Dupont sandwich the PVDF stacks as a protective non-stick barrier to the metal of the hot press

platens. The sandwich structure was then inserted into a uniaxial hot press with its platens held at

150oC. Pressing took place for 30 min under constant pressure (~20MPa). Hot-pressed films had

dimensions of approximately 5 cm x 7 cm, and thickness uniformity across the multilayered

laminates was measured in the same way as described for 1-layer films. Results of thickness

measurements for hot-pressed films 1- through 4-layers is presented in Table 2-I. Hot-pressing

increases the % variation of the thickness across the film which is thought to be due to a number

of different influencing factors: uneven pressure applied to the stack due to mis aligned platens,

minor variation in 1-layer thickness becoming more pronounced when stacking, fluctuating

26

pressure during the press (measured between 17 and 24 MPa), and wrinkling in the films. For these

reasons, each hot-pressed film was carefully examined prior to electroding to ensure only the most

uniform spots were used for measurements.

2.2.2 P(VDF-TrFE) Spin Casting

Challenges associated with repeatability in the hot-pressing procedure as well as limitations

on achievable thickness of cast PVDF films motivated the development of spin cast processing

protocols. Solutions of DMF and P(VDF-TrFE) were made using the processing procedures

outlined in Figure 2-1a and 1b. Figure 2-2 shows the spin cast processing and thickness

measurement procedure. Three solution batches were made with different copolymer solid wt% of

15%, 7.5% and 3%. The solution was then poured onto a 10.16 cm diameter silicon wafer and spun

for 50s at varying spin speeds ranging from 500 rpm – 2000 rpm. After spinning, wet wafers were

placed onto a hot plate exposed to atmosphere at a temperature of 100oC and dried for 15 min,

resulting in a thin P(VDF-TrFE) film adhered to the wafer.

The method used to assess film uniformity is shown in the schematic Figure 2-2. Thickness

measurements were performed by scanning a stylus profilometer over a step edge created by gently

scratching into the film with a razor blade. 10 step edges were created by scratching and each step

edge was scanned 3 times, resulting in a total of 30 scans per film. Two separate samples spun at

1,000 rpm using the 3% wt solution were fabricated to determine the repeatability in the processing

conditions. The results of thickness measurements across both samples are presented in Table 2-

II. It was found that the mean thickness of each sample was quite close (139 and 142 nm

respectively) with standard deviations (6 nm) of the mean thickness overlapping each other. An

unpaired Student’s T-test was performed using Microsoft Excell’s built in T-Test function to assess

the statistical significance between the two sample’s means. The analysis yielded a p value of

Figure 2-2: Spin cast procedure depicting a) 3 – 15 wt% P(VDF-TrFE) solution deposition, wet film drying at 100oC

for 15 min and c) schematic of dried film with 10 scratched in profilometer scan areas.

27

Table 2-II: Profilometer scan thicknesses t for two films processed at 3% solid wt., 1,000 rpm measured as described

in Figure 2-2.

0.035 which is less than 0.05 indicating the null hypothesis should be rejected and that there is a

statistically significant difference in sample thickness for the films processed at 1,000 rpm for 50s.

While blade casted films can be controlled by solution viscosity and blade height, spin

casting introduces a third parameter that can be used to control film thickness and uniformity:

wafer rotational speed. In order to understand the effect of solution viscosity (controlled by solid

wt %) and spin speed on resultant film thickness and uniformity, a spin cast parameter study was

performed within the range of copolymer solution wt% used in this dissertation. Results are shown

in Figure 2-3, suggesting a strong dependence on both solution wt% and wafer spin speed on

resultant film thickness. Due to statistical differences in individual films processed under the same

cast parameters (shown in Table II), the trends in copolymer thickness as a function of spin speed

and solution wt% are taken only as a general guide. A film thickness measurement protocol

(discussed in section 2.2.4) independent of the data shown in Figure 2-3 was developed and

implemented for each spin casted sample used in this dissertation prior to interpreting electrical

measurements.

2.2.3 Electrode Deposition

Methods used to deposit electrodes onto dielectric films for electrical measurements vary

depending on the material selection and desired measurement. As mentioned in the introduction

section of this dissertation, the polymer film capacitor industry typically uses metallization as the

electrode deposition process involving the “spraying” and adhesion of the electrode material

directly to the polymer film. One method typically employed in industry and research is RF

28

Figure 2-3: Spin cast parameter study varying spin speed (rpm) and solution solid wt%. a) contains data for 15 and

7.5% wt films while b) shows thicknesses measured for 3% wt thin films.

magnetron sputtering which utilizes a gaseous plasma to erode the target material via ionic

bombardment. This technique is inadequate for this work due to the presence of an active gas

plasma during the deposition process and PVDF’s surface sensitivity to plasma treatment [17].

The work in this dissertation implements electron beam evaporation using a Lab-18 tool provided

by Kurt J. Leskar instead of RF magnetron sputtering. In this technique, a beam of electrons is

focused on a crucible containing the electrode material of choice causing evaporation (or

sublimation) and consequentially deposition onto the substrate. Since the sample is held under

high vacuum (~1x10-6 Pa) in absence of reactive chemical species, metal/dielectric interactions

uncharacteristic of the two materials naturally coming in contact are prevented.

Pure PVDF films were used for hot-press lamination and ranged in thickness between

approximately 10 - 35μm depending on desired hot-press film thickness. After processing, these

films were cut into small squares and mounted onto an aluminum shadow mask using Kapton tape.

Electrode size was 1 cm in diameter. The electrode material used was Ag, deposited 100 nm thick

at a deposition rate of 2 A/s with the sample stage held at 0oC to prevent sample damage from

heating during deposition.

P(VDF-TrFE) films varied in thickness between thin (1 μm) and thick (10 μm) films. Thick

films of P(VDF-TrFE) were electroded using the same deposition parameters and shadow mask as

pure PVDF films. Typically films of 10 μm were intended for TSDC measurements, and thus Au

was used as the electrode material because of its good adhesion and chemical inertness under

poling conditions relative to other common materials such as Ag and Al, as demonstrated by

29

literature [12]. Thin films of 1 μm in thickness used electrode masks that were fabricated by laser

cutting circular holes into plastics such as mylar and taped down to the surface of the film.

Electrode diameters ranged from 1 mm – 3 mm. Due to the small electrode diameter, shadowing

during electrode deposition occurred. To account for shadowing, a Nikon Profile Projector V-12

optical comparator was used to approximate electrode diameter after evaporation and adjust

electrode area in calculations for permittivity and current density.

2.2.4 Plasma Treatment

A significant portion of this work is dedicated to understanding the influence of chemical

modification at the electrode/dielectric interface on high field conduction and charge injection in

P(VDF-TrFE) and PI. Reactive plasma treatment is used to chemically alter dielectric film surface

chemistry prior to electrode deposition. This process involves the generation of a plasma using RF

energy within a process reactor to ionize the reactive gas. A mixture of ions, radicals, neutral

species and charged species (electrons and protons) are accelerated in the direction of the sample

surface via application of an electric field. Decision of etching tool used is dependent on the desired

application. For example, tools such as the Alcatel Speeder 100 Si and SiO2 feature Bosch high

frequency fast etching and low frequency etching for silicon removal processes. Other tools such

as the Plasma-Therm 720 and Plasma-Therm Versalock exhibit a wider repertoire of etch material

capabilities that cover etching of silicon based dielectrics, metals (Au, Cr, Ti, Al), semiconductors

(GaAs, InP, InGaAs, AlGaAs, GaMnAs, poly and a-Si) and polymers (BCB, lift off resist, photo

resist, parylene, PDMS, etc.).

Equipment used for surface modification of organics must graft foreign moieties to the

dielectric surface without damaging the quality of the film surface and bulk. This requirement

makes systems such as the Plasma-Therm line of reactive ion etchers unsuitable for surface

modification in this study. An M4L RF gas plasma system provided by PVA TePla was used as

the reactive ion etching system in this study. The M4L is does not feature a strong plasma/sample

stage potential drop characteristic of the other previously mention systems, making the tool ideal

for the cleaning of organic surfaces and plasma surface modification where polymer film damage

is minimized. Plasma treatment parameters for the surface modification of P(VDF-TrFE) and PI

are presented in Table 2-III. Plasma treatment conditions were optimized for surface modification

for PI prior to data collection described in Meddeb et al. [13] and are not the focus of analysis of

30

Table 2-III: Plasma treatment parameters used on P(VDF-TrFE) and PI in this work

high field conduction in plasma treated PI films in this dissertation. Since analysis of PI films in

subsequent sections is leveraged off work previously done by Meddeb et al. [13], no further

discussion on plasma’s influence on PI is mentioned here.

Plasma treatment of P(VDF-TrFE) was performed as a function of treatment time ranging

from 45 – 180s shown in Table 2-III. A study measuring the etch rate of the treatment as a function

of treatment time (schematically shown in Figure 2-4) was performed to understand its effect on

thickness and surface heterogeneity of thin 1 μm copolymer films. A series of copolymer thin films

were deposited onto 1.25in x 1.25in square silicon wafers via spin casting 7.5% wt solution at 600

rpm for 50s. A step edge was gently scratched along the center and scanned with a stylus

profilometer confirming the film’s thickness to be 1μm. The film was then placed into the M4L

and administered plasma treatment using parameters specified in Table 2-III for P(VDF-TrFE) at

30s time intervals. After each 30s exposure its thickness was measured to develop film thickness

as a function of plasma exposure time presented in 2-5. Linear regression using Microsoft’s linear

regression function indicates film thickness obeys a linear relationship with plasma exposure time.

The slope represents the etch rate calculated to be 0.74 nm/s which must be accounted for during

film thickness dependent calculations. Although no significant change in the spread of

measurement as a function of treatment time was calculated (as indicated by nearly unchanging

standard deviation in measured thickness), the possibility that plasma interaction with copolymer

surface causes heterogeneity in surface roughness of the film remained a possibility. This was

studied using optical profilometry techniques and is discussed later in Chapter 4 section 4.3.4.

31

Figure 2-4: Schematic showing stepwise process of determining plasma process etch rate. a) film deposition onto

square silicon substrate, b) scratched groove spanning substrate, c) profilometry over step edge (5 scans total) d)

application of 30s plasma treatment (see Table III for parameters), and e) profilometry on treated film. Steps e – d are

repeated 3 times.

Figure 2-5: Copolymer film thickness as a function of plasma treatment exposure time. A calculated R2=9.97 indicates

a linear relation between film thickness and exposure time where an etch rate of 0.74 nm/s can is extracted.

32

2.3 MATERIAL CHARACTERIZATION EQUIPMENT AND METHODS

The following section presents material characterization methods used in material

characterization found in this dissertation. Each analysis technique is first presented from a

theoretical perspective where the sample set up and basic underlying physics is explained. Each

section ends with a brief review of the associated technique’s implementation for PVDF or PI

characterization when appropriate.

2.3.1 Bulk Chemical Characterization

2.3.1.1 Differential Scanning Calorimetry (DSC)

Processing’s effect on the crystal structure of pure PVDF and P(VDF-TrFE) films was

analyzed thermally using DSC. The experimental set up involves two identical Al pans, one

containing the test material and the other left empty as reference. The experiment measures heat

flows in and out of the sample in relation to the reference pan at a constant temperature ramp rate

(chosen to be 10oC/min). Heat flow can be approximated as enthalpy changes since the experiment

is performed at constant pressure:

𝑑𝑄

𝑑𝑡 𝑝=

𝑑𝐻

𝑑𝑡 (2 − 1)

Here, Q is heat, t is time, and H is the enthalpy. For a given sample in relation to the reference pan,

the change in enthalpy over time is defined as the following:

Δ𝑑𝐻

𝑑𝑡=

𝑑𝐻

𝑑𝑡 𝑡𝑒𝑠𝑡 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙−

𝑑𝐻

𝑑𝑡 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (2 − 2)

As temperature of the experiment (dictated by temperature ramp rate) approaches a phase

transition associated with the test material’s structure, the sample will begin to consume or release

heat causing a change in enthalpy. This results in a peak in the DSC signal. Integration of the

change in sample enthalpy over the phase transition peak time will then yield enthalpy change of

the sample shown below.

Δ𝐻𝑠𝑎𝑚𝑝𝑙𝑒 = ∫𝑑𝐻

𝑑𝑡 𝑠𝑎𝑚𝑝𝑙𝑒

𝑡−𝑝𝑒𝑎𝑘 𝑒𝑛𝑑

𝑡−𝑝𝑒𝑎𝑘 𝑜𝑛𝑠𝑒𝑡

𝑑𝑡 (2 − 3)

In the context of performing DSC on polycrystalline organic materials, peaks recorded in the DSC

are due to crystalline domain phase transitions such as curie transitions in ferroelectric phases,

crystal melting, or re-crystallization (nucleation and growth). The % crystallinity of the sample

33

can be calculated by comparing integration of the melting peak to a theoretically derived melting

enthalpy ΔHo pertaining to the material’s crystal phase:

∆𝐻𝑠𝑎𝑚𝑝𝑙𝑒

∆𝐻0× 100 (2 − 4)

Since the initial amount of material loaded into the Al pan has a mass associated with it which will

affect the intensity of peaks in the DSC signal, calculations of crystallinity are normalized to

sample mass, ensuring accurate results (where ΔHsample and ΔHo have units J/g).

DSC’s sensitivity to polymer phase transformation has made the technique appealing for

work involving structural characterization of PVDF in relation to processing, specifically

mechanical deformation. One example is a study done by Lanceros-Méndez et al. [97] which

targeted structural changes occurring (crystallinity % and lamellae thickness) during mechanical

deformation in β-PVDF as a function of strain. Other research uses DSC to understand how

graphene oxide inclusion into the PVDF matrix as well as defect formation post exposure to

ionizing radiation (gamma) affect polymer crystalline structure. The technique is commonly used

in P(VF-TrFE) systems as well, informing on how nanofiller concentration in P(VDF-TrFE) films

effects crystalline phase % and order [98] and how poling and annealing conditions impact

ferroelectric phase formation [99]. Finally, DSC has also been implemented in the study of how

polymer crystallinity influences electrical properties of PVDF such as molecular mobility [100],

motivating its use to link polymer crystal structure to low and high field conduction properties in

this dissertation.

2.3.1.2 Fourier Transform Infrared Spectroscopy FTIR

Polymer phase development as a result of processing parameters in PVDF and P(VDF-

TrFE) is analyzed using FTIR. The technique involves the exposure of a test sample to a broad

frequency range of infrared radiation where either a) molecular bonds absorb incoming radiation

of a given energy dependent on its structure or b) transmission of IR radiation through the sample

occurs. A unique absorbance spectrum characteristic of the test material is formed depending on

crystal phase quantity, structure, and chemical bonding affiliated with the pristine material. The

characteristic bands pertaining to vibrational modes and crystalline phases of PVDF is presented

in Table 2-IV at the end of the section.

34

The process by which data is collected begins with a coherent black body radiation source

emitting in the IR wavelength spectrum (ranging from ~2.5x10-5 – 1.67x10-6 m corresponding to

400 cm-1 and 6000 cm-1 respectively). Radiation is passed into a Michaelson interferometer

containing one adjustable mirror panel of controlled position. Mirror panel movement causes the

periodic interference of radiation resulting from wave superimposition, thus modulating the

spectrum leaving the interferometer. This modulated beam is then exposed to the sample in which

its transmission or absorption is sensed by a detector as a function of the adjustable mirror panel’s

position. In order to convert light absorption/transmission and mirror panel position to light

absorption/transmission and radiation wavelength, a computer program performs a Fourier

transform. Mathematically this is represented by the following relation:

𝐺(𝑥) ↔𝐹

𝑔(𝜆) (2 − 5)

where the functions G(x) (a function of position x) and g(λ) (a function of wavelength λ) form a

Fourier pair and relate via the given relation.

𝐹[𝑔(𝜆)] = 𝐺(𝑥) = ∫ 𝑔(𝜆)𝑒−𝑖2𝜋𝑥𝜆 𝑑𝜆

∞

−∞

(2 − 6)

𝐹[𝐺(𝜆)]−1 = 𝑔(𝜆) = ∫ 𝐺(𝑥)𝑒−𝑖2𝜋𝑥𝜆 𝑑𝑥

∞

−∞

(2 − 7)

The results of the experiment are typically presented as a function of % transmission or %

absorption at the discretion of the author as a function of wavenumber with units cm-1.

Sensitivity to the abundance and conformation (during polarized measurements) of

crystalline phases in PVDF makes FTIR a powerful tool to determine bulk structure. Lanceros-

Méndez et al. [97] complemented the analysis of β-phase crystal development using DSC with

polarized FTIR in parallel and perpendicular modes. Measurements indicated a strong dependence

of polymer chain alignment direction within the crystalline phase on the axis of applied tension

while uniaxial drawing. Work done on the characterization of composite dielectrics formed by

compression molding P(VDF-TrFE) with natural rubber latex in the absence of solvent

implemented FTIR to measure the degree of interactions between P(VDF-TrFE) and additives

[101]. The analysis was able to conclude that there is no strong interactions between polymer and

additive materials due to an absence of absorption band intensity and peak wavenumber. Finally,

FTIR has also been used to understand how PVDF chain chemistry associated with CF2 chemical

35

groups impacts Li+ cation complexation in solid and wet polymer electrolytes [102]. In this regard,

the technique is seen as a powerful tool to link ionic interactions with polymer structure and

improve understanding of ionic conduction in polymer films.

Table IV: Characteristic features of PVDF FTIR spectra by wave number, adopted from Lanceros-Mendez et al. and

other contributing authors [25, 26, 27, 28, 29, 30, 31].

36

2.3.2 Surface Chemical Characterization

2.3.2.1 Optical Profilometry

Optical profilometry (also referred to as “optical profiling”) is an optical technique used to

measure variation in surface height of a sample over a specific scan area. In this technique, light

of a known wavelength is used as the source probing the sample surface, thus allowing for very

high resolution (~1 nm) in the vertical direction when measuring film properties such as surface

roughness. The optical profiler uses similar methods to detect variation in surface height as the

Michaelson interferometer (section 2.3.1.2). In this set up, the adjustable mirror is a light source

detector that is moved creates constructive and destructive interference with light reflected off the

test sample’s surface. When the distance from the sample surface to the interferometer’s beam

splitter equals the distance of the detector to the beam splitter, constructive/destructive interference

occurs. Optical path differences between sample and beam splitter and detector and beam splitter

are due to variations in height across the sample surface. Adjustment of detector height allows

focusing as a function of position along the sample surface, enabling reconstruction of sample

surface topology within the scan area.

Controlling dielectric film surface morphology is known to be important in order to realize

high breakdown strength and low loss films. Research done by Burlingame et al. [103] uses optical

profilometry to understand physical surface defects in Polythiourea films in relation to solvent

used during processing. Increased surface roughness and irregularity correlated directly to reduced

characteristic breakdown strength calculated using Weibull statistics. Similar results were obtained

in BaO – Al2O3 – B2O3 – SiO2 glass thinned by hydrofluoric acid etching reported by Lee et al.

[104] where roughness measured via optical profilometry was correlated to reduced breakdown

strength as well as Weibull modulus. Results reported by Burlingame and Lee motivate use of

optical profilmometry in this study to determine the effect of plasma surface treatment on P(VDF-

TrFE) film topology and is discussed in Chapter 4 section 4.3.4.

2.3.2.2 H2O Water Contact Angle

The contact angle between a liquid and sample surface quantifies the wettability of the

tested material. Test set up typically employs a syringe filled with the test liquid (in this case H2O)

connected to a hydraulic pump capable of depositing droplets in the range of 1 – 10μL. A water

37

droplet of known volume is deposited onto the surface of the test sample and imaged using a

camera and computer software that tracks the contact angle as a function of time.

The liquid’s contact with the solid surface is dictated by intermolecular forces arising from

sample surface chemistry as well as test liquid chemistry. A simplified model of the interaction

between test liquid and sample surface is the Young relation:

𝛾𝑆𝐺 = 𝛾𝑆𝐿 + 𝛾𝐿𝐺 cos 𝜃 (2 − 8)

where γSG is the interfacial energy between the solid phase (sample surface) and vapor phase

(liquid), γSL the solid-liquid interfacial energy, γLG the liquid-vapor interfacial energy, and θ is the

angle created between the liquid’s contact with the surface and the solid phase. Since the interfacial

energy is a quantification of molecular bond disruption occurring upon creation of a surface, the

contact angle θ is sensitive to surface state of the test liquid as well as sample. The contact angle

is also highly dependent on physical characteristics of solid surfaces including crystallinity, grain

size and shape, porosity, and surface roughness. Although the nature of how surface roughness

impacts wetting properties during experimentation is not well understood, effective surface area is

known to control surface energy, and thus roughness is determined to be a non-negligible

parameter contributing to the contact angle.

Literature using contact angle as a characterization tool covers wide range of applications

such as the surface characterization of rocks and minerals, and understanding wetting properties

in relation to sand blasted PMMA surface roughness to control cell adhesion and migration [105]

[106]. Some of the most pertinent literature surrounding the use of contact angle is the calculation

of surface polarity before and after plasma surface treatment in a variety of common polymers.

Table 2-V showing the polar component divided by the dispersive component of the free energy

extracted from literature is presented below and highlights contact angle’s sensitivity to surface

chemical properties in organic materials.

38

Table V: Surface polarity calculated for a number of common polymers using contact angle experiments, depicting

influence of plasma treatment on surface properties [32, 33, 34, 35, 36, 37, 38].

2.3.2.3 X-ray Photoelectron Spectroscopy

XPS is a universally used chemical characterization technique because of its applicability

to a broad range of test materials as well as its ability to provide quantitative information on the

chemical state of the surface of materials being studied. During experimentation, the sample

surface is excited using a monochromatic X-ray source (typically Al kα x-rays at 1486.6 eV) of

given energy hν which interacts with bound electrons at the sample’s surface. Inelastic scattering

events result in the liberation of photoelectrons from the material surface with kinetic energies KE

characteristic of the chemical species and surrounding molecular environment. The KE is related

to the binding energy of the detected electron Eb via the following relationship where φspec is the

XPS spectrometer’s work function:

𝐾𝐸 = ℎ𝜈 − (𝐸𝑏 + 𝜑𝑠𝑝𝑒𝑐). (2 − 9)

39

Spectral data is plotted as a function of Eb displaying peaks which correspond to the shell

(1s, 2s, 2p, etc.) by which the detected photoelectron originates. Similarly, high resolution scans

within the vicinity of a detected peak can be performed, revealing not only peak position on the Eb

axis, but also its salient features such as peak convolution or shifting. Peak shifting can be

indicative of the electronegativity of atoms such as fluorine in the local environment or electron-

nucleus attractions creating screening effects. Similarly, complexity in peak shapes are

characteristic of conformational and chemical characteristics of moieties containing elements that

emit photoelectrons within the specified energy range.

Data analysis of XPS spectra is performed by peak fitting, where synthetic peaks are

introduced to best fit XPS spectra. Information about chemical moieties present as well as

elemental %’s can be obtained through careful selection of peak position and integration. Accuracy

of data reduction by peak fitting depends on the following: 1) photoelectric spectral line

assignment validity (dependent both on equipment calibration and expertise of the scientist in

chair), 2) background signal treatment and 3) correctness of line shape implemented in the fitting

[107]. Much of the analysis involved in this dissertation involved peak fitting of the C1s spectra

allowing for a linear background to be used in fitting which is deemed adequate by past work done

by Beamson and Briggs [108]. Choice in line shape is more complex due to the line shape’s

dependence on a number of instrumental and physical factors: response function of electron

analyzer, X-ray line shape profiles, intrinsic lifetime broadening of core-level hole states, phonon

broadening, differential surface charging, and contributions from surface core-level shifts [109]

[107]. XPS fitting can be done using a number of different line shapes to account for these effects,

which are reviewed in Fairly [107], however only practical Gaussian and Lorentzian line shape

functions were used in this dissertation because of their simplicity and no demonstratable need for

more complex analytical interpretation. Casa XPS was used as the peak fitting software for XPS

spectra and employs the following Gaussian / Lorentzian functions for synthetic fitting:

𝐺𝐿𝑃(𝑥, 𝐹, 𝐸,𝑚) =𝑒𝑥𝑝 [−4𝑙𝑛2(1 − 𝑚)

(𝑥 − 𝐸)2

𝐹2 ]

1 + 4𝑚(𝑥 − 𝐸)2

𝐹2

(2 − 10)

𝐺𝐿𝑆(𝑥, 𝐹, 𝐸,𝑚) = (1 − 𝑚)𝑒𝑥𝑝 [−4𝑙𝑛2(𝑥 − 𝐸)2

𝐹2] +

𝑚

1 + 4(𝑥 − 𝐸)2

𝐹2

(2 − 11)

40

Both equations are characterized by a mixture of Gaussian and Lorentzian line shapes,

whose contributing quantity is controlled by the value of m. Other parameters involved are x

corresponding to the abscissa of a data point, E is the peak center, and F is the full width half max

parameter. Due to the symmetry of the GLP and GLS, asymmetries in the fit C1s signal relative to

control samples during analysis are assumed to arise due to introduction of foreign chemical

species and are fit accordingly in context of data interpretation in Chapter 4 section 4.3.2.

XPS has been used in past research to better understand the effect of various surface

treatments on polymer surface chemistry. One report by Vandencasteele et al. [110] implements

the technique to learn how fluorine containing polymers (PTFE, PVDF and PVF) react to N2 and

O2 rf plasma surface treatments. It was found that chemical species grafted to the surfaces was not

only gas plasma chemistry dependent, but also material dependent: O2 serving as an etchant to

PTFE while O uptake at the surface was detected in other tested films. Similarly, it was found that

fluorinated materials resulted in a de-fluorination at the sample surface after plasma treatment,

coinciding well with past work done by Duca et al. [111] that reports a similar phenomenon in

PVDF exposed to Ar plasma. Finally, XPS has been used to understand plasma treatment’s role in

surface modification of PVDF as a substrate for polyamide thin film composite membranes [112].

Despite the quantity of research done implementing XPS to better understand wetting and adhesion

properties of plasma treated organics, gaps exist in the literature concerning surface chemical

characterization in plasma treated PVDF dielectrics for high field applications which is addressed

in Chapter 4.

2.3.2.4 Time of Flight Secondary Ion Mass Spectrometry

ToF-SIMS is a destructive chemical characterization technique unlike XPS in which a

pulsed ion beam is used to liberate molecules from the sample surface. Sputtered material is

accelerated into an analyzer used to measure the mass of ions and clusters emitted from the sample.

Molecular and elemental identities can then be determined from the intensity of the detected signal

and exact mass of measured chemical constituents. ToF-SIMS has analysis depth capabilities on

the order of 2nm making it an ideal technique for surface chemical characterization, however its

ability to sputter test material enables chemical depth profiling. In this dissertation, ToF-SIMS is

used as a complimentary surface chemical analytical tool to XPS and to depth profile plasma

treated P(VDF-TrFE) thin films to estimate the length scale that M4L plasma modification affects

41

the material. This analysis is discussed when implementing Schottky theory to quantify Schottky

barrier height change after plasma treatment in Chapter 4 sections 4.3.3 and 4.3.6.2.

2.3.3 Electrical Characterization

2.3.3.1 Impedance Spectroscopy and Equivalent Circuit Modeling

Impedance spectroscopy is a low voltage analytical technique in which a sinusoidal voltage

is applied across a test material and charge measured as a function of signal frequency. The

impedance of the test material can be described using Ohm’s law via the following relationship

between impedance Z, voltage V, and current I:

𝑍 =𝑉

𝐼. (2 − 12)

The applied AC signal used is small (in the range of 10mV – 1V) so that the sample’s generated

current follows a linear relationship with the applied excitation signal. In this scenario, I will follow

V with a given phase shift φ:

𝑉𝑡 = 𝑉𝑜 sin(𝜔𝑡) (2 − 13)

𝐼𝑡 = 𝐼𝑜 sin(𝜔𝑡 + 𝜑) (2 − 14)

where ω is angular frequency calculated by 2πf, t is time and φ is a phase shift depending on the

properties of the device under test (φ = 90o for an ideal capacitor and 0o for an ideal resistor). The

impedance can then be expressed as a function of time:

𝑍𝑡 =𝑉𝑜 sin(𝜔𝑡)

𝐼𝑜 sin(𝜔𝑡 + 𝜑) (2 − 15)

and in complex notation:

𝑍(𝜔) = 𝑍𝑜(cos(𝜔𝑡) + 𝑗 sin(𝜔𝑡)) (2 − 16)

where j is (-1)1/2. Due to Z’s dependence on I which is strongly influenced by microscopic material

structure, impedance spectroscopy is a powerful tool used to characterize how morphology of the

test sample impacts conduction mechanisms dominating various frequency ranges.

The analysis of dielectric materials typically links current propagation through the material

to the dominating polarization mechanism occurring at different test frequencies. The impedance

for a capacitor is given by the following equation:

𝑍(𝜔) =1

𝑗𝜔𝐶 (2 − 17)

where C is the capacitance and follows the relationship

42

𝐶 =휀𝑟휀𝑜𝐴

𝑡. (2 − 18)

Since the impedance of the material is dependent on material permittivity εr, dielectric conduction

is usually analyzed by accounting for the polarization mechanisms associated with device charging

and discharging within the range of test frequencies. Spectroscopy used in analysis of PVDF and

P(VDF-TrFE) capacitors in this dissertation was performed in the broad frequency range of 0.1

kHz – 100 kHz, capturing the following polarization mechanisms: 1) electronic polarization

contributing at the highest frequencies of applied signal (f > 100kHz). In frequency regimes

dominated by electronic polarization (1014 – 1016 Hz [113]) , the permittivity of the material is

assumed to be equal to the refractive index squared (n2) because the active polarization mechanism

is electron cloud density displacement surrounding atoms. 2) permanent dipole polarization

dominates the room temperature impedance response in PVDF materials within ~100 Hz – 1 MHz.

In this mechanism, polarization is induced by the rotation of C-F dipoles associated with the

polymer backbone in PVDF. 3) Bulk ionic conduction arising from the migration of impurity ions

at low frequencies (0.1 Hz – 10 Hz). At these frequencies of measurement, the conduction through

the material is not intrinsically generated via the material structure and causes dielectric losses and

leakage current at low frequencies. Finally, 4) blocking polarization due to the build-up of ionic

species at the electrode/dielectric interface occurs at quasi DC frequencies and high temperatures.

This polarization process is typically not defined as a bulk response of the material.

An attempt to link material structure to impedance behavior as a function of

frequency is typically made via equivalent circuit (EC) modeling where an EC of ideal electrical

components is constructed in order to describe each polarization and conduction mechanism

associated with the material. EC’s used to describe the behavior of polymeric materials under test

typically account for polarization mechanisms 1 – 3, and in simplicity adhere to a general form

depicted in Figure 2.6. Contributions to the impedance arising from electronic polarization are

described by C1 which assumes an ideally capacitive response and takes permittivity as n2. Induced

dipole polarizations are described by C2 (8 < εr < 12 for PVDF) in series with a current limiting

resistor R2 which controls the frequency at which the polarization mechanism relaxes out by the

product τ=C2R2. Finally ionic conduction through the material at low frequencies is modeled by

R3 and takes on a value representing the bulk resistance of the material under test. Values for each

circuit element are usually determined via a nonlinear regression procedure in which the functional

43

Figure 2-6: Simplified model for a dielectric material under impedance spectroscopy test, incorporating ideal

capacitive and resistive components to describe electronic, orientational, and ionic polarizations. The EC used in this

dissertation is leveraged from this and discussed in section 2.4.2.

equivalent impedance of the chosen model is parametrically adjusted to best fit impedance data

over the entire tested frequency range. This process is described in greater detail in section 2.4.2.1.

Impedance spectroscopy techniques are a staple in literature studying electrical

conductivity in solid state polymer electrolytes. One such work by He et al. [114] prepares battery

separator membranes out of P(VDF-HFP)/HDPE for enhanced ionic conductivity using non-

solvent induced phase separation. Impedance spectroscopy was used to determine enhanced bulk

conductivity in P(VDF-HFP)/HDPE blends relative to pure P(VDF-HFP) suggesting improved

conductivity and battery performance was due to expanded amorphous area and high porosity.

Other literature uses impedance spectroscopy to describe conductivity contributions from material

structure. Work done by Marzantowicz et al. [115] performs impedance spectroscopy on PEO

dielectrics around the melting temperature of the crystalline phase. It was found that the ionic

conductivity was controlled by the presence of the crystal phase, impedance spectra exhibiting

unique characteristics above and below the melting temperature Tm = 324.4 K. EC modeling was

then implemented to describe this behavior. The EC used by Marzantowicz et al. [115] was of

similar form to that presented in Figure 2-6, however modification involving the introduction of

a constant phase element (CPE) parallel with a resistor in series with R3 was used to account for

ionic charge/polymer crystal interaction. This was verified by the necessity of the CPE/R element

to describe impedance below the melt temperature and its absence when the material is molten.

Similar analysis is presented in Chapter 6I section 6I.5.1 which also includes discussion of fit

parameter statistics for P(VDF-TrFE) impedance spectra fitting.

44

2.3.3.2 Current Voltage (IV) Charging Experiments

Current-voltage (IV) experiments are a powerful tool in interpreting the mechanism by

which conduction occurs in organic dielectrics. Typically, a metallized dielectric is inserted into a

test fixture where a voltage source is connected to apply a DC bias (Vapp) across the material. The

potential is held for a sufficiently long enough time t that allows for the achievement of steady

state current after the emptying of occupied trap states and ionic migration relaxation. Hold times

required to achieve true steady state currents are beyond time scales practical for measuring I vs

V, and thus experiments measuring I(t) at constant V are performed prior to I(V) measurements to

obtain a reasonable hold time in which a quasi-steady state in I is achieved. Once this time is

reached, a pA meter measures current. The applied voltage is then linearly increased, and the

process repeated until the relationship between current and voltage over a range of Vapp is obtained.

Analysis of I(V) characteristics of polymer dielectrics is not a straightforward task and

usually involves multiple conduction mechanisms within a given measurement range. One factor

which affects the I(V) characteristics of the material is the amorphous / polycrystalline structure of

organics. Unlike single crystals, disordered materials have trap energy levels which are distributed

according to specific distribution functions [116, 117]. Furthermore, the contact properties

between dielectric and metallization create their own unique trap states and distributions, typically

following different mathematical behavior in comparison to those distributed within the material’s

bulk. Since the analysis of high field conduction currents in this dissertation involves measurement

of two polycrystalline materials (PI and P(VDF-TrFE)), both bulk dominated and interface

dominated conduction mechanisms are considered. The following is a review of the three theories

used to describe I(V) data of plasma treated PI and P(VDF-TrFE) in this dissertation.

Interface Dominated Conduction – Schottky Theory: High field current injection effects resulting

from electric field assisted thermionic emission or tunneling through a potential barrier separating

electrode from dielectric is described by Schottky theory [117]. The potential barrier height

existing between electrode and dielectric under the application of electric field E is defined as the

following:

Ψ(𝑥) = ϕ𝑚 − 𝜒 −𝑞2

16𝜋휀𝑟휀𝑜𝑥− 𝑞𝐸𝑥 (2 − 19)

45

where φm is metal work function of the deposited electrode, χ is the electron affinity of the

dielectric, q is elementary charge, and x is distance into the dielectric from the surface of the

material. The term q2/16πεr εox is a potential energy term accounting for the image force generated

upon the emission of a charge from the metal into the dielectric, and qEx accounts for barrier height

lowering under field E. These two terms represent competing forces on the emitted charge:

attraction back to electrode from the image force and repulsion away from the electrode due to

field assisted barrier height lowering. The point at which net force acting on the charge is a

minimum and can be obtained by dΨ(x)/dx = 0, representing the point x = xmin such that the barrier

height is a minimum:

𝑥𝑚𝑖𝑛 = (𝑞

16𝜋휀𝑟휀𝑜𝐸)

12. (2 − 20)

At the position xmin, Ψ(xmin) equals the effective potential barrier height φB and the lowering of the

barrier height due to the application of electric field ΔφB can be derived by the following:

Δ𝜙𝐵 = (𝜙𝑚 − 𝜒) − 𝜙𝐵. (2 − 21)

By relationship Ψ(xmin) = φB:

Δ𝜙𝐵𝑆 = (𝜙𝑚 − 𝜒) − [(𝜙𝑚 − 𝜒) −𝑞2

16𝜋휀𝑟휀𝑜𝑥𝑚𝑖𝑛− 𝑞𝐸𝑥𝑚𝑖𝑛], (2 − 22)

substituting for xmin and canceling like terms:

Δ𝜙𝐵𝑆 =𝑞2

16𝜋휀𝑟휀𝑜(

𝑞

16𝜋휀𝑟휀𝑜𝐸)

12+ 𝑞𝐸 (

𝑞

16𝜋휀𝑟휀𝑜𝐸)

12, (2 − 23)

and by algebraic simplification, the following relation for field assisted barrier height lowering is

obtained:

Δ𝜙𝐵𝑆 = (𝑞3𝐸

4𝜋휀𝑟휀𝑜)

12

= 𝛽𝑠𝐸12. (2 − 24)

In this equation, the βS parameter is called the Schottky constant and depends on material

permittivity εr. Since this theory is descriptive of charge emission occurring on the time scale of

electronic processes, εr is usually thought to be representative of n2 for the material in question

(similar to electronically dominated polarization processes as discussed in section 2.3.2.1),

however fitting Schottky conduction behavior of polar polymers has suggested εr values

accounting for dipolar orientational polarization mechanisms to be more appropriate based on

goodness of fit.

46

Thermionic emission processes link current generation in the material to temperature via

an exponential relationship similar to the Arrhenius relationship:

𝐽 = 𝐴𝑅𝑇2𝑒𝑥𝑝 [−𝜙

𝑘𝑏𝑇]. (2 − 25)

In this formalism, J is the emitted current density at temperature T, φ is considered the work

function that must be energetically achieved for emission to occur, and AR is Richardson’s

constant. The AR term is a material dependent constant assuming the form AR = 4πqemekb2/h3

relating current to electrical particle mass (me) and charge (qe), however its derivation is not

discussed in this dissertation. In context of dielectrics during the I(V) experiment, the field assisted

thermionic emission assumes a similar form to that of pure thermionic emission that accounts for

field enhanced barrier height lowering:

𝐽 = 𝐴𝑅𝑇2𝑒𝑥𝑝 [𝛽𝑠𝐸

12

𝑘𝑏𝑇] 𝑒𝑥𝑝 [−

𝜙𝑆

𝑘𝑏𝑇]. (2 − 26)

In this equation, φS describes the electrode/dielectric contact’s barrier height at E=0. In systems

displaying Schottky type behavior, the natural logarithm of the current density ln(J) plotted as a

function of the square root of electric field E1/2 will yield a linear relationship from which the

slope can be related to βS by the following:

𝑙𝑛(𝐽) =𝛽𝑆𝐸

12

𝑘𝐵𝑇−

𝜙𝑆

𝑘𝐵𝑇+ 𝑙𝑛(𝐴𝑅𝑇2). (2 − 27)

Implementation of this relationship in the analysis of I(V) data will be discussed in context of

plasma treated P(VDF-TrFE) thin film and PI high field conduction analysis in Chapter 4 and 5

respectively.

Bulk Limited Conduction – Poole-Frenkel Theory: Poole-Frenkel (PF) charge emission is

descriptive of the filed enhanced thermionic emission of charges injected into the dielectric from

trap states distributed throughout the bulk of the dielectric under test [117]. The physics involving

charge emission in PF theory is very similar to that of Schottky since they both describe emission

of an electronic carrier from a bound trap state imposing coulombic interaction between escaping

electron and a positive charge. While Schottky describes coulombic interaction via creation of a

mobile image charge, the positive charge center involved in PF emission is fixed, resulting in an

altered field enhanced barrier height lowering term:

47

Δ𝜙𝐵𝑃𝐹 = (𝑞3𝐸

𝜋휀𝑟휀𝑜)

12

= 𝛽𝑃𝐹𝐸12 (2 − 28)

where βPF is called to Poole-Frenkel constant and is larger than βS by a factor of 2. The current

density described by PF conduction follows a similar double exponential relationship as Schottky:

𝐽 = 𝐸𝜎𝑜𝑒𝑥𝑝 [𝛽𝑃𝐹𝐸

12

𝑘𝑏𝑇] 𝑒𝑥𝑝 [−

𝜙𝑃𝐹

𝑘𝑏𝑇] (2 − 29)

with σo being a term proportional to the conductivity of the material and φPF representing trap site

barrier height at E=0. Linearization of the current density divided by the electric field produces a

similar result to that of Schottky emission:

𝑙𝑛 (𝐽

𝐸) =

𝛽𝑃𝐹𝐸12

𝑘𝐵𝑇−

𝜙𝑃𝐹

𝑘𝐵𝑇+ 𝑙𝑛(𝜎𝑜). (2 − 30)

In this format, linearization of the data and fitting to the above equation enables computation of

βPF and thus εr of the test material.

The analysis of Schottky and PF type conduction mechanisms relies heavily on

computation of permittivity from linearized I(V) data for both mathematical and physical reasons.

Both theories are described by the multiplication of two exponentials, making linearization through

taking the natural logarithm a mathematically simple task. Physically, both conduction

mechanisms give rise to behavior defined by a natural logarithm of the conductivity ln(σ) that is

proportional to E1/2. Therefor validation of the active conduction mechanism is reliant on

comparison of the permittivity extracted by linear fitting to known values of the test material’s

permittivity.

Bulk Dominated Conduction – Hopping Theory: Hopping conduction theory is based off the

structure of polycrystalline and amorphous organic dielectrics: intrinsic defects due to structural

disorders and extrinsic defects relating to impurities associated with material fabrication processes

acting as trap sites and in some instances charge carriers creating unique conduction

characteristics. These defects contribute to intermolecular charge transport processes which are

described using hopping theory. Derivation of the current density as a function of applied electric

field begins with an equation accounting for diffusional dependent conduction through the test

material written as:

48

𝐽 = 𝜎𝐸 + 𝑞𝐷𝑜

𝜕𝑛𝑐

𝜕𝑥+

𝜕𝐷

𝜕𝑡, (2 − 31)

where D is the diffusion coefficient for migrating charge species, q is the charge of the associated

carrier (typically taken as the elementary charge) and nc is a concentration of contributing charge

carriers. Considering measurement protocol which mandates measurement at steady state currents

as a function of applied field, the term ∂D/∂t = 0. Similarly, space charge and electronic charge

neutrality within the dielectric is assumed to be true, making ∂nc/∂x = 0 as well. This leaves the

following expression:

𝐽 = 𝜎𝐸 = 𝑛𝑞𝜇𝐸 (2 − 32)

where material conductivity σ is represented by the typical product of carrier concentration, charge,

and mobility (nqμ). Probabilities associated with charge trap state escape through random thermal

fluctuation are then considered and are written as:

𝑃𝑇 = 𝜐𝑜𝑒𝑥𝑝 [−𝜙𝐻

𝑘𝑏𝑇]. (2 − 33)

The term νo is the carrier vibrational frequency and φH typically referred to as an activation energy

or barrier height/trap depth for the hopping conduction process [113] [118].

Similar to Schottky and PF conduction theories, application of electric field E causes field

assisted barrier height lowering to occur. In context of carrier hopping, this reduces the energy

required to escape in the direction of applied field by - qeEd and increases it opposite of applied

field by +qeEd where d is hop distance. This makes the probability of escape (PE) to be the sum of

probabilities associated with escape in the direction of applied field and against applied field,

creating the following expression:

𝑃𝐸 = 𝜐𝑜𝑒𝑥𝑝 [−𝜙𝐻

𝑘𝑏𝑇] [𝑒𝑥𝑝 (

𝑞𝑒𝐸𝑑

2𝑘𝑏𝑇) − 𝑒𝑥𝑝 (−

𝑞𝑒𝐸𝑑

2𝑘𝑏𝑇)] (2 − 34)

and is simplified by using the definition of the hyperbolic function to the following:

𝑃𝐸 = 𝜐𝑜𝑒𝑥𝑝 [−𝜙𝐻

𝑘𝑏𝑇] [2 sinh (

𝑞𝑒𝐸𝑑

2𝑘𝑏𝑇)]. (2 − 35)

Considering the relationship between charge drift velocity, PE and d defined by vD = PEd as well

as μ= vD/E, and general formula for conductivity σ=nqμ, an expression for the conductivity can be

obtained:

𝜎𝐻 =2𝑛𝑣𝑑𝑞

𝐸𝑒𝑥𝑝 (−

𝜙𝐻

𝑘𝑏𝑇) [sinh (

𝑞𝑒𝐸𝑑

2𝑘𝑏𝑇)]. (2 − 36)

49

Multiplication of the conductivity by the electric field yields an expression for current density

𝐽 = 𝐽𝑜𝑒𝑥𝑝 (−𝜙𝐻

𝑘𝑏𝑇) [sinh (

𝑞𝑒𝐸𝑑

2𝑘𝑏𝑇)]. (2 − 37)

where 2nvdq is absorbed by the term Jo. Unlike previously discussed Schottky and PF conduction

theories, analysis of I(V) data implementing hopping theory is not straight forward due to its

complexity surrounding a multitude of unknown variables such as n, v, d, and φH. Similarly its

mathematical form does not permit linearization, leaving its use in analysis to be determined by

low and high field approximations, goodness of fit, and to the discretion of the scientist who passes

judgement on its validity based on the nature of the material being measured and past literature.

This dissertation provides an alternative approach to the fitting of I(V) data implementing hopping

theory not commonly found in literature, imparting a rigid statistical interpretation on parameter

estimates extracted via nonlinear regression to enhance the significance of the analysis. A detailed

discussion of the technique is found in section 2.4.1.

Each of the discussed conduction theories have been implemented to better understand I(V)

charging characteristics in polymers. One such study by Saxena and Gaur [119] implements I(V)

characteristics to explain high field conduction in PVDF-polysulfone (PDF) blends. PF and

Schottky modeling indicate that blended films exhibit a more PF bulk limited type behavior at high

temperatures relative to Schottky type. Bulk dominated conduction processes have been used to

describe high field conduction in other fluorocarbon-based materials such as PTFE [19] and also

polyimides where contributions made by Sawa et al. [120] and Sacher [121] suggest hopping is

the dominant charge conduction mechanism. Contributions by Meddeb et al. [13] and Vecchio et

al. [122] use I(V) in conjunction with PF and Shottky theory analysis to describe the effect of

surface chemical grafting on PI and P(VDF-TrFE) high field conduction properties. These works

are described in detail in chapters 4 and 5 of this dissertation.

2.3.3.3 Thermally Stimulated Depolarization Current Measurements (TSDC)

Equipment limitations on the lowest achievable frequency using impedance spectroscopy

(see section 2.3.2.1) motivate alternative approaches for measuring field induced space charge

conduction processes in polymer dielectrics. TSDC is a technique which enables the measurement

of currents generated by the buildup and release of charges induced by polarization of a capacitor

[123]. The general experimental procedure involves four main steps: 1) a DC voltage Vp is applied

50

across the dielectric material under test at a poling temperature Tp for set amount of time tp. 2) The

test material is then cooled to initial temperature To with Vp simultaneously applied. To is typically

below the glass transition of the material in question. 3) Applied bias Vp is changed to 0 and 4) the

material is short circuited, and the current is measured during heating from To to a final temperature

Tf. The heating rate chosen is constant (typically in the range of 1oC/min – 5oC/min) and current

is analyzed as a function of temperature.

Polarization occurring in dielectrics exposed to external DC fields can be achieved by a

variety of mechanisms including electronic polarization, atomic polarization, orientational

(dipolar) polarization, interfacial polarization, and space charge polarization [123]. In context of

this dissertation, orientational and various space charge polarizations are discussed. Dipole

polarization occurs in dielectrics containing permanent dipoles distributed through the bulk and

exhibit time scales as low as 10-12s. TSDC current generation during application of applied field

Ep for time t resulting from dipole depolarization is described by Bucci-Fieschi theory. The

following equation shows the build-up polarization in the material resulting from an applied field

Ep for time t at Tp:

𝑃(𝑡) = 𝑃𝑒 [1 − 𝑒𝑥𝑝 (−𝑡

𝜏)] (2 − 38)

where τ is the dipole relaxation time and Pe is the equilibrium polarization. Assuming polarization

times for polarizing and depolarizing are identical, polarization decay upon Ep removal is given

by the exponential:

𝑃(𝑡) = 𝑃𝑒𝑒𝑥𝑝 (−𝑡

𝜏). (2 − 39)

Since TSDC is performed with a constant heating rate over a set temperature range, t must be

transformed to T using the relationship T = To+qt where q is the heating rate dT/dt. Thus,

polarization decay can be rewritten as the following:

𝑃(𝑡) = 𝑃𝑒𝑒𝑥𝑝 [−∫𝑑𝑡

𝜏

𝑡

0

]. (2 − 40)

Assuming this relation holds over all temperatures, initial frozen in polarization equals polarization

at To and the temperature dependence of τ behaves the following Arrhenius relation:

𝜏(𝑇) = 𝜏𝑜𝑒𝑥𝑝 [𝜓

𝑘𝑏𝑇] (2 − 41)

51

with τo being relaxation time at infinite temperature, kb is Boltzmann’s constant and ψ is activation

energy of dipolar disorientation, the current density generated during a TSDC experiment can be

represented by the following:

𝐽(𝑇) =𝑃𝑒(𝑇𝑝)

𝜏𝑜𝑒𝑥𝑝 (−

𝜓

𝑘𝑏𝑇) 𝑒𝑥𝑝 [−

1

𝑞𝜏𝑜∫ 𝑒𝑥𝑝 (−

𝜓

𝑘𝑏𝑇′) 𝑑𝑇′

𝑇

𝑇𝑜

]. (2 − 42)

Due to the complexity of the integral contained within the second exponential term, an analytical

expression for the current density is typically employed in data analysis and fitting:

𝐽(𝑇) =̃𝑃𝑒(𝑇𝑝)

𝜏𝑜𝑒𝑥𝑝 (−

𝜓

𝑘𝑏𝑇) 𝑒𝑥𝑝 [−

𝑘𝑏𝑇2

𝑞𝜏𝑜𝜓𝑒𝑥𝑝 (−

𝜓

𝑘𝑏𝑇)]. (2 − 43)

Theories involving space charge polarization and depolarization processes are inherently

more complex than dipolar polarization processes. In this scenario, both injected charges occurring

during the poling process of the material as well as impurity ion polarization through the sample

resulting in heterocharging during poling contribute to the measured current. Space charge

relaxation processes are highly dependent on parameters that are not intrinsic to the material. In

the case of charge migration due to preexisting impurity ions within the material, counteracting

action of diffusion, charge recombination events causing migrating charge loss, blocking effects

of the dielectric/electrode interface and trapping properties of the material all influence the

measured current [123]. These aspects of space charge measurements by TSDC make analytical

analysis difficult of peaks arising from heterocharge processes (ionic relaxations). In this

dissertation, Bucci-Fieschi theory is used in the analysis of all relaxation peaks observed in TSDC

in order to make comparison between undoped, ionically doped, and multilayered films, however

initial assumptions surrounding the theory’s derivation must be respected during data

interpretation.

Literature typically uses TSDC as a supplementary technique used to further understand

polarization and depolarization mechanisms in relation to material structure. One example of this

is work done by Sauer and Kim [124] which uses TSDC to identify tacticity related molecular

relaxations occurring at the Tg of poly(methyl methacrylate). The data processing techniques

involved in this work are of interest to TSDC peak deconvolution and can be read about in detail

in work by Neagu et al [125]. More recent work on PVDF systems attempt to correlate structural

morphology, TSDC molecular relaxation, and the nature of d33 coefficient in PVDF/BaTiO3

composites [126]. This research reports TSDC peaks occurring in the temperature range of 135 –

52

170oC and is attributed to the merger of two relaxation processes: dipolar relaxations combined

with interfacial polarizations occurring between PVDF matrix and nanofillers to produce a single

relaxation. Other reports by Yang, et al. [12] also use TSDC to gain greater insight into molecular

relaxation processes involved in dipole polarization in BOPVDF. In this report, experiments are

done more systematically than in Gaur et al. [126] and perform TSDC with changing Ep, tp, and

electrode material [12]. It was found that current peaks occur within 50oC – 110oC and correspond

to electronic injection during poling as well as charge migration due to impurity ions controlled

by electrode metal chemistry.

2.3.3.4 High Field Dielectric Breakdown Measurements and Weibull Statistics

The characteristic dielectric strength of a material is measured by performing high field

dielectric breakdown experiments. In this technique, a dielectric film of known thickness is

exposed to a gradually increasing applied voltage until the material becomes conducting, marking

the point of dielectric breakdown. The method by which this is done is typically a ball and plate

experimental set up, where the sample is sandwiched between a grounded copper plate and

approximately 5mm diameter ball electrode whose electrical potential is ramped at a constant ramp

rate of 500 V/s. The small contact area characteristic of the ball electrode minimizes extrinsic

defects contribution to the breakdown measurements, enabling extraction of a breakdown strength

as close to the material’s intrinsic strength as possible given experimental limitations. During the

experiment, breakdown voltage (VBD) is measured many times on a given sample to form a

distribution of VBD values. Although no set requirement exists for the number of breakdowns

required for analysis, analysis in this dissertation involves >25 breakdown events.

The distribution of breakdown values is analyzed statistically by implementing Weibull

failure statistics to estimate parameters that quantify the material’s behavior. A two parameter

Weibull distribution is typically used to model the behavior of dielectric breakdown events and is

chosen in this dissertation based on of goodness-of-fit to data, use in other literature studying

similar systems and its IEEE standardization [127]. The probability distribution function describes

the distribution of breakdown events and exhibits the following form:

𝑓(𝑡, 𝛽, 𝛼) =𝛽

𝑡(𝑡

𝛼)𝛽

𝑒𝑥𝑝 [− (𝑡

𝛼)𝛽

] (2 − 44)

53

where α is the scale parameter (characteristic breakdown voltage), β is the shape parameter, and t

is the measured variable during tests (in this case measured VBD of the sample). The characteristic

breakdown strength is the dielectric breakdown strength (α) reported for the material and the shape

parameter is a quantity describing the spread in successive breakdown events. In order to calculate

these parameters from the data, the cumulative distribution function (CDF) is used which is

obtained by integration of the probability distribution function:

𝐹(𝑡, 𝛽, 𝛼) = 1 − 𝑒𝑥𝑝 [− (𝑡

𝛼)𝛽

]. (2 − 45)

By taking the double natural logarithm of F(t,β,α) the CDF can be linearized into the following

equation used for data analysis:

𝑙𝑛[−𝑙𝑛(1 − 𝐹(𝑡, 𝛽, 𝛼))] = 𝛽 ln(𝑡) − 𝛽ln(𝛼). (2 − 46)

When handling breakdown data, an approximation of F(t,β,α) is made based on the rank i of the

ith breakdown event from a total population of n breakdowns. An approximation formula for

F(t’β,α) takes on the following form:

𝐹(𝑡, 𝛽, 𝛼) =̃ 𝐹(𝑖, 𝑛) =𝑖 − 0.44

𝑛 + 0.25 (2 − 47)

which was empirically determined to be a good descriptor of dielectric breakdown data and listed

in the IEEE standard on breakdown analysis [127]. Successive breakdown events are ordered from

lowest VBD to highest. Plotting ln[-ln(1-F(i,n))] as a function of ln(t) enables the extraction of β

from linear fitting via the slope of the fit line. Characteristic breakdown voltage (α) is extracted

where ln(α) equals ln(t) at the point ln[-ln(1-F(i,n)] is zero. Since F(i,n) is an approximation of the

cumulative distribution function, its value represents probability of failure for a given voltage t, or

in this case rank i, and has a range 0 < F(i,n) < 1. The value α occurs at the point F(i,n) = 0, and

thus corresponds to the 63% probability of failure of the material.

Dielectric breakdown is an integral experiment in the understanding of electrical failure

and high field conduction properties of dielectric material. We have seen in the introduction of this

dissertation how dielectric breakdown experiments inform on organic dielectric material strength

when doped with nano-particles [4] [5], reactive plasma processing’s role on high field conduction

characteristics [13] [17], and related to IV experiments as a function of deposited electrode material

[11]. Other work done by Ahmed et al. [128] exemplifies breakdown’s ability to detect failure

mechanisms involved with breakdown events. Weibull analysis was used to study the phenomenon

54

of self-clearing on high field dielectric performance in metalized P(VDF-TrFE-CTFE) [128].

Clearing events were separated from intrinsic breakdown of the material by observation of bi-

modal behavior in the Weibull distribution of Ag electroded P(VDF-TrFE-CTFE). Extraction of

slope parameters for clearing events (β approximately 6) where twice as low as that for intrinsic

breakdown (β approximately 12) highlighting the techniques sensitivity to dielectric breakdown

mechanism. Work done by Wang et al. [129] also uses breakdown experiments with Weibull

analysis to extract high field characteristic strength of BaTiO3/PVDF composites, enabling the

calculation of field dependent energy density and BaTiO3 fraction dependent energy density of the

material. In this dissertation, dielectric breakdown is used to link blocking at low frequencies to

dielectric strength in multilayers structures, and is discussed in Chapter 6II and Chapter 7 in

greater detail.

2.4 SPECIAL ANALYTICAL TECHNIQUES

Theoretical interpretation of electrical data was used to draw a link between the behavior

of the material based on processing conditions to its structure. This was done by implementing a

variety of data fitting techniques with statistical interpretation of fit results to assess validity in the

model and in some cases, identify experimental conditions in which the model breaks. In this

section, three techniques are discussed in the context that they are presented in this dissertation: 1)

Bootstrap statistical methods to interpret the significance of hopping conduction theory parameters

estimated via non-linear regression, 2) Equivalent circuit analysis combining basic circuit theory

of ideal and distributed electrical components with complex non-linear regression and 3) TSDC

peak deconvolution used to extract Bucci-Fiechi theory fit parameter estimates for TSDC signals

characterized by overlapping relaxations.

2.4.1 Bootstrap Statistics Applied to I(V) Data

Non-linear regression using Hopping theory to fit current density vs. electric field (J(E))

data involves the estimation of unknown parameters Jo and d. Similarly, these fit parameters

exhibit unknown probability distributions. Nonlinear regression utilizes a sum of squares

minimization scheme through R-Studio software to estimate the two parameters in question,

however determining the accuracy of these estimates is not trivial because the variance of their

55

probability distributions is not clearly defined. This prevents the direct calculation of their standard

errors, necessitating the use of statistical tools implemented to score the accuracy of fit results.

In the bootstrap statistical procedure, a probability distribution for fit parameters is

empirically estimated via a Monte Carlo type procedure that effectively eliminates the need for a

formula to compute standard errors and confidence intervals. This method enables parameter

estimates to be scored in terms of confidence intervals which in turn reflect the behavior of the

total sample population, revealing information on the repeatability of measurement within the

sample set. The following sections focus on implementation of this procedure applied to the

analysis of J(E) data in this manuscript, however work done by Efron and Tibshirani [130] should

be referenced for further insight into bootstrap theory and application.

For simplicity, description of this method focuses on the PI sample set recorded at 25oC

only found in Chapter 5, section 5.3.2.1, Figure 5-2. In practice, it was applied to both PI and

PPIDS sample sets at all measurement temperatures during analysis. The procedure begins with

the raw J(E) data of each sample of the untreated polyimide. This set of data is represented blow

as PI:

PI:

𝑆𝑎𝑚𝑝𝑙𝑒 1 {(𝐸1𝐽1,1), (𝐸2𝐽1,2), … , (𝐸15𝐽1,15)}

𝑆𝑎𝑚𝑝𝑙𝑒 2 {(𝐸1𝐽2,1), (𝐸2𝐽2,2), … , (𝐸15𝐽2,15)}

𝑆𝑎𝑚𝑝𝑙𝑒 3 {(𝐸1𝐽3,1), (𝐸2𝐽3,2), … , (𝐸15𝐽3,15)}

Current is measured at a series of 15 progressively increasing electric fields labeled En where “n”

ranges from 1 (lowest applied field) to 15 (highest applied field). The fields used are the same

from sample to sample, however each sample responds uniquely to the applied field and produces

a unique current density Ji,n where “i” denotes the sample tested and “n” corresponds to the nth

electric field. PI is thus comprised of a total of 45 unique (En, Ji,n) pairs that describe the behavior

of the material at 25oC.

PI is then used to create a distribution of fit parameters Jo and d by employing the technique of

“resampling with replacement”. During a single iteration of this procedure, PI will be re-sampled

a total of 45 times to produce the following new data set:

𝑃𝐼∗: {(𝐸1𝐽2,1)∗, (𝐸13𝐽3,13)

∗, (𝐸2𝐽1,2)

∗, (𝐸2𝐽1,2)

∗, (𝐸7𝐽2,7)

∗… , (𝐸15𝐽1,15)

∗}

56

In this expression, the superscript “*” is used to denote the created bootstrap sample set. Due to

the concept of replacement, the PI remains unchanged during the sampling process. This produces

a new set PI* that can contain duplicate (En, Ji,n)* pairs since the state of PI is constant throughout

resampling. Visual representation of the PI set in comparison to a potential PI* resampled set is

shown below in Figure 2-7 for comparison.

Figure 2-7: J(E) behavior of a) PI sample set displaying 45 data points taken at 25oC and b) the bootstrapped sample

set PI* containing 45 data points resampled with replacement from PI. The outcome of resampling with replacement

can be seen by gaps in data due to duplicate sampling.

The set PI* is fit by standard nonlinear regression using R-studio’s built in non-linear regression

command “nls()”. The product yields a Jo* and d* estimated from PI*. The fit parameters are then

stored in a set of parameter estimates called set PE.

The generation of PI* from PI is then reinitiated, fit using nonlinear regression to produce

new estimates of Jo* and d*, which are then stored in set PE. This process is performed a total of

10,000 iterations, producing the following set of parameter estimates:

𝑃𝐸 = {(𝐽𝑜1∗ , 𝑑1

∗), (𝐽𝑜2∗ , 𝑑2

∗),… , (𝐽𝑜10,000∗ , 𝑑10,000

∗ )}

From the set PE, statistical information reported imperative to scoring the significance of

parameter estimates are calculated: a mean for Jo* and d* is computed using R-studio’s mean()

command, a histogram created for the parameter estimates using the hist() command, and 95%

confidence intervals extracted using the quantile() command1.

1 An annotated version of the R-Studio code used for bootstrap statistics can be found in Appendix A.

57

2.4.2 Equivalent Circuit Modeling

Impedance data analysis employed in this dissertation relies on EC fitting to link

conduction properties to material structure. This type of complex non-linear regression attempts

to fit the analytical expression for impedance derived from a user defined EC to dielectric data

recorded as a function of frequency. In doing so, polarization mechanisms occurring with the

material over a given frequency range can be quantified using estimated values of capacitive and

resistive components. Furthermore, the defined EC exhibits a form that links polarization events

to the material’s structure. The EC used in the analysis of P(VDF-TrFE) impedance as a function

of frequency and LiClO4 content (discussed in Chapter 6I section 6I.5) is shown below in Figure

2.7. Similar to Figure 2-6, the EC used accounts for typical polymer polarization behavior

associated with electronic, dipole orientation and ionic transport at low frequencies. To account

for P(VDF-TrFE)’s polycrystalline structure as well as included ionic content introduced into the

material by LiClO4 doping, two adjustments are made: a nested CPE3/R4 element is introduced to

account for Li+ cation interaction with crystalline structures at low frequency and a CPE4 in series

with the bulk circuit is added to account for blocking polarization associated with Li+ cation

interaction with the electrode at quasi DC frequencies. The following sections show the impedance

formula for each polarization mechanism associated with the EC in Figure 2-8, and derive the EC

equivalent impedance formula used in complex nonlinear regression of P(VDF-TrFE) data in

Chapter 6I section 6I.5.1.

Figure 2-8: EC model depicting polarization mechanisms associated with P(VDF-TrFE) polycrystalline structure at

frequencies spanning 10-1-105 Hz. Nested CPE3/R4 and CPE4 distributed circuit elements are incorporated to describe

low frequency ion interaction with crystals and the electrode/dielectric interface respectively.

58

2.4.2.1 Equivalent Circuit Theory

i) Electronic Polarization: This portion of the circuit is described by C1 and has the following

expression for impedance:

𝑍𝑒𝑙𝑒𝑐 =1

𝑗𝜔𝐶1 (2 − 48)

The electrical response is purely imaginary since the circuit element is a perfect capacitor. Thus

this element is not considered to contribute to the bulk resistance of the material involved in real

processes such as ionic transport.

ii) Permanent Dipole Orientation: The impedance caused by permanent dipole rotation under an

applied AC field is represented by the following expression:

𝑍𝑑𝑖𝑝 =1

(𝑗𝜔)𝑛𝑄𝑜2+ 𝑅2 (2 − 49)

The impedance for this leg of the bulk response has both real and imaginary components. The

imaginary component depends on distributed circuit element CPE2 imperfection factor n that

corresponds to distribution of relaxation times in dipole response of the material and is very close

to 1 (0.98 at the lowest from the fitting). For this reason, the impedance is approximated as that of

an ideal capacitor:

𝑍𝑑𝑖𝑝 =1

𝑗𝜔𝐶2+ 𝑅2 (2 − 50)

and extends purely into the imaginary plane. R2 is real, and controls the frequency at which the

polarization mechanism relaxes out by the product τ=C2R2.

iii) Ionic Polarization: The impedance for this leg of the bulk response is more complex,

depending on R-CPE3/R4 network. The ZCPE3,R4 is addressed first:

𝑍𝐼𝑜𝑛 = 𝑅3 + 𝑍𝑅4,𝐶𝑃𝐸3 (2 − 51)

First we focus on the impedance response of the nested CPE3/R4 circuit. The admittance of this

network is written as the following:

𝑌𝑅4,𝐶𝑃𝐸3 =1

𝑍𝑅4,𝐶𝑃𝐸3= [

1

𝑅4+

1

𝑍𝐶𝑃𝐸3] (2 − 52)

The impedance is then the reciprocal of the admittance

59

𝑍𝑅4,𝐶𝑃𝐸3 =1

[1𝑅4

+1

𝑍𝐶𝑃𝐸3] (2 − 50)

It is easy to see the admittance of CPE4 embedded within the denominator of the expression for

the impedance of the nested CPE3/R4 element. Invoking the definition of complex admittance for

a CPE circuit element Y*CPE, equation 6 can be transformed into the following expression:

𝑍𝑅4,𝐶𝑃𝐸3∗ =

1

1𝑅4

+ 𝑄3𝜔𝑛3[cos(𝑛3𝜋2

) + 𝑖 sin(𝑛3𝜋2

)] (2 − 53)

The complex impedance of the circuit is then broken into its real and imaginary components. This

equation is multiplied by the complex conjugate of the CPE admittance to remove imaginary

components from the denominator of the expression:

𝑍𝑅4,𝐶𝑃𝐸3∗ =

1

1𝑅4

+ 𝑄3𝜔𝑛3[cos(𝑛3𝜋2

) + 𝑖 sin(𝑛3𝜋2

)]×

1𝑅4

+ 𝑄3𝜔𝑛3[cos(𝑛3𝜋

2) − 𝑖 sin(𝑛3𝜋

2)]

1𝑅4

+ 𝑄3𝜔𝑛3[cos(𝑛3𝜋2

) − 𝑖 sin(𝑛3𝜋2

)]

Calculation of the numerator for Z*R4, CPE3 is trivial. We focus on simplification of the denominator

to a more useful form:

Define:

1

𝑅4= 𝐴

𝑄4𝜔𝑛3 cos (

𝑛3𝜋

2) = 𝐵

𝑄4𝜔𝑛3 sin (

𝑛3𝜋

2) = 𝐶

Simplified denominator multiplication using definitions:

(𝐴 + 𝐵 + 𝑖𝐶)(𝐴 + 𝐵 − 𝑖𝐶)

= 𝐴2 + 𝐴𝐵 − 𝑖𝐴𝐶 + 𝐵𝐴 + 𝐵2 − 𝑖𝐵𝐶 + 𝑖𝐴𝐶 + 𝑖𝐵𝐶 − 𝑖2𝐶2

= 𝐴2 + 2𝐴𝐵 + 𝐵2 + 𝐶2

Substituting back for physical quantities:

=1

𝑅42 + 2 [

1

𝑅4𝑄3𝜔

𝑛3 cos (𝑛3𝜋

2)] + [𝑄3

2𝜔2𝑛3cos2 (𝑛3𝜋

2) + 𝑄3

2𝜔2𝑛3sin2 (𝑛3𝜋

2)]

=1

𝑅42 + 2 [

1

𝑅4𝑄3𝜔

𝑛3 cos (𝑛3𝜋

2)] + 𝑄3

2𝜔2𝑛3 ; ∈ 𝐑𝐞 (2 − 54)

This simplified expression for Z*R4, CPE3’s denominator is now placed back into equation 7 and

further simplified:

60

𝑍𝑅4,𝐶𝑃𝐸3∗ =

1𝑅4

+ 𝑄3𝜔𝑛3[cos(𝑛3𝜋

2) − 𝑖 sin(𝑛3𝜋

2)]

1𝑅4

2 + 2 [1𝑅4

𝑄3𝜔𝑛3 cos (𝑛3𝜋2 )] + 𝑄3

2𝜔2𝑛3

(𝑅4

2

𝑅42)

=𝑅4 + 𝑅4

2𝑄3𝜔𝑛3[cos(𝑛3𝜋

2) − 𝑖 sin(𝑛3𝜋

2)]

1 + 2 [𝑅4𝑄3𝜔𝑛3 cos (𝑛3𝜋2 )] + 𝑅4

2𝑄32𝜔2𝑛3

(2 − 55)

It is now possible to include series resistance R3 to formulate an expression for the overall

frequency response of the ionic leg as expressed in equation 4:

𝑍𝑖𝑜𝑛∗ = 𝑅3 +

𝑅4 + 𝑅42𝑄3𝜔

𝑛3[cos(𝑛3𝜋2

) − 𝑖 sin(𝑛3𝜋2

)]

1 + 2 [𝑅4𝑄3𝜔𝑛3 cos (𝑛3𝜋2

)] + 𝑅42𝑄3

2𝜔2𝑛3

(2 − 55)

Equation (2-55) can then be broken into its real and imaginary components:

𝑍𝑖𝑜𝑛 ∈ 𝑹𝒆 = 𝑅3 +𝑅4 + 𝑅4

2𝑄3𝜔𝑛3[cos(𝑛3𝜋

2)]

1 + 2 [𝑅4𝑄3𝜔𝑛 cos (𝑛𝜋2 )] + 𝑅4

2𝑄32𝜔2𝑛

(2 − 56)

𝑍𝑖𝑜𝑛 ∈ 𝑰𝒎 =−𝑅4

2𝑄3𝜔𝑛3[𝑖 𝑠𝑖𝑛(𝑛3𝜋

2)]

1 + 2 [𝑅4𝑄3𝜔𝑛3 𝑐𝑜𝑠 (𝑛3𝜋2 )] + 𝑅4

2𝑄32𝜔2𝑛3

(2 − 57)

iv) Blocking Polarization: The impedance of CPE4 that represents polarization due to blocked

space charge at the electrode/dielectric interface is given by the following expression:

𝑍𝑏𝑙𝑜𝑐𝑘 =1

(𝑗𝜔)𝑛4𝑄𝑜4 (2 − 58)

This expression can be displayed in its complex form:

𝑍𝑏𝑙𝑜𝑐𝑘 =1

𝑄4𝜔𝑛4[cos(𝑛4𝜋2

) + 𝑖 sin(𝑛4𝜋2

)] (2 − 59)

Using a similar mathematical analysis as performed on circuit elements R4 and CPE3, the

blocking impedance can be broken into its real and imaginary impedance values shown below:

𝑍𝑏𝑙𝑜𝑐𝑘∗ =

cos(𝑛4𝜋2

) − 𝑖 sin(𝑛4𝜋2

)

𝑄4𝜔𝑛4 (2 − 60)

𝑍𝑏𝑙𝑜𝑐𝑘 ∈ 𝑹𝒆 =cos (

𝑛4𝜋2 )

𝑄4𝜔𝑛4 (2 − 61)

𝑍𝑏𝑙𝑜𝑐𝑘 ∈ 𝑰𝒎 =−i sin (

𝑛4𝜋2 )

𝑄4𝜔𝑛4 (2 − 62)

61

In the case n4 = 1, the impedance is purely capacitive and equation (14) goes to 0 while equation

(15) gives the impedance of an ideal capacitor (1/iωQ4). In the case n4 = 0, the response is purely

resistive and equation (15) goes to 0.

v) Complete EC Response: The total response as a function of frequency for the EC can be

derived by considering each individual component discussed. The general formula for the

impedance of the EC in Figure 2-8 is given by the following equation:

𝑍𝐸𝐶 = (1

𝑍𝑒𝑙𝑒𝑐+

1

𝑍𝑑𝑖𝑝+

1

𝑍𝑖𝑜𝑛)

−1

+ 𝑍𝑏𝑙𝑜𝑐𝑘 (2 − 63)

The total impedance for the model is formulated by substituting equations (2-48), (2-50), (2-55),

and (2-62):

𝑍𝐸𝐶 = (𝑗𝜔𝐶1 + [1

𝑗𝜔𝑄2

+ 𝑅2]−1

+ [𝑅3 +𝑅4 + 𝑅4

2𝑄3𝜔𝑛3[cos(𝑛3𝜋

2 ) − 𝑖 sin(𝑛3𝜋2 )]

1 + 2 [𝑅4𝑄3𝜔𝑛3 cos (

𝑛3𝜋2

)] + 𝑅42𝑄3

2𝜔2𝑛]

−1

)

−1

+ [cos(𝑛4𝜋

2 ) − 𝑖 sin(𝑛4𝜋2 )

𝑄4𝜔𝑛4

] (2−64)

Complex nonlinear regression using the electrochemical software Z-view is used to fit Q2, n2, R3,

Q3, n3, R4, Q4, and n4 from the above relation to impedance spectra for P(VDF-TrFE) in this

dissertation.

2.4.2.2 Statistical Interpretation of Fit Parameters

Complex non-linear regression fitting was performed on impedance data for the tested

P(VDF-TrFE) samples in the manuscript. During each fit, 4 impedance formalisms were assessed

to ensure a good fit to data: 1) real and imaginary capacitance, 2) complex impedance in cole-cole

plot format, 3) the magnitude of impedance and phase angle, and 4) real and imaginary modulus.

The impedance data is converted to each formalism using Z-View software. Each formalism is

easily displayed using the program as well. The goodness of fit was assessed in the following three

ways:

i) Regression fit result superimposed on the 4 mentioned impedance formalisms. This is a

qualitative assessment to ensure the behavior of the data is captured by using the proposed EC at

each temperature and LiClO4 concentration.

ii) Calculation of material and bulk properties from the appropriate circuit elements. This

was a useful step used to validate CPE2’s accuracy in estimating dipolar response by calculating

62

material permittivity from fit results and comparing to values calculated directly from capacitance

measurements within the frequency range 102 – 105 Hz.

iii) Reference to statistical reports generated by Z-view. The fitting of impedance data was

performed using built in complex non-linear regression software embedded in Z-view. The

statistical output used in data analysis of parameter value significance was % error of fit parameter,

which is explained in further detail in the Z-view Impedance/Gain Phase Graphing and Analysis

Software Operating Manual version 3.5. Calculation of statistical quantifiers such as % error is

sensitive to the weighting formalism used when fitting data. Using a weighting scheme such as

“unit weighting” will overemphasize data values of large magnitude, which is likely when fitting

a broad frequency spectrum. In this work, calc-proportional weighting is used since each data

point’s weight is normalized by its magnitude. In this weighting scheme, the real and imaginary

components are weighted separately.

2.4.3 TSDC Peak Deconvolution

As mentioned in section 2.3.3.3 Bucci-Feischi theory is used to describe relaxation

processes associated with pure copolymer in this dissertation. Similar to EC modeling and bulk

limited conduction analysis via hopping theory, the mathematical expression for TSDC is not

linearizable (equation 2-43) an requires the use of nonlinear regression for parameter estimation

and fitting. One challenge during fitting is the separation of coalescing TSDC signals. Equation

2-43 is intendend to describe only one depolarization event with a single relaxation time. Thus if

a borad temperature spectrum consisting of multiple peaks exists, peak deconvolution exposing a

single pronounced peak must be performed. A data subtraction technique was used, described

visually in a schematic presented in Figure 2-9a, 9b, and 9c. Initially the strongest peak in the

spectrum is selected in 9a. Nonlinear regression is performed producing parameter estimates that

describe the depolarization of peak 1. From these estimates, a function over the entire temperature

range is produced and subtracted from the raw data portrayed in 9b, exposing peak 2 without

contribution from peak 1. Fitting is then performed on peak 2 depicted in 9c and parameter

estimates recorded.

Non-linear regression performed using equation 2-43 necessitates the estimation of three

parameters: Po which is a polarization constant, activation energy ψ and relaxation time τo. Since

3 parameters must be estimated, a custom R-Studio script was written implementing nested “for

63

loops” which compute J for a user defined range of Po, ψ, and τo which follows the following

functional form:

𝜏𝑜 =𝑘𝑏𝑇𝑚

2

𝑏𝜓𝑒𝑥𝑝 (𝜓

𝑘𝑏𝑇𝑚) (2 − 65)

where b is the heating rate of the experiment.2

Figure 2-9: Schematic of TSDC peak deconvolution procedure depicting a) fitting of strongest signal in convoluted

spectrum, b) subtraction of fit function from raw data over temperature range and c) fitting deconvoluted low

temperature peak.

2 An annotated version of the R-Studio code used for TSDC peak deconvolution can be found in Appendix B.

64

CHAPTER 3

HOT-PRESSED PVDF LAMINATES – THE EFFECT OF INTERFACES IN SINGLE

MATERIAL LMINATED DIELECTRICS3

ABSTRACT

This chapter is focused on the development and characterization of multilayer PVDF

dielectric laminates for preliminary analysis of the effect of interfaces on charge transport and high

field dielectric breakdown in all organic dielectrics. Unlike work by Mackey et al. [14] and Zhou

et al. [15] on dielectric breakdown strength of P(VDF-HFP)/PC composites, this chapter only

incorporates PVDF as the laminated material, eliminating composite effects and focusing on how

the interface created by hot-press lamination impacts electrical properties. An outline of chapter

contents is provided below:

Introduction – motivates the work discussed along with the most impacted scientific field.

Materials and Methods – presents processing methods used to create multilayered

laminates (leveraged from process outlined in Chapter 2, section 2.2.1), as well as

structural and electrical characterization techniques.

Results – discusses outcomes of structural and electrical characterization of laminated

dielectrics in comparison to 1-layer control films.

Conclusions – summarizes results and provides avenues for further research.

Results obtained from this portion of this dissertation provided a proof-of-concept frame-work

demonstrating the impact interfaces can have on electrical conduction without need for composite

materials, leveraging research performed in subsequent chapters.

3.1 INTRODUCTION

Modern age high-powered electronic applications require the development of new

materials that exhibit high-energy storage capabilities. Although batteries currently have higher

electrical energy storage capabilities than capacitors, they lack the power output to fulfill most

3 A significant portion of this work was published at CEIDP Toronto 2016 conference [228].

65

high-powered applications. Currently, polymer capacitors are sought after for high-powered pulse

applications due to their high breakdown strengths, low losses, low cost, and ease of

manufacturability. Although these characteristics are seen as favorable, polymer capacitors suffer

from low dielectric permittivity and thus relatively low energy densities. Strategies used to blend

polymer composites and add inorganic inclusions to increase permittivity are met with limited

success, resulting in local electric field distortions that decrease the effective breakdown strength

[131].

In this study, we investigate the effect of added interfaces within the dielectric structure

created by lamination. Polyvinylidene fluoride (PVDF) is a widely used polymer for its excellent

mechanical, chemical and ferroelectric properties [132]. Due to its technological importance and

impact on many applications, we have selected it as the model polymer for our study. Past research

has shown that PVDF/Polycarbonate (PC) dielectric composite structures fabricated by layer

stacking improve dielectric breakdown strength in comparison to polymer blends [14]. Similarly,

it has been shown that self-assembled multilayered diblock4copolymers display significantly

higher breakdown strengths than stand-alone cast films [133]. Our main goal is to better understand

the effect of added interfaces on charge transport in all-organic laminates and provide insight into

conduction through layered organic dielectric media. We believe that with the addition of

interfacial elements created by a multilayer laminate structure, charge trapping at interfaces

distributed throughout the structure will enhance high field capacitor performance. This study

uses high voltage dielectric breakdown in conjunction with impedance spectroscopy to investigate

interfacial effects on capacitor performance.

3.2 MATERIALS AND METHODS

3.2.1 Materials Selection

Pure PVDF powder provided by Arkema, USA, and N,N-Dimethylformamide (DMF)

Anhydrous DrySolv were the raw materials used in this study. Protective Kapton PI sheets used

during hot pressing were provided by Dupont.

3.2.2 Multilayer Laminate Fabrication

This material is based upon work supported by NSF as part of the Center for Dielectris and Piezoelectrics under Grant N. IIP-1361503.

66

The procedure followed to fabricate laminates as well as dielectric film quality control is

explained in detail in Chapter 2, section 2.2.1, however the essentials are outlined here. Sample

fabrication is a two-step process: 1) solution casting to prepare PVDF monolayers, and 2) stacking

and hot pressing of monolayers to make multilayer laminates.

1: PVDF/DMF solutions are mixed in 100 ml beakers and magnetically stirred for

approximately 3 hours. The resulting solution is then de-gassed under vacuum for approximately

30 minutes prior to casting. The solution is then poured onto a glass plate (previously cleaned

with Acetone and Kimtech wipe) and spread uniformly over the plate using a doctor blade. Films

are dried at 180 oC under vacuum for 1 hour, leaving a freestanding film ready for hot pressing.

2: The cast films are cleaned using a Kimtech wipe damp with ethanol, then assembled into

a rectangular stacking of 1-4 layers. The stack is sandwiched between two Kapton sheets to

prevent the films from melting and sticking to the hot-press’s platens during pressure application.

The Kapton/PVDF assembly is placed into the vice and pressed at 150 oC for 30 min at

approximately 20 MPa. Samples are then removed and allowed to thermally equilibrate back to

room temperature.

3.2.3 Structural Characterization

Film thickness uniformity before and after hot pressing was assessed using a Heidenhain

model ND-280 dial gauge. SEM cross sectional images of a hot pressed 2-layer film were made

using by freeze fracturing in liquid nitrogen. The crystalline phase assemblage in PVDF for 1-

layer solution cast, 1-layer solution cast film subjected to hot-pressing, 2-, 3-, and 4-layer samples

is assessed by a combination of differential scanning calorimetry and Fourier Transform Infrared

Spectroscopy (FTIR) using a TA Instruments Q2000 DSC and Burker Vertex-70 FTIR

spectrometer.

3.2.4 Dielectric Measurements

Two forms of dielectric analysis were conducted for this study: 1) high voltage dielectric

breakdown at room temperature and 2) low voltage impedance spectroscopy at room and elevated

temperatures.

1: High voltage experimentation utilized a homemade configuration consisting of a TREK

amplifier model 30/20, National Instruments IO DAQ, and Labview software to record data. A

67

copper plate and ballpoint served as bottom and top electrode respectively. The sample is

submerged in insulating (Galden) oil throughout the duration of the experiment to prevent arcing

from top ball electrode to bottom copper plate.

2: Impedance spectroscopy was performed within the frequency range of 1 mHz – 100 kHz

using a Modulab impedance analyzer from Solartron Analytical. Temperature was swept using a

Delta Design 9010 oven. Values for the real and imaginary parts of impedance were collected with

Modulab and converted to capacitance and loss tangent using the general electrochemistry

software Z-view provided by Scribner Associates Inc.

Prior to dielectric measurement, electrodes are deposited onto each sample via electron

beam evaporation using Lab-18 (Kurt J. Lesker). Electron beam evaporation is used over

sputtering to avoid exposing PVDF samples to plasma and higher energy deposition characteristic

of RF magnetron sputtering, which may cause polymer surface degradation [111]. The electrode

material used is Ag, 100 nm in thickness, and is deposited in a circular pattern with a diameter of

1 cm. Lastly, capacitance and loss tangent for each sample are measured using a high-precision

LCR meter at 1 kHz and 1V. This step is done to provide a reference for acquired electrical data.

3.3 RESULTS

3.3.1 SEM Imaging the Interface

Imaging of the cross section of a 2-layer hot-pressed sample was performed to confirm the

presence of interfacial elements within the bulk of the laminate. The sample was prepared by freeze

fracturing in liquid nitrogen. The sample imaged was a 2-layer laminate of 30 μm in total thickness,

processed by hot pressing two individual 15 μm 1-layer films together. Imaging was able to capture

the interface generated by the hot-pressing procedure, confirming the presence of a layered

microstructure, as seen in Figure 3-1a.

3.3.2 DSC PVDF Thermal Analysis

Thermal characterization of PVDF was performed in order to understand the effect of

layering after the hot-pressing procedure. In these experiments, a monolayer exposed to the

outlined hot-pressing procedure as well as a 4-layer hot-pressed stack was measured between the

temperatures 25oC and 200oC with a heating ramp rate of 10oC/min and the results compared in

Figure 3-1b. It was found that the monolayer exhibited a single melting peak at Tm~160oC, which

68

is consistent with the expected value of Tm reported for PVDF films in the literature[17]. This is

also featured by the 1-layer film exposed to the hot-pressing protocol signifying not significant

structural changes occur due to hot pressing alone. The 4-layer stacked samples however showed

a much different thermogram than that of either monolayer. In these samples, the melting peak

split in two distinct signals, one at Tm1~160oC and the other at Tm2 ~170oC. Both crystal phase (α-

or β-phase) as well as crystal size can affect the melting temperature of the crystalline phase,

implying further structural characterization is required to fully understand how layering affects

PVDF crystal morphology.

Figure 3-1: a) SEM image of 2-layer cross section (displaying developed interface) and b) DSC thermogram of un-

pressed, 1-layer hot-pressed, and 4-layer laminate.

3.3.3 FTIR PVDF Crystal Structure Analysis

The dielectric behavior of PVDF’s polymorphic structure is sensitive to the phase (α, β, or

γ) composition of the material. Each phase exhibits a unique dielectric property, for example, β-

phase’s polar nature enabling PVDF’s characteristic piezo and ferroelectric properties in

comparison to the non-polar α-phase of higher dielectric constant [71] [134]. For this reason,

Attenuated Total Reflectance (ATR)-FTIR characterization was performed to compare phase

development across all samples (Figure 3-2).

The most common vibrational modes for the α-phase occur at wave numbers 532, 614,

764, and 796 cm-1. Vibrational modes corresponding to the β-phase are seen at wavenumber 840.

69

Figure 3-2: ATR-FTIR morphological characterization of hot-pressed laminates. Absorbance spectra of PVDF films

from top to bottom A) 1-layer, B) 1-layer hot-pressed, C) 2-layer D) 3-layer and E) 4-layer laminates. Salient

spectral features are discussed in this section. All PVDF vibrational modes are presented in Chapter 2 section

2.3.1.2 Table 2-IV.

Finally, 880 pertains to active vibrational modes for both α- and β-phases [135]. The combination

of these vibrational modes in the absorbance spectrum for the 1-layer PVDF sample exist,

suggesting a combination of α-phase and β-phases are present in solution cast films. Hot-pressing

did not cause a significant change in the 1-layer hot pressed film, however minor changes in peak

intensity increase of the α-phase occurs in 2- through 4-layer laminates. Ultimately the

combination of α- and β-phase in 1-layer and multilayer films is unchanged after hot pressing

suggesting DSC results for melting characteristics of 4-layer films are not due to a change in phase

distribution in the material.

3.3.4 Dielectric Breakdown

Samples undergo a 5-hour drying procedure at 100 oC under vacuum prior to breakdown

to ensure residual solvent does not alter material response. After releasing vacuum, samples are

immediately submerged in Galden oil to minimize exposure to atmosphere as much as possible.

Voltage is ramped 500 V/s until samples fail (determined by a current spike under test conditions).

All testing was performed at room temperature.

The electrical strength of PVDF laminates was analyzed using two parameter Weibull

statistics with the associated most likely probability of failure function:

𝐹(𝑖, 𝑛) =𝑖 − 0.3

𝑛 + 0.4 (3 − 1)

70

where i represents the ith failure in a stress test consisting of n total failures. Methods for estimating

statistical confidence intervals in Weibull modulus and characteristic breakdown strength are

based on the IEEE 930, 2004 standard [127]. Structures tested were a 1-layer solution cast, 1-layer

hot-pressed sample (HP), 2-layer, and 3-layer. The amount of data points recorded for each sample

ranged between 23-28 total breakdown events, which qualify the data as a “larger data set” as seen

in [127]. Computation of linear fits for Weibull data was done using Microsoft Excel’s built in

least squares regression function and correlation coefficients were compared in conjunction with

figure A.8 in [127]. The values of characteristic breakdown strength reported are extracted from

the best-fit line’s intersection with the Ln[Ln(1-F(i,n))] axis equal to 0, indicating the 63rd

percentile of failure. In order to derive statistical significance in this value, an associated 90%

confidence interval was computed for each characteristic breakdown value by methodology

offered in [10].

Figure 3-3a summarizes the characteristic breakdown values of tested samples extracted

from two parameter Weibull distributions. An attempt was made to maintain a similar total

thickness of each tested film to avoid the effect of thickness on dielectric breakdown results [136]

[137], however controlling sample thickness using stacking/hot pressing method was challenging.

The initial 1-layer sample achieved a characteristic breakdown field of 385 MV/m. After exposing

a 1-layer film to hot pressing, we note an increase in characteristic breakdown field to 415 MV/m.

This 8% increase in breakdown strength was expected due to the suspected healing of defects

formed through solution processing upon exposure to high temperatures around the melting

temperature (Tm) of the polymer. The 1-layer HP sample is most closely related to the 2-layer and

3-layer due to its exposure to thermal loading and pressure. With the addition of a single

interface (2-layer) characteristic breakdown field is seen to increase to a value of 480 MV/m

yielding a 16% increase that displays a 90% confidence range that falls outside of 1-layer HP. The

3-layer sample containing two interfaces achieved a characteristic breakdown field of 490 MV/m.

This is not considered a statistically significant increase in the durability of the dielectric structure

relative to the 2-layer. The breakdown strength of the films were then fit as a function of their

thickness t in order to test if their spread in film thickness (37μm for the 1-layer and 23μm for the

3-layer) contributed to the increase in breakdown strength in Figure 3-3b. Fitting the breakdown

strength as a function of t using Microsoft’s linear regression function revealed a poor fit

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Figure 3-3: a) dielectric breakdown strength shown for 1-layer films, 1-layer hot pressed, 2- and 3-layer films and b)

dielectric breakdown strength plotted as a function of t for 1-layer hot pressed, 2- and 3-layer films.

dependent on t-0.38 which disobeys breakdown strength’s expected thickness dependence on t-1/2

[138]. Work measuring the breakdown strength of solution casted PVDF as a function of film t

has also shown no thickness dependence on the breakdown strength in films ranging 20 - 40 μm,

which spans the thickness range of films tested in this chapter [139]. The combination of fitting as

well as previous literature suggest that changes in dielectric breakdown strength are in fact due to

the introduction of planar interfaces by hot pressing.

3.3.5 Impedance Spectroscopy

Capacitance and loss data was captured for samples containing 1- through 4-layers and

converted to dielectric permittivity plotted as a function of frequency, as seen in Fig. 3. The

permittivity for a 1-layer sample is at 8.75 at 100 Hz and remains stable between 8 and 8.5 until

the onset of the dipolar relaxation regime at approximately 0.1 MHz. Samples ranging from 2- to

3-layers display increased permittivity as follows: 2-layer has permittivity of 9.10 at 100 Hz and

3-layer has 9.86 at 100 Hz. This trend breaks at 4-layers with saturation between 3- and 4-layers.

If we consider the 3-layer sample as having the highest achieved permittivity, we note a 13%

increase in dielectric permittivity through interfacial element addition. The loss tangent between

the range of 1 kHz – 100 Hz displays a decreasing trend with increasing layer count. This

observation motivates investigation of dielectric response at the quasi DC frequency range.

Analysis is expanded to include equivalent circuit (EC) modeling to characterize interfacial

effects at elevated (70 oC) temperatures. In Figure 3-4, room temperature permittivity and loss

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Figure 3-4: Dielectric permittivity and loss tangent calculated from impedance spectroscopy measurements between

10-2 Hz – 105 Hz for 1-layer and 4-layer PVDF laminates. EC modeling performed using the shown circuits for each

sample set (bottom left) with parameter estimates (bottom right).

tangent are plotted against the equivalent circuit model corrensponding to 1- and 4-layer samples

as solid bold lines running thorugh the data. Fitting for each data set was done using Z-View

electrochemical circuit modeling software. The frequency range spans 100 kHz – 10 mHz.

The circuit model for the 1-layer consists of a parallel circuit element containing a

capacitor, resistor and constant phase element (CPE) in parallel. A similar circuit consisting of

CPE with a resistor in parallel is seen in another study modeling the electric response of bulk

poly(vinyl alcohol) (PVA) with yittrium modifyed barium zirconium titanate (BYZT) micro

particles [140]. Although similar, it does not completely incorporate circuit elements

corresponding to the three mechanisms typically seen in bulk polymer behavior: induced dipoles,

static dipoles, and ionic conductivity. This behavior can be rationalized through three respective

elements: capacitor, capacitor-resistor in series, and stand alone resistor [141]. For our proposed

model, the capacitor-resistor componant is replaced with a CPE; a capacitor like circuit element

with the following form of impedance:

𝑍′ =1

𝑄(𝑗𝜔)𝑛 (3 − 2)

where Q is the value of the CPE element, j the square root of negative one, ω is angular frequency

and n is an exponential imperfection factor ranging from zero to one. The precise origin of the

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CPE is not wholly understood, however its occurrence in systems with electrode imperfections

such as roughness or porosity, as well as electrochemical diffusion mechanisms at play has been

studied [142] [143]. For systems involving polycrystalline solid state devices, CPE behavior has

been rationalized to arise due to alpha relaxation process. This EC describes the behavior of the 1-

layer by itself, yielding a good fit to data with accurate componant values diplaying low errors.

When performing the fitting for the 4-layer sample set, using the bulk model alone gives rise to

elevated errors in circuit elements, as well as deviation from the permittivity at 10 mHz. The

addition of a CPE in series (labeled CPE2) produced a more precice fit in the low frequency regime

as well as yielding reasonable values for circuit elements. This circuit element is believed to arise

from the development of added interfacial polarization afforded by the layered structure, and is

necessary in modeling the dielectric response of the 4-layer sample set.

3.4 CONCLUSIONS

We have successfully developed processing protocol to fabricate structurally robust

multilayered laminates comprised of pure PVDF. The interface was initially characterized using

IEEE standard dielectric breakdown protocol. Measurements yielded increased dielectric

breakdown strength with increasing layer count of the structure. 1-layer samples exhibit a 415

MV/m breakdown while 2- and 3-layers increase to 480 and 490 MV/m respectively. The origin

of this enhancement in breakdown strength is attributed to the blocking of mobile charged species

at high fields. Another potential cause for this increase in durability could be due to a reduction

in processing defects. Monolayers processed for lamination are thinner to match the equivalent

thickness of a single layer, and potentially contain less defects.

Room temperature dielectric spectroscopy data displays an increase in permittivity of the

samples, saturating at 4-layers. Likewise, the dielectric loss was seen to decrease within 1 kHz –

100 Hz with the 4-layer sample displaying lowest loss tangent at 100 Hz, similarly seen in [144].

Through impedance spectroscopy techniques, the DC limit was pushed yielding the effects of

lamination on space charge relaxation mechanisms. Below 10 Hz, layered samples exhibit an

increase in the permittivity in comparison to a 1-layer sample which may be linked back to slight

structural changes in hot pressed layered films seen in DSC and FTIR charaterization. Exposure

to elevated temperatures amplifies the effect of the interface in the 4-layer sample set. This

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behavior was described by the addition of a CPE element in EC modeling, indicating layered

elements within the dielectric promote the blockage of mobile space charges at low frequencies.

In order to continue the study of interfaces in dielectric media on charge transport, total

thickness of the dielectric must be reduced while layer count increased. Increasing the ratio of

interfacial elements to total thickness will serve to amplify the effect of the interface on charge

transport. A switch to solution spin casting is made in subsequent chapters to reduce layer thickness

while increasing resultant dielectric film thickness uniformity and repeatability in processing.

Simialrly, DSC and FTIR results confirm difficulties surrounding PVDF crystal phase control

during processing. A switch the P(VDF-TrFE) as the model material is also made to enable

consistent phase distribution (predominantly β-phase) in the films to aid in accurate electrical data

interpretation.

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CHAPTER 4

PLASMA SURFACE MODIFICATION OF P(VDFTrFE): INFLUENCE OF SURFACE

CHEMISTRY AND STRUCTURE ON ELECTRONIC CHARGE INJECTION5

ABSTRACT

In this chapter, the effect of the electrode/dielectric interface’s role on low and high field

conduction is studied by using reactive plasma treatment as a tool to change thin film surface

chemistry and electrical properties. P(VDF-TrFE) as a dielectric material as well as spin cast thin

film processing is introduced to 1) implement a material system in which crystallinity and crystal

phase are well controlled and 2) reduce film thickness relative to blade casted films to increase the

contribution of the interface to the electrical signal. An outline of the chapter contents is provided:

Introduction – A brief literature review emphasizing research targeting plasma

modification for dielectric applications is presented and concluded with the scope of the

work done in this chapter.

Experimental Section – materials and processing methods used to create plasma treated

P(VDF-TrFE) thin films are discussed. Specifics pertaining to chemical, structural and

electrical characterization techniques are listed.

Results and Discussion – outcomes of plasma surface modification on dielectric film

surface topology and chemical structure are first addressed, then linked to altered

conduction properties relative to untreated control samples.

Conclusions – the results are summarized in broader scientific context and used to inform

on avenues for further research as well as analysis of interfacial modified dielectric films.

The results obtained in this section of the dissertation highlight the impact of the

electrode/dielectric interface on electrical conduction in P(VDF-TrFE) and suggest its ability to

influence high field leakage currents in other systems.

5 A significant portion of this chapter has been published in Vecchio et al. [122] in the Journal of Applied Physics, a proceedings for the2017 18th

US-Japan Seminar on Dielectric and Piezoelectric Materials, Santa FE NM 2017 and a proceedings for CEIDP 2018 in Cancun Mexico [227].

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4.1 INTRODUCTION

The modern age of high-powered electronic applications demands the development of new

dielectric materials that reliably support both high power densities and high energy densities.

Traditionally, polymer film capacitor technologies focus on the use of biaxially oriented poly

propylene (BOPP) because of its high breakdown strength (Eb) of 850 V/μm, self-healing

capabilities, low equivalent series resistance (ESR) and relatively low cost of production [145]

[65]. Although the aforementioned qualities of BOPP make it an excellent material for high-power

applications, its low dielectric constant (εr) of 2.2 hinders the functionality of the material for

devices in which high energy density is a necessity [145] [146] [147]. In this regard, the polar

dielectric polyvinylidene fluoride (PVDF) exhibits a breakdown field comparable to BOPP, as

well as a high permittivity of ~8-12, achieving εr as high as ~50 when polymerized with

trifluoroethylene and chlorotrifluoroethylene [71] [148] [149]. Although the polar nature of this

material allows for a desirably high dielectric constant, PVDF films exhibit large loss tangents that

approach ~0.5-1%, and consequentially high leakage currents [150] [149]. In order for PVDF to

realize its full potential as a material in high energy density and power applications, considerable

work needs to be done to understand conduction through PVDF at low and high fields. In this

work, the impact of surface chemistry on low and high field conduction through poly(vinylidene

fluoride trifluoroethylene) (P(VDF-TrFE)) is studied by using a reactive plasma surface

modification, with a focus on the role of surface chemistry on the electrical properties of polar

polymer dielectrics.

Surface modification via plasma treatment has proven to be both simple and effective in

altering dielectric properties of organic capacitor materials. The application of plasma to the

surface of organic films typically results in surface modification by chemical functionality grafting

that is dependent on both plasma composition and treated material [151]. The addition of these

moieties results in tailorability of the surface chemical composition [152] [153] [154], altered film

wettability [34] [155], adhesion to other surfaces [35] [156] [157] [158], and tuning of electrical

properties [152] [159] [17]. Meddeb et.al. [152] studied the effect of surface treatments using

oxygen based plasma on the wettability and electrical properties of polyimide Kapton® films at

room and elevated temperatures. It was found that increased presence of oxygen at the film’s

surface was coupled with enhanced hydrophilicity of the material post plasma exposure. High field

dielectric breakdown and current-voltage measurements also indicated increased Eb as well as

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reduced leakage currents at 150 oC in treated films relative to the untreated control. The changes

measured in dielectric properties were associated with the evolved surface chemical structure,

leading to charge scattering effects of trapping regions at the electrode/material interface.

Similarly, Mammone et al. [159] studied the effect of plasma treating polypropylene resin with a

mixture of 96% CF4/4% O2 gas plasma prior to melt extrusion on dielectric breakdown strength.

The results demonstrate that 20% increase in the Eb occurred after the 4 min plasma treatment

procedure. These results and others motivate the incorporation of plasma treatment in the

processing of dielectrics for high field applications, however it should be noted that the majority

of current research focuses on nonpolar systems.

Past research performed on PVDF terpolymer focused on the electrode metal’s effect on

charge injection and dielectric breakdown of the material [11]. The high field dielectric strength

was observed to depend on both electrode material and electrode deposition technique. Similarly,

it was found that charge injection varied depending on electrode material selection, demonstrating

the importance of the metal/dielectric interface on the high field conduction properties of PVDF.

This study by Chen et al. [11] does not use plasma surface treatment to study high field properties

of PVDF, however the study by Mammone et al. [17] does. Mammone investigated the effect of

CF4/O2 plasma treatment on dielectric permittivity and breakdown strength of pure PVDF. The

researchers found that plasma treatment resulted in both an 11% increase in the Eb of the material

and reduction in the bulk dielectric constant of the system. IR measurements indicated a reduction

in absorbance in the alpha crystal absorbance bands (766 cm-1, 855 cm-1, and 978 cm-1), however

the study did not correlate the altered molecular structure to changes in polymer chemistry and

dielectric performance, nor did it identify the specific transport mechanism responsible for these

changes.

The goal of this study is to address the gap in the literature in terms of understanding how

reactive plasma treatments impact high-field performance of polar polymers, by providing greater

insight on the relationship between chemical structure, surface wetting properties and electrical

conduction in polar organic systems. We have devised a processing protocol for a CF4/O2 reactive

plasma surface treatment and successfully modified the surface chemistry of P(VDF-TrFE) thin

films. In doing so, the nature of film surface structure and electrode/dielectric contact for

copolymer dielectrics is changed. The effect of plasma treatment on the film’s surface chemistry

is first analyzed by X-ray Photoelectron Spectroscopy (XPS). The results are used to investigate

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changes in surface chemical environment, and then correlate to changes in contact angle and

surface polarity of the polymer. Finally, current-voltage (I(V)) measurements were performed to

analyze how surface modification impacts conduction through the material. It is discovered that

the addition of carbonyl chemical moieties to the films via plasma treatment reduces net polarity

of the system and increases low and high field steady state conduction due to altered

metal/dielectric contact properties.

4.2 EXPERIMENTAL SECTION

4.2.1 Materials

The copolymer P(VDF-TrFE) 70/30 mol% was purchased from Arkema in powder form

with molecular weight Mn= 205 kg/mol, reported in the provided safety data sheet. The solvent

N,N-Dimethylformamide (DMF) purchased from DriSolv® was used to dissolve P(VDF-TrFE)

powder. P(VDF-TrFE)/DMF solution was spun onto platinum coated silicon wafers purchased

from Nova Electronic Materials.

4.2.2 Thin Film Fabrication

Solutions of P(VDF-TrFE)/DMF were prepared at 7.5% solid weight content. The solution

was then subjected to a degassing procedure to remove trapped air bubbles resulting from magnetic

stirring. The degassed solution was then transported into a clean room where it was spin casted

onto platinum coated silicon wafers forming a thin continuous film over the surface of the

substrate. A KLA-Tencor P16+ stylus profilometer was used to determine the thickness and

uniformity of the resultant films. Using a spin speed of 600 rpm for 50s consistently produced 1

μm thick films of good thickness uniformity (only a standard deviation of +/- 80 nm across the 4in

diameter substrate) and were used in all processing and experiments in this study. Samples

fabricated for electrical measurements had Ag electrodes deposited 50 nm thick, 1 mm in diameter

using a Lab-18 electron beam evaporator provided by Kurt J. Lesker. The sample stage temperature

was held at 0 oC during electrode deposition to prevent sample damage.

4.2.3 Plasma Surface Modification

All plasma treatments were performed in an M4LTM RF gas plasma system provided by

PVA TePla using a constant flow rate of 250sccm for CF4 and O2. An additional 50sccm of He to

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control chamber temperature was flowed during the process. The chamber pressure was allowed

to naturally reach an equilibrium pressure between 720 – 740mTorr before plasma ignition. All

treatments were administered at 500W system power and treatment duration varied at 45s, 90s,

135s and 180s. After treatment, the samples remained under gas flow until chamber pressure re-

equilibrated and were then removed and immediately stored under vacuum until further

measurements.

4.2.4 Investigated Processing Conditions.

Samples were processed under two separate conditions for experiments involving plasma

treatments via methods outlined in sections 4.2.1 – 4.2.3 (as well as Chapter 2 section 2.2.2 –

2.2.4). The first is the “As-Spun” processing condition, where plasma treated films only underwent

the spin casting and 15min drying procedure outlined in section 4.2.2. The second is the “Post-

Anneal” processing condition, where films underwent the initial fabrication process in 4.2.2

followed by the plasma treatment protocol outlined in 4.2.3, and finally annealed after plasma

treatment for 24 hrs at 142 oC under vacuum. All plasma treated samples remained under vacuum

after processing until the time of electrical measurement and surface characterization.

4.2.5 Characterization Techniques

4.2.5.1 Chemical and Structural

The thermal properties of the spin casted films were measured using a Q2000 differential

scanning calorimeter provided by TA Instruments. Samples were prepared by scratching 5-7mg of

copolymer off of the wafer into an Al DSC pan using a carefully cleaned razor blade.

XPS experiments were performed using a Physical Electronics VersaProbe II equipped

with a monochromatic Al kα X-ray source (hν = 1,486.6eV) and a concentric hemispherical

analyzer. Charge neutralization was performed using both low energy electrons (less than 5eV)

and Argon ions. The binding energy axis was calibrated using sputter cleaned Cu foil (Cu 2p3/2 =

932.7eV, Cu 3p3/2 = 75.1eV). Peaks were charge referenced to CF2 band in the C1s spectra at

291.7eV. Measurements were made at a takeoff angle of 45° with respect to the sample surface

plane which resulted in a typical sampling depth of 3-6nm. Quantification was done using

instrumental relative sensitivity factors (RSFs) that account for the X-ray cross-section and

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inelastic mean free path of the electrons. Carbon 1s and oxygen 1s spectra were analyzed using

CasaXPS data processing software.

Time of flight secondary ion mass spectrometry (ToF-SIMS) was used as a depth profiling

technique to estimate the depth at which plasma surface modification affects the material. Depth

profiling was performed using a PHI nanoTOF II SIMS. A pulsed 30 keV Bi32+ primary beam

was used for spectroscopy. Sample etching was achieved with a 5 keV Ar2500+ cluster ion beam.

Both electron and ion charge neutralization occurred during depth profiling, and the LMIG and

GCIB raster sizes were 100 x 100 microns, and 500 x 500 microns respectively.

Surface roughness of the copolymer before and after plasma treatment was measured on a

NextView 3D Optical Profilometer provided by Zygo. A series of measurements with scan areas

of 87μm x 87μm were taken on each sample. Sq values were then averaged over a series of 8 scans

per sample.

The H2O contact angle for each plasma treatment condition and exposure time was

measured using a Ramé-Hart Model 295 goniometer and deionized water. Sessile drop

experiments began by depositing a 5μL volume of H2O onto the sample using a small remote

controlled hydraulic pipette. The measured contact angle is taken as the mean between left and

right contact angle of the water droplet at first impact on the sample surface. A total of 5

measurements at separate locations on each sample were made to produce a standard deviation in

the measurement.

4.2.5.2 Electrical

A Cascade Probe Station equipped with DCM 210 series Precision Positioner 20μm probes

were used to capture low and high field dielectric behavior. Dielectric spectroscopy was performed

using an Agilent Precision LCR meter. Each sample was exposed to 1V rms ranging from 100Hz

– 1MHz.

I(V) experiments were performed using the same experimental set up as used for dielectric

spectroscopy. A 4140 pA meter provided by Hewlett-Packard that served as its own DC source

was used to measure current as a function of applied voltage. Initially, a series of low voltages (2V

– 10V) were applied to the samples and the current as a function of time was measured to determine

the required hold time to achieve a steady state current for current/voltage measurements. The hold

time of 20s was chosen by comparing current densities measured at 20s vs 200s. Showing

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approximately a 2.4x10-6A/m2 difference in the current density at 2V, it was reasoned that a 20s

hold time is sufficient to record data with fluctuations in current being well outside the data’s

range. The samples were cycled from 5V – 100V a total of two times: the first cycle is used to poll

the ferroelectric copolymer and the second cycle is used in data analysis. This process eliminated

polarization domain wall movement as a contributing factor to displacement current in high field

measurements, allowing the focus to be the effect of plasma treatment on high field J-E behavior

and charge transport. All measurements were taken at room temperature (22oC) and averaged over

three separate electrode pads to produce a standard deviation in the data for each sample set.

4.3 RESULTS AND DISCUSSION

4.3.1 Differential Scanning Calorimetry

DSC was performed between a temperature range of 20oC – 200oC for 1μm thick

copolymer using a ramp and cooling rate of 10 oC/min. It is common for P(VDF-TrFE) to display

two endothermic phase transitions because of its ferroelectric nature [132]: one corresponding to

its Curie temperature (TCurie) and another marking the melting temperature (Tm) [160]. Although

pure PVDF exists in different crystalline phases, the copolymer P(VDF-TrFE) is chemically

modified such that it only crystallizes in the piezoelectric beta phase. The TCurie of the material

thus marks the temperature that differentiates between the ferroelectric (T<TCurie) and paraelectric

(T>TCurie) phase of the material. Our scans indicate two distinct peaks in the data pertaining to

TCurie=110oC and Tm= 148oC peaks that are congruent with similar values reported for P(VDF-

TrFE) fabricated via various processing techniques in literature [160] [161] [162]. Calculations on

percent crystallinity were made by integrating the melting endotherm of three samples originating

from the same batch of copolymer. A melting enthalpy of ΔHm = 91.45 J/g [98] estimated from a

70/30 ratio of melting enthalpies of fully crystalline PVDF and TrFE, respectively was used. For

the as-spun (control) sample, an average of 30% crystallinity is calculated using three samples

originating from the same film. Annealing temperature was then chosen based on previous work

that investigated annealing temperature’s influence on crystal percent and morphology [163].

Samples in this study were annealed at a temperature of 142 oC for 24 hours under vacuum.

Applying this procedure increased the percent crystallinity of our samples to approximately 33%,

which is comparable to crystallinity reported for P(VDF-TrFE) cited in literature [164].

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4.3.2 X-Ray Photoelectron Spectroscopy: Surface Chemistry and Structure Analysis

As expected the untreated control film contained peaks (Figure 4-1) due to CH2 (from

PVDF), CHF and CF2 located at 287.2±0.1eV, 289.5±0.1eV and 291.7eV, respectively [165]. In

addition, small peaks at 294.1±0.1eV due to CF3 end groups and adsorbed hydrocarbons at ~285eV

were observed. The elemental composition for the material was determined from C1s, F1s, and

O1s peak integration and is presented in Table 4-I. Untreated samples yielded a 45.9% C and

53.1% F after peak integration. This is in good agreement with the theoretical values of 47.0% C

and 53.0% F computed assuming a 70/30 molar ratio of PVDF to TrFE.

Plasma treated samples exhibit a noticeably different line shape in the C1s spectra.

Examination of the line shape and synthetic peak distribution between the 45s – 180s treatment

times indicated no significant change with increasing plasma exposure beyond 45 seconds,

therefore comparisons in spectral shape are made exclusively between the control (untreated) and

180s treated samples for simplicity.

Table 4-II contains the atom% of carbon and oxygen in the different chemical

environments calculated from the curve fits for all processing conditions and treatment times.

Small shifts in the synthetic fit components are observed; CFx generally displaying a slight shift

downward in energy (0.5 – 0.9eV) and CHx components shifting upward in energy (0.3 – 0.4eV).

In general, a reduction of total C from 45.9% to 35.3% and increase in O (1.0% - 6.6%) and F

(53.1% – 57.9%) species are observed after treatment. Peak fitting for the untreated and treated

samples supports O and F increase, and also indicate a large decrease of PVDF CH2 from 19.0%

Figure 4-1: C1s and O1s spectra for as-spun control as well as post-anneal samples. Line shape does not vary between

45s – 180s treatment times for all sample sets. Intensity axis heights share the same scaling for easy comparison in

each C1s and O1s group respectively.

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Table 4-I: Elements detected by XPS in atomic percentage

Table 4-II: Chemical species determined by XPS in atomic percentage

to 5.1% after treatment. Peak fitting at 287.4eV indicates the addition of C=O constituents at a

relative quantity of 3.5%, previously un-seen in the untreated copolymer film. Use of the CHx fit

component after plasma treatment was no longer necessary to improve fit quality in the as-spun

processing conditions. This indicates the eradication of hydrocarbon-based contaminants adsorbed

onto the film’s surface after plasma treatment. The CHx component’s return for the post-anneal

processing condition could indicate that the environment inside the oven used for annealing is

responsible for a small degree of surface contamination.

Samples tested from the post-anneal sample set yield a C1s line shape that exhibits qualities

of both the untreated control and plasma treated samples from the as-spun sample set. The peak

integration of the 292.9eV synthetic component corresponding to either CF2-O or CF3 is increased

from 0.7% to 2.4% relative to the untreated control, however it remains below that which is

detected in the as-spun condition. This trend is observed for the C=O component at 287.4 eV as

well, yielding 0.8% in comparison to 3.5% detected in the as-spun sample set. Finally, the decrease

84

in CH2-CFx is measured to be less than that detected in the previous samples. The general trends

in atom percent of the post-anneal films differ than that of the former for F. Detected F% shows a

slight drop from 52.9% (untreated control) to 50.6% after processing, which is consistent with the

less pronounced CF3 peak in Figure 4-1. Similarly, C% also shows a decrease (from 47.0% to

43.3%), which is approximately half the decrease in C% measured in as-spun films. Similar to C,

the measured amount of O shows the same trend as the former processing condition but in lower

quantity, reflected by decreased C=O synthetic component intensity.

High resolution scans of the O1s core level spectra also show considerable change with

plasma treatment conditions. A similar trend in the line shape as seen in the C1s spectrum is noted:

untreated and plasma treated samples differ in shape however there is no distinction between line

shapes corresponding to 45s – 180s exposure times. In general, ≤ 1.0% O is detected on the surface

of each of the three control samples. This low quantity is expected for untreated films and could

be an artifact of processing while exposed to atmosphere. Although low in quantity, the signal is

strong enough for the as-spun control sample to be fit with two separate synthetic components. A

lower binding energy component centered at 532.2eV is attributed to O-C species where a weak

adjacent peak at 535.0±0.2eV is attributed to O-CF. After plasma treatment the band in the O1s

spectra at 535.0±0.2 eV due to O-CF species is considerably increased [165]. Although there is

growth in O-C, its increase is small in comparison to O-CF, a phenomenon that may be driven by

the plasma composition. Again, the post-anneal sample set produces a plasma treated O1s line

shape that is between untreated and plasma treated samples in the as-spun set. In this set, the O-C

signal remains relatively unaltered, however a decrease in the O-CF relative to other 180s treated

condition is noted. Lastly, a small but significant percentage of N is detected seen in Table 4-I.

This element is only present in films that have been exposed to plasma treatment.

4.3.3 ToF-SIMS Depth Profiling

An untreated copolymer film was first analyzed to obtain a baseline profile representative

of unmodified material. Measurable CFO+ and CO+ ion signals were detected in the untreated

samples (data not shown). Although these ions would not be expected in the spectra of pristine

P(VDF-TrFE), the XPS data indicate the presence of small amounts of O within the first 10 nm of

the untreated films.

85

Figure 4-2: ToF-SIMS depth profiles for CFO+ and CO+ ions in a plasma-treated film. This plot was generated by

taking the ratio of the corresponding profiles of the treated film to those of the untreated control film (plasma treated

signal/untreated signal).

Figure 4-2 shows that after plasma treatment, the intensities of the CFO+ and CO+ peaks

increase by 1 to 2 orders of magnitude near the surface of the film. The SIMS and XPS data thus

both indicate the presence of increased oxygen concentrations in the near-surface region of the

plasma-treated samples. As sputtered material emanated from deeper within a sample, the signal

for both oxygen-containing ions decays rapidly. At a depth of roughly 3 nm, the profiles flatten

out around about a value of 1 indicating the plasma treated sample is giving off an identical signal

to the untreated control film. Although determining a plasma-treated layer thickness with high

accuracy is not possible due to limitations in the depth resolution of the technique, it can be

concluded that the plasma modified layer thickness is less than 5nm, demonstrating the plasma

treatment processing procedure only modifies dielectric/electrode contact properties. This

information will be referred to later in section 4.3.6.2 when modeling is used to quantify the effect

of plasma treatment on charge injection.

4.3.4 Surface Roughness and Contact Angle Analysis

The root mean squared height (Sq) is plotted as a function of plasma exposure time in

Figure 4-3a. The as-spun untreated control sample was measured to have a surface roughness of

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Figure 4-3: a) Copolymer surface roughness (Sq) as a function of plasma exposure time for the as-spun control and

post-anneal sample sets. Data is averaged from 8 separate 87μm x 87 μm scans per sample. b) Images of film surface

topology for each treatment condition taken by optical profilometry. Each image corresponds to the average Sq in a.

8.8 nm which is within the standard error of the control sample for the post-annealed sample set.

Plasma treated films between 45s and 180s in the as-spun sample were not able to be accurately

measured using the optical profilometer, presumably due to significant surface damage during the

plasma treatment process. This could be due to the processing of the as-spun sample set: films

were not annealed for an extended period of time after processing leaving them less structurally

robust than films in the post-anneal set. For this reason, the untreated control is used as a baseline

to compare films from the post-anneal set that did undergo annealing prior to measurement. Post-

anneal samples exhibit minor variation in surface roughness as a function of plasma treatment

time. The maximum value of surface roughness is 11.9nm occurring at 135s, which is the only

measured roughness that displays a statistically significant increase in comparison to the untreated

control. It is believed that application of thermal annealing after plasma treatment serves to repair

a significant portion of surface damage caused by exposure to plasma that is reflected by the near

identical surface topology of the post-anneal samples to the untreated control. A potential

mechanism for this phenomenon could be due to the close proximity of Ta to Tm of the material

resulting in polymer chain ordering which increases crystallinity. This motion acts to restore

surface topology to a similar state as that of the undamaged control sample. In this scenario, the

annealing procedure can be viewed as a method to restore the surface topology of the film, similar

to what has been accomplished in other systems such as PLLA [166]. The similarity in surface

87

Figure 4-4: a) Contact angle measured as a function of treatment time as-spin and post-anneal conditions. b) Images

of H2O sessile drops at first impact on copolymer surface for each treatment time.

roughness can also be observed in 2D topographical micrographs of the untreated control in

comparison to the post-anneal samples in Figure 4-3b.

It is suggested by the nature the chemical species involved in the plasma treatment that a

grafting process dependent on plasma composition alters the surface chemistry of the films [110].

Figure 4-4a shows the contact angle for untreated and plasma treated samples. The as-spun sample

set shows a near identical value in contact angle after 45s exposure in comparison to the control

sample, followed by a sharp increase at 90s. The contact angle then gradually increases as a

function of plasma exposure time to a value of 103o after 180s exposure. The post-anneal sample

set shows different behavior, starting with a sharp increase from the untreated 84o to 109o for the

45s treatment and then gradually increasing to a value of 111o for the 180s treated sample. These

trends are prominent considering visible changes in the sessile drop images in Figure 4-4b,

88

showing the evolution of the contact angle as a function of plasma exposure time for both sample

sets.

The contact angle can be affected by many parameters including surface chemistry, texture,

and probe liquid used [105]. Given the chemical homogeneity for all treatment times measured in

XPS, as well as plasma’s damage to the surface of as-spun films, the data suggest that both sample

surface topology and chemistry influence contact angle. The nearly unchanged contact angle

measured for the 45s treatment time (Figure 4-4a) in the as-spun set is likely due to a combination

of surface damage and chemical modification caused by plasma exposure. This observation is

similar to reductions in contact angle observed in sessile drop experiments performed on

sandblasted surfaces of PMMA using diiodomethane and glycerol [106]. The steady increase in

the contact angle beyond 45s exposure times could indicate the chemical environment gradually

dominating the damaged surface, which implies surface damage could decrease for longer etch

times. The 180s treatment time in the post-anneal set exhibits the highest contact angle, as well as

a surface roughness similar to the untreated sample. With nearly identical film topology to the

untreated control sample, surface chemistry can dominate the contact angle. With surface

chemistry determining the outcome of the measurement and the highly polar nature of H2O,

increase in contact angle indicates decreased surface polarity afforded by the grafting of the

aforementioned chemical species via plasma treatment in section 4.3.2.

4.3.5 Low Field Electrical Measurements.

Electrical testing concentrated on the post-annealed P(VDF-TrFE) which demonstrated the

largest change in contact angle in comparison to the pre-anneal and as-spun sets. Similarly, the

uniform surface topology allows the discussion to focus mainly on how chemical modification at

the electrode/dielectric interface impacts electrical performance without contributions from

damaged film surface topology.

4.3.5.1 Dielectric Spectroscopy

Dielectric spectroscopy was performed over the frequency range of 100 Hz – 0.1 MHz in

order to analyze dipolar contributions to the permittivity. Typically, the permittivity of PVDF

based materials shows gradual reduction between 100Hz and 100kHz at room temperature[227].

This decrease in permittivity is due to the ferroelectric nature of the material arising from polar

89

Figure 4-5: Dielectric response under 1V rms AC electrical signal for the post-anneal processing condition. Untreated,

45s, and 180s treated samples were tested.

crystalline domains distributed throughout the material that exhibit a broad distribution of

relaxation times at room temperature [167]. As frequency increases, the permittivity decreases and

loss tangent increases (Figure 4-5) marking the onset of the dipolar relaxation regime where the

response from permanent dipoles distributed throughout the material no longer contribute to

measured displacement current.

Examination of the permittivity as a function of frequency indicates similar behavior in

dielectric data reported for plasma treated PVDF within the range of 100Hz – 10kHz: CF4/O2

plasma treatment resulting in slightly decreased permittivity [17]. Although the trend is similar,

the decrease in the permittivity is not statistically significant in the 45s treated sample determined

by considerable overlap of measurement standard error bars in the sample set. There is however a

slightly larger reduction in the permittivity observed for the 180s treated sample relative to the

control that is calculated to be lower by 7.3% at 1kHz. This reduction is analyzed by considering

the +/- 80nm standard deviation in 1 μm film thickness measured via stylus profilometry in section

2.2. The 80nm fluctuation indicates an 8% error in the thickness of the film which is larger than

the decrease in permittivity calculated for the 180s sample. Since relative permittivity εr scales

linearly with sample thickness t via the relation εr=Ct/Aεo, it is not appropriate to conclude that

the decrease in permittivity observed is significant. This indicates that the plasma treated layer is

not thick enough to impact bulk permittivity properties of the treated films. It should be noted that

90

this result is in good accordance considering the plasma processing technique, where plasma

treatments typically achieve very shallow depths on the order of 10’s of nm [151].

4.3.5.2 Ohmic Current – Voltage (I-V) Experiments

In Figure 4-6, linear fitting for low voltage I-V experiments was done using a built in

Microsoft Excel linear regression function. The fitting was forced to intercept the point that I=V=0

to better represent a 0 current situation given by Ohm’s Law when the applied voltage is 0. The R2

value for each fit is used to verify that the data accurately represents the sample’s ohmic behavior.

All linear fits yielded a R2 ≥ 0.97, indicating a good fit within the voltage range of 0-3V. A decrease

in material resistivity is calculated for plasma treated samples. The resistivity of P(VDF-TrFE)

70/30 has been cited at 1x1012 Ω-m for solvent cast films 200μm thick molded by a hot pressing

procedure [98]. Although we use a different processing, our result for annealed thin films falls

close in resistivity at 8x1011 Ω-m. The lowering of resistivity in plasma treated films is believed

to result from changed contact properties between the metal and dielectric surface. This result is

consistent with past research that focused on the interplay between conduction and electrode

contact in PVDF Terpolymer (PVDF-TrFE-CTFE) films, indicate that conduction depends on both

electrode metal reactivity with the surface of the material and also interfacial barrier height [11].

Although Chen, et al. performed exclusively high field measurements, there is still a contact

Figure 4-6: Low field I(V) measurements for the post anneal sample set. The untreated control, 45s treated, and 180s

treatment times are shown.

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limiting effect in low field I-V present in our systems. In treated films, a lowering of

metal/insulator contact resistance could result from a change in polymer surface chemistry prior

to electrode deposition increasing conduction even at low fields.

4.3.6 High Field Current Density – Electric Field (J-E) Measurements

4.3.6.1 Conduction Mechanism Identification: Schottky and Poole-Frenkel Modeling

I(V) data at high voltages is converted to current density as a function of electric field (J(E))

and plotted in Figure 4-7. Measurements display a similar trend to low field measurements that

indicate increased conduction in plasma-modified samples. Typically, the addition of polar

chemical moieties after plasma treatment to non-polar polymers result in lower conduction. This

is observed in polyimide (PI) films measured at high temperature after surface modification via O2

plasma treatment [152]. In this system, XPS and water contact angle experiments confirm the

surface of PI is chemically modified after plasma treatment. It is believed that this evolved

chemical environment at the surface of the film controls contact resistance between electrode and

material and enhances charge trapping and scattering effects at high fields and temperatures.

Another similar study examined the effect of non-reactive Ar plasma treatment on poly-p-xylylene

(PPX) films [168]. In this study, argon plasma was generated in a plasma reactor during the

polymerization process of PPX films and was expected to introduce chemical and physical defects

to the film. Current density was then measured as both a function of field ranging from 1 to 7

MV/m, and temperature ascending from -170 oC to room temperature at a rate of 6 oC/min. Results

indicated a two orders of magnitude reduction in the current density for all measured temperatures

in the plasma treated PPX relative to untreated, as well as increase in breakdown strength form 7

MV/m to 10 MV/m. Similar to Meddeb, et. al [152], suppression in the current density and increase

in the breakdown strength for plasma treated PPX is attributed to introduced defects acting as

scattering centers or localized charge trap sites. This conclusion coincides with literature that

suggests high

field performance will improve with increased quantity of dipolar groups within the material to

serve as electron scattering centers, as well as by adding polar moieties such as C-F groups in

plasma polymerized PPE, PPEF and PPET [169] [170].

92

Figure 4-7: High field J(E) measurements for the post-anneal processing condition. Again, the untreated control, 45s

and 180s treatment times are shown.

Clearly, P(VDF-TrFE) supports the trends reported in the literature, exhibiting a direct

correlation between high field conduction and surface environment altered by plasma treatment.

Due to the proximity of the treated layer to the metal electrode in contact with the film during

measurement, changes in high field conduction are likely related to Schottky emission, i.e., field

assisted thermionic emission from electrode contact into the dielectric under high electric fields

[113]. The functional form of the current density as a function of electric field is expressed in

equation (4-1):

𝐽 = 𝐴∗𝑇2𝑒𝛽𝑆𝐸

12

𝑘𝑏𝑇 𝑒−𝜙𝐵𝑘𝑇 (4 − 1)

where J is the current density, E is the electric field, T is absolute temperature in kelvin, ϕB is the

Schottky barrier height of the electrode/material contact at E=0, and A* is the Richardson constant

for the material under test. The βS parameter represents field-assisted barrier height lowering and

is expanded as such:

𝛽𝑆 = (𝑞3

4𝜋𝜖𝑜𝜖𝑟)

12

(4 − 2)

q being the value of elementary charge, and εoεr are vacuum and relative permittivity respectively.

Equations (4-1) and (4-2) indicate that current is dependent on the polarity of the material linked

by the relative permittivity εr.

93

Both Schottky and Poole-Frenkle (PF) conduction mechanisms must be considered in

plasma treated P(VDF-TrFE). Past research has applied PF theory to describe high field

conduction through bulk polytetrafluoroethylene (PTFE) under the assumption that its

polycrystalline and amorphous structure and high density of impurity centers lends itself to bulk-

limited PF conduction [171]. In this case, current emission as function of electric field is expressed

in the following manner:

𝐽 ∝ 𝐸𝑒𝛽𝑃𝐹𝐸

12

𝑘𝑏𝑇 𝑒−𝜙𝑃𝐹𝑘𝑇 (4 − 3).

The primary difference between Schottky and PF emission functional forms are ϕPF that now

describes the trap-state barrier height at E=0 and βPF that pertains to field-assisted trap-state barrier

height lowering. The functional form for βPF is the following:

𝛽𝑃𝐹 = (𝑞3

𝜋𝜖𝑜𝜖𝑟)

12

(4 − 4)

and differs by βs by a factor of 2. Typically high field data for Schottky and PF emission is handled

by plotting Ln(J) vs. E1/2 and Ln(J/E) vs. E1/2 respectively, and is plotted using the J(E) data

presented in Figure 4-7 for E > 60MV/m in Figure 4-8. A linear fit using Microsoft Excels linear

regression function is applied for each curve in Figure 4-8 with its associated equation shown. In

this format, the slope m of the data is equal to the quantity βs,PF/kbT. Given the expressions for βs

and βPF in equations 4-2 and 4-4, a value of relative permittivity for the films can be back

calculated from linear fit slopes found in the Schottky and PF plots via the two mathematical

relationships:

𝜖𝑟,𝑃𝐹 = [(𝑚𝑘𝑏𝑇)2𝜋𝜖𝑜

𝑞3]

−1

(4 − 5)

𝜖𝑟,𝑆 = [(𝑚𝑘𝑏𝑇)24𝜋𝜖𝑜

𝑞3]

−1

(4 − 6)

where m is the slope of the data obtained from linear fits to the data in Figure 4-8. Using equation

(4-5), permittivity from the PF plot for untreated films yield εr=124 and for plasma treated films,

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Figure 4-8: Both Schottky and Poole-Frenkel plots for untreated and plasma treated P(VDF-TrFE) J(E) data are

displayed. The linear fit equation used to calculate permittivity from equations (4-5) and (4-6) for each set of data are

labeled and displayed next to the corresponding curve.

εr=171, both of which are an order of magnitude beyond the measured material permittivity for

P(VDF-TrFE) (Figure 4-5). Calculation of the material permittivity from the Schottky plot using

equation (4-6) yields εr=9.4 and εr=11.2 for untreated and plasma treated films respectively. This

is in very good agreement with the values of permittivity measured in Figure 4-5, supporting that

high field conduction is due to a Schottky type emission mechanism and not bulk limited under

high electric fields.

4.3.6.2 Quantifying the Change in Barrier Height

It is thought that the increase in the high field current density after plasma treatment is the

result of field emission across the metal/insulator boundary due to surface states created at the

plasma modified interface. The influence of surface states on high field conduction have been

documented for a number of systems including polymers (PI by Meddeb et al. [152]) and also

inorganic semiconducting materials such as Indium Phosphide (InP) and Zinc Oxide (ZnO) [172]

[173]. In the case of InP, the presence of surface states and defects at the interface between metal

and semiconductor limits the achievable barrier height due surface Fermi level pinning [174].

Similarly in the case of ZnO, a 20% O/80% He based plasma surface treatment showed both

evolved surface chemistry and a change in the contact properties between ZnO and Au electrodes

[172].

95

In the case of P(VDF-TrFE), a similar process is considered where increased high field

conduction is posited to be induced by decreased Schottky barrier height relating to grafted

chemical species at the electrode interface. Since the charge conduction mechanism in P(VDF-

TrFE) thin films fits well to Schottky injection theory, the Schottky equation is parametrically

explored to determine the most influential parameter in current density generation. The results of

a parametric study are shown in Figure 4-9 where the effect of each variable on the conduction

current was analytically determined. In this study, values for A* ranged two orders of magnitude:

from an upper value of 1.2x106 A(m-1K-2) calculated from its theoretical form of A*=4πqemekb2/h3

down to a lower value of 1.2x104 A(m-1K-2) [173]. The relatively small change in current density

is expected considering A* is a pre-exponential factor and is shown in Figure 4-9a.

The εr ranged from 2-20, where a permittivity of 2 reflects a non-polar material such as

polytetrafluoroethylene and 20 approaches values reported for terpolymer P(VDF-TrFE-CTFE)

[175]. In this analysis, current density has a larger dependence with the permittivity than the

Richardson constant; however, a large change in material permittivity would be required to

significantly alter high field emission. In the case of low values of εr and high fields, permittivity

must double from 2 to 4 to cause a change in current density by an order of magnitude. Similarly,

as the permittivity becomes large, as is the case for PVDF, the value of the exponential term,

(βSE1/2/kbT), from equation (4-1) becomes less sensitive to small changes in permittivity because

εr is in the denominator of the exponent. Here, doubling the εr from 10 to 20 increases current

density by less than an order of magnitude from 5x10-3 – 1.3x10-3 A/m2 which are values taken

from Fig 4-9b. The Schottky barrier height at E=0, ϕs. ranges from 0.55eV – 1.45eV and results in

16 orders of magnitude change in the current density with all other parameters from equation (4-

1) held constant. This result is reflective of the direct relationship between barrier height and

current density, where J α EXP(-ϕs), and indicates that the Schottky barrier height has the greatest

impact on the injected current under high electric fields.

The change in permittivity calculated from Schottky fitting using equation (4-6) in section

4.3.6.1 is now considered. Calculated permittivities from equation (4-6) for untreated and plasma

treated films yield εr=9.4 and εr=11.2 respectively, resulting in less than a factor of 2 decrease in

calculated current density. It is also noted that the permittivity calculated directly from capacitance

and loss measurements of the material shows no statistically significant change due to plasma

treatment by Figure 4-5 in section 4.3.5.2, indicating that permittivity is not an dominating factor

96

Figure 4-9: Parametric study of current generation during a Schottky emission process. Graph a, b, and c demonstrate

the impact of ranging A*, εr, and ϕS, respectively. Variables held constant and their respective values are shown above

each plot, while the upper and lower limits of the parameter ranged is indicated within the plot.

in controlling conduction. This suggests that a change in barrier height controls the increase in

conduction in plasma treated films.

The geometry of the applied surface coating is used to enable the calculation of

barrier height change in treated films relative to the untreated control. ToF-SIMS experiments

(section 4.3.3) indicate the plasma treatment process has little to no impact on chemical structure

of the material beyond the first 5 nm of the sample surface, thus behaving as a surface coating

only. This allows A* to be treated as a constant term which is similar to work done by Reddy [173]

where A* for n-type Indium Phosphide (n-InP) is used to calculate change in barrier height in films

both with and without a 30nm thick surface coating of PVDF. The change in material properties

for plasma treated samples relative to untreated films are isolated by way of a curve subtraction

procedure, where the linear fits in Figure 4-8 for the Schottky plot are subtracted as follows:

𝑙𝑛(𝐽1) − 𝑙𝑛(𝐽2) = [𝛽𝑆1

𝑘𝑏𝑇𝐸

12 −

𝜑𝑆1

𝑘𝑏𝑇+ 𝑙𝑛(𝐴∗𝑇2)] − [

𝛽𝑆2

𝑘𝑏𝑇𝐸

12 −

𝜑𝑆2

𝑘𝑏𝑇+ 𝑙𝑛(𝐴∗𝑇2)] (4 − 7)

where the subscripts 1 and 2 represent plasma treated and untreated curves in Figure 4-8

respectively. In this format, both Ln(A*T2) terms cancel in equation (4-5) due to constant

measurement temperature and A* between the samples, leaving the following expression:

𝑙𝑛(𝐽1) − 𝑙𝑛(𝐽2) =1

𝑘𝑏𝑇[(𝛽𝑆1 − 𝛽𝑆2)𝐸

12 + (𝜑𝑆2 − 𝜑𝑆1)] (4 − 8)

and at E=0, the change Schottky barrier height φs is solved in terms of change in ln(J):

∆𝜑𝑠 = 𝑘𝑏𝑇[∆𝑙𝑛(𝐽)]𝐸=0 (4 − 9)

Change in the Schottky barrier height can be simply computed by multiplying the curve’s change

in Ln(J)E=0 intercept by kbT. Using equation (4-9), a barrier height lowering of 0.05eV is

calculated. This reduction in barrier height is in good agreement with an order of magnitude

97

increase in current density computed using equation (4-1) from the parametric study when A* and

εr are held constant.

Due to similarity in the surface topology of the post-annealed plasma treated film tested

and the untreated control sample, the calculated change in barrier height is attributed

predominantly to surface chemical modification by plasma treatment. In this scenario, grafted

foreign chemical groups to the surface of the film behave like defects, decreasing the barrier height

from its natural level. Another cause for lower barrier height and increased emission could relate

to the increased amount of electronegative O and F based chemical moieties detected at the surface

of the film which may behave as acceptor type states. An increase in acceptor states at the surface

would provide a higher density of hole carriers at the plasma modified interface in comparison to

the bulk. This increase in available carrier density could relate to enhanced hole injection under

high fields, correlating well to past research that demonstrates conduction through PVDF based

polymers is dominated by a predominantly hole transport process [11] [176].

4.4 CONCLUSIONS

Plasma treatment with a 50/50 CF4/O2 gas composition was applied to P(VDF-TrFE)

polymer film between 45s and 180s at a constant power of 500W. Synthetic peak fitting of the

XPS C1s spectrum indicated the addition of carbonyl C=O groups on treated films. Fitting of the

O1s spectrum also indicated the uptake of CF-O and C-O moieties. It was determined that the

treatment time duration had no effect on the quantity of chemical species detected by XPS,

however annealing after plasma treatment does affect the ratio of F/C detected.

The water contact angle showed a statistically significant change as a function of treatment

time for as-spun and post-anneal samples. The near constant contact angle for various plasma

treatment durations in the post-anneal set reflects both constant surface chemistry detected in XPS

after treatment as well as uniform surface roughness measured via profilometry. Constant surface

topology allows the impact of introduced chemical species to dominate, revealing that of the

grafted chemical species after plasma treatment cause surface polarity to decrease.

Low field dielectric spectroscopy was used to further investigate the effect of grafted

chemical species on the polarity of the films. Data indicates that there is no statistically significant

relationship between exposure time to CF4/O2 plasma and change in the material’s dielectric

constant. This indicates that plasma treatment only impacts P(VDF-TrFE) material structure local

98

to the surface of the film, leaving the bulk of the films unaltered. Plasma treatment duration was

linked to low and high field I-V measurements where leakage current increased as a function of

plasma treatment time. Lowered contact resistance of the electrode/dielectric interface is thought

to influence conduction through the films at low fields. Enhanced high field current generated in

plasma treated films is found to be describable by Schottky theory. Mathematical analysis

implementing approximations acquired by a parametric study of the Schottky equation as well as

work done by Reddy [173] linked increased conduction to a lowered Schottky barrier height by

0.05 eV after plasma treatment. Finally, two potential scenarios linking enhanced conduction to

processing and surface chemistry are proposed: 1) grafted chemical constituents behave as defects

that lower Schottky barrier height and 2) increased F and O moieties behaving as acceptor type

states that increase hole carrier density at the electrode contact, linking enhanced conduction to

hole transport across the metal dielectric interface.

The effect of plasma surface treatment on high field conduction emphasizes the importance

of interface chemistry between metal electrode and dielectric in thin P(VDF-TrFE) films. Although

application of CF4/O2 plasma results in degraded high field performance of the material, the plasma

processing technique shows the potential to significantly impact leakage current under large

electrical loading. This study demonstrates the viability of surface chemical modification

techniques to change conduction properties in P(VDF-TrFE) and should be explored further to

develop new ways of limiting current leakage in materials for high field applications.

In the next chapter, the effect of plasma treatment is studied on a non-polar polymer

currently being considered for high voltage and high temperature applications: polyimide.

Techniques used for high field data analysis are expanded upon to incorporate curve fitting

procedures that can account for hopping theoretical analysis in which linearization is not possible.

4.5 ACKNOWLEDGEMENTS

The Authors of this publication would like to acknowledge the support of the National

Science Foundation as part of the Center for Dielectrics and Piezoelectrics under grant Nos. IIP-

1361571 and IIP-1361503.

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CHAPTER 5

CONDUCTION THROUGH PLASMA-TREATED POLYIMIDE: ANALYSIS OF HIGH-

FIELD CONDUCTION BY HOPPING AND SCHOTTKY THEORY6

ABSTRACT

In this chapter, analysis on high field current density vs electric field (J(E)) on plasma

treated P(VDF-TrFE) is expanded upon to describe conduction through plasma treated Polyimide

(PI) as a function of electric field and temperature. Unlike copolymer, PI has a non-polar material

structure as well as excellent thermal stability to temperatures upwards of 400oC. These

characteristics cause the material to exhibit a different high field conduction dependence on plasma

treatment than that of P(VDF-TrFE), requiring the use of bulk dominated conduction theories to

accurately describe its behavior. Hopping theory is now considered by using nonlinear regression

techniques because of its non-linearizable mathematical form. Chapter 5 is broken into the

following sections:

Introduction – presents the scope in which PI is considered as a dielectric for high power

applications as well as introducing work by Meddeb et al. [13] which is the parent study in

which data in this chapter originates.

Analytical Methods – past work concerning PI conduction is reviewed, as well as the basics

of theory implemented in high field conduction analysis of PI in this chapter. A more

detailed description of theory can be found in Chapter 2 section 2.3.3.2.

Results and Analysis – high field J(E) data from Meddeb et al. [13]

https://doi.org/10.1016/j.cplett.2016.02.037) are analyzed using PF, Hopping and Shottky

theory and the results discussed.

Discussion and Conclusions – results from theoretical analysis are discussed in context of

plasma treatment as a tool to tailor dielectric surface properties.

6 This chapter is based off of published work by Vecchio et al. in the Journal of Materials Science. Data analyzed via Hopping, PF, and Shottky

theories is acquired from Meddeb et al. [13]

100

The results of analysis not only inform on plasma treatment’s impact on electrical properties of PI,

but also provide more rigorous analytical techniques to quantify material properties associated

with conduction using hopping theory.

5.1 INTRODUCTION

There exists a need to develop next generation materials for power electronic applications

with lighter weights and smaller volumes, yet capable of operating with high efficiency at high

temperatures. Organic dielectric materials are one option, due to their ease of manufacturability,

light weight and favorable electrical properties such as high breakdown strength. Currently,

biaxially oriented polypropylene (BOPP) is considered the state-of-the art in capacitor films,

exhibiting a breakdown strength on the order of 850 MV/m [65] and theoretical power densities

calculated to be in the range of 108 W/cm3 [177]. Other materials relevant to high voltage dielectric

applications are polar polymers such as polyvinylidene fluoride (PVDF) along with its associated

copolymer poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) and terpolymer

poly(vinylidene fluoride-trifluoroethylene-chlorotrifluoroethylene) (P(VDF-TrFE-CTFE)).

Recent research done on blended PVDF/ P(VDF-TrFE-CTFE) composites show impressive

breakdown strengths (640MV/m) and energy densities measured as high as ~20 J/cm3 [9] [83].

Routes to improve the high field performance of pure organic dielectrics that depend on more

involved processing procedures have also been studied. Past research done on organic dielectrics

fabricated by the coextrusion of P(VDF-HFP) and polycarbonate (PC) demonstrate the ability for

the composite material to achieve a breakdown strength that exceeds that of either constituent

material [14].

Although these materials show promise to develop the class of next generation power and

energy dense organic electronics, their low melting temperatures near 160oC limits their ability to

withstand energy dissipation attributed to high dielectric loss and leakage currents. This can be

conceptualized by a device’s performance represented by a Ragone plot: in the case of power

electronics the boundaries of capacitor performance are represented by power vs. energy density

and are determined by the material’s internal losses and/or leakage [8]. In the case of PVDF, its

polar nature causes the material to be inherently susceptible to high dielectric loss [149] exhibiting

loss tangents that reach as high as ~0.5-1.0% [71].7 As a result, PVDF experiences high leakage

7 See Chapter 4, sections 4.3.5.2 and 4.3.6 for conduction characteristics at low and high field of P(VDF-TrFE).

101

currents at DC frequencies even at low temperatures, within the range of 10-3 – 10-2 A/m2 at fields

exceeding 20 MV m-1 depending on material geometry and processing technique [71] [122]. In the

case of non-polar BOPP, dielectric absorption is very low, exhibiting dielectric loss tangents as

low as 10-4 at low fields [178]. However, the application of high electric fields required for high

power and energy applications causes energy dissipation in the form of leakage current. This leads

to joule heating, a precursor to dielectric breakdown [179] [180], causing temperature elevation of

the material regardless of ambient operating conditions, and bringing the material closer to its

relatively low derating temperature of 80oC [149].

Another influence which limits the applicability of these materials is ambient operating

temperatures for applications that require thermal stability within the range of PVDF’s and BOPP’s

melting temperatures. For example, passive electronics fabricated for automotive applications

must retain continuous structural and electrical stability within 150oC – 200oC, measured on-

engine and in-transmission during vehicle operation [181] [182]. This creates a demand for

volumetrically efficient capacitors that can maintain high voltage/temperature stability

manufactured at low costs. Unlike BOPP, PC, and PVDF blends and composites, polyimide (PI)

exhibits a combination of large breakdown strength measured at 615 MV m-1 [13] and high glass

transition temperatures reported in the range of 370oC – 470oC depending on chemical structure

and processing [67] [183]. Low dielectric dissipation factor in the range of 10-3 (provided by

DupontTM Kapton® HN material data sheet as well as literature [184]) and a potential of high

energy and power density add to its appeal as a next generation high field dielectric material.

Despite these favorable properties of PI, high temperature environments combined with charge

injection at the electrode/dielectric interface put the material at risk for joule heating and high

leakage currents during operation. Implementation of processing procedures that can limit the

leakage current through PI at high temperatures are required to achieve its full potential as a high

temperature dielectric polymer.

Reactive plasma treatments of polymers have been shown to have a significant impact on

material chemistry [13] [153] [154], and properties such as wettability [34] [155] and adhesion

[35] [156] [157] [158]. In addition, plasma treatment has been demonstrated to influence electrical

properties. In previous work by Mammone et al. [159], plasma treatment processing using 96%

CF4/ 4% O2 on polypropylene resin prior to melt extrusion was shown to increase the dielectric

breakdown strength of the material by 20%. Similar work done that uses 96% CF4/ 4% O2 plasma

102

treatment on the surface of 12-micron PVDF films led to 11% increase in dielectric breakdown

strength relative to untreated control samples [17]. Recently, research done in our group by

Meddeb, et al. [13] showed that plasma surface treatment using pure O2 on PI resulted in reduced

spread in dielectric data, improved Weibull modulus at low temperatures and improved breakdown

strength at elevated temperatures. Among these observations, an order of magnitude reduction in

leakage current at 150oC was also noted. This study provided a thorough chemical analysis using

XPS and H2O sessile drop experiments to characterize the surface of the films after plasma

treatment and surmised that the inclusion of O containing species at the surface of the film resulted

in charge trapping and scattering effects at the electrode / dielectric interface at high temperatures.

Meddeb et al. [13] also posited that the mechanism dominating conduction through the material

could potentially be changed and controlled using surface chemical modification. To this date and

to the best of our knowledge, this hypothesis remains untested. In the present work, the current

density vs electric field [J(E)] behavior of PI films measured in Meddeb et al. [13] (DOI:

10.1016/j.cplett.2016.02.037) is analyzed using a series of theoretical frameworks that describe

conduction through insulators and semiconductors to investigate the effect that O2 plasma surface

treatment has on high field conduction in polyimides over a broad temperature range. This study

will leverage further research that focuses on the role of dielectric/electrode interface in controlling

conduction in PI and other organic dielectrics.

5.2 ANALYTICAL METHODS8

Past research on PI has demonstrated the material’s propensity to conduct via various

charge transport mechanisms. Work by Diaham et al. [24] investigated conduction characteristics

of thin (1.4 μm) PI films under high electric fields (in the range of 100MV/m) and high

temperatures (320 – 400oC). In Diaham’s work [24], analysis of pre-breakdown currents as a

function of field and temperature suggests conduction at very high temperatures and fields

preceding dielectric breakdown is a space charge dominated process. This result coincides well

with results obtained by Kishi, et al. [185] where pulsed electroacoustic measurements

demonstrate hetero space charge formation increase as a function of field intensity and temperature

prior to breakdown. Both of these studies involve either application of very high electric fields for

8 This section provides a general framework for Hopping, PF, and Schottky theory used in this section, however a detailed explanation high field

conduction theory can be found in Chapter 2 section 2.3.3.2.

103

long times (Kishi ~260 MV/m at t>10min [185]) or sample exposure to extremely high temperature

(Diaham T=400oC [24]) to stress the material in the range of pre-dielectric breakdown. Space

charge measurements under less extreme conditions by laser intensity modulation method in 10

μm PI films for long time scales (t~30 min) and moderate fields ranging 0.5 – 2 MV/m show

charge accumulation within the samples dependent on electronic charge injection at the anode and

cathode [186]. Given these results, the analysis in this manuscript will be carried out using a

combination of theoretical frameworks that describe both bulk dominated and interface dominated

processes which are reviewed in the following section.

5.2.1 Bulk Dominated Conduction

Conduction through polymer dielectrics are typically analyzed using one of two theoretical

frameworks: Poole-Frenkel (PF) or Hopping [187]. The PF model for conduction describes field-

enhanced thermal de-trapping of electrons or holes from impurity centers distributed through the

bulk of the material [113]. In the case of PI and other organics such as polytetrafluoroethylene

(PTFE), this framework is typically considered because of the high density of impurity centers

located within the bulk of the film arising from its partly amorphous structure [19]. The PF

transport current is defined by equation (5-1):

𝐽𝑃𝐹 = σ𝑜𝐸𝑒𝑥𝑝 (𝛽𝑃𝐹𝐸

12

𝑘𝑏𝑇)exp (−

𝜙𝑃𝐹

𝑘𝑏𝑇) (5 − 1)

where JPF is the current density, σo is a constant related to charge, carrier density, and carrier

mobility, E is the electric field, kb is Boltzmann’s constant, T is temperature, ϕPF is the trap barrier

height at zero field, and βPF is a constant. In equation (5-1), βPF = (q3/πεoεr)1/2 where q is the

elementary charge and is related to field assisted barrier height lowering in the material and εr is

the material’s dielectric constant.

Hopping conduction theory is similar to PF theory in that it describes a conduction process

occurring through the material’s bulk. In hopping, the charge carrier undergoes a diffusion based

carrier hopping process [187] [113] [188]. The mathematical framework that governs this process

is presented in equation (5-2):

𝐽𝐻 = 𝐽𝑜𝑒𝑥𝑝 (−𝜙𝐻

𝑘𝑏𝑇) sinh [

𝑞𝑑𝐸

2𝑘𝑏𝑇] (5 − 2).

104

In equation (5-2), Jo is a constant of the form nfdq with n defined as a carrier density, f carrier

vibration frequency, d the distance between trap sites termed the “hop distance”, and q the

elementary charge. The term ϕH is typically referred to as an activation energy or barrier height for

the hopping conduction process [113] [118].

5.2.2 Interface Dominated Conduction

In this work we also consider the possibility of Schottky type emission. Schottky theory

assumes that conduction is dominated by charge emission through the dielectric / electrode

interface. This framework is considered in the analysis of plasma treated PI for two reasons: 1)

the fact that plasma treatment is a surface modification process, and 2) the treatment’s influence

on conduction that has been observed at high temperatures [13]. The mathematical framework

for Schottky emission is very similar to PF type conduction and is presented in equation (5-3)

below.

𝐽 = 𝐴∗𝑇2𝑒𝑥𝑝(𝛽𝑆𝐸

12

𝑘𝑏𝑇)exp (−

𝜙𝑆

𝑘𝑏𝑇) (5 − 3)

Equation (5-3) differs from (5-1) by the three main parameters A*, ϕS and βS. The constant A* is

the Richardson constant and has the form 4πqmek2/h3, with me being the mass of an electron and h

is Plank’s constant. ϕS is the Schottky barrier height defined by the difference between metal

contact work function and electron affinity of the test material, and βS is a constant related to field

assisted barrier height lowering. In Schottky, βS = (q3/4πεoεr)1/2 and is slightly different than that

of PF emission because it takes into account the image force potential associated with charge

leaving the electrode during injection.

5.3 RESULTS AND ANALYSIS

5.3.1 Leakage Current Results

Kapton® PI samples, 13 μm-thick, were obtained from Dupont. The PI and PPIDS sample

sets consists of three untreated and plasma treated samples (respectfully) electroded using 100nm

evaporated silver. During electrode evaporation, each sample set was exposed to high vacuum (10-

6 Pa) for approximately 2 hours. Electrodes were circular and 1 cm in diameter for each sample.

The three samples labeled PPIDS are plasma treated with O2 on both sides of the film prior to

electrodes deposition. The flow rate was held at 200 sccm and the treatment power was 200W that

105

lasted 5 min/side. During plasma treatment, low vacuum was applied, stabilizing between 0.42 –

0.45 Pa. Details concerning specifics about PI surface chemical characterization as well as J(E)

data acquisition are present in the parent study and made available to the dedicated reader in

Meddeb et al. [13] (DOI: 10.1016/j.cplett.2016.02.037).

Current voltage measurements were performed using a Hewlett Packard 4140B pA meter

that served as its own DC source connected to a Trek voltage amplifier model 10/10B-HS. Initial

measurement of the charging current transients in PI was done at the lowest fields of measurement

used in this study (8 MV/m – 23 MV/m) and at room temperature. Figure 5-1 shows charging

current as a function of time. The lowest current measured was 40pA (after a 100s voltage hold

time) with 8 MV/m applied, which is well above the minimum 1pA that can be measured by the

pA meter. Steady state in the measurement begins at 20s indicated by a plateau in charging current.

At higher temperature and fields, plateauing in the current occurs at shorter times, making 20s a

reasonable hold time where a) steady state in the current is achieved and b) the chance for sample

degradation at high fields and high temperatures is minimized.

A significant reduction in leakage current through PI was measured following O2 plasma

surface treatment in our previous study by Meddeb et al. [13] and is shown in Figure 5-2. At low

temperatures the average current density of both the untreated PI and O2 plasma treated PPIDS

data sets are within the same range. As temperature increases to 150oC, the average current density

for PI at 115 MV m-1 is 4.04x10-4 A m-2 which is an order of magnitude larger than the PPIDS

Figure 5-1: Charging current measured for PI as a function of charge time at room temperature.

106

measured to be 4.07x10-5 A m-2. At all temperatures there is less scatter in the data for plasma

treated samples relative to the untreated control set, however this is especially true at high

temperatures and electric fields. Due to the similarities in sample storage and processing

between the PI and PPIDS sample sets, changes in current magnitude and scatter are linked to a

change in surface chemistry after the plasma treatment procedure: increases in hydroxyl as well as

carbonyl and carboxyl groups due to treatment are detailed in Meddeb et al. [13], and have also

been reported by Inagaki et al. [189] to be present in Kapton® films post oxygen plasma treatment.

The impact that plasma treatment has on the magnitude of leakage current through

the film as a function of temperature and field can be seen from the data presented in Figure 5-2,

however the exact mechanisms responsible for this reduction are not yet determined. It is important

to seek out the exact mechanisms by which plasma surface treatment limits conduction so that

similar results can be exploited to decrease leakage currents and improve high field and high

temperature performance of dielectric films. This requires quantitative analysis under a set of

theoretical frameworks that describe high field conduction through dielectrics. The following

sections use the theoretical frameworks that describe bulk dominated and interface dominated

conduction to quantify how plasma surface treatment achieves reduced leakage current and discuss

its impact for future high temperature capacitor development.

5.3.2 Data Analysis

5.3.2.1 Modeling Bulk Conduction

Initially, PF theory is considered. The linearization of equation (5-1) leaves the following

expression for conduction under PF framework:

𝐿𝑛 (𝐽𝑃𝐹

𝐸) =

𝛽𝑃𝐹𝐸1/2

𝑘𝑏𝑇−

𝜙𝑃𝐹

𝑘𝑏𝑇+ 𝐿𝑛(𝜎) (5 − 4)

The slope of linearized data can be directly related to βPF at a single temperature T. Since J(E) data

was recorded isothermally at temperatures ranging between 25 oC – 175 oC, the permittivity of PI

can be extracted directly from the slope of the PF plots using the expression for βPF stated in

section 5.2.1. This procedure is done at each temperature by applying a linear regression fit to the

data plotted in PF plot format (Ln(J/E) vs. E1/2). The slope m of the regression function is then

converted to permittivity using the following equation:

107

Figure 5-2: J(E) data for untreated and O2 plasma surface treated PI at a) 25oC, b) 100oC, and c) 150oC. Applied

voltage is held for 20s (time required to obtain steady state conduction) before current measurement at each field.

108

𝜖𝑟,𝑃𝐹 = [(𝑚𝑘𝑏𝑇)2𝜋𝜖𝑜

𝑞3]

−1

(5 − 5)

Treatment of the data in this manner produces εr,PF values that range between 500 and 20

depending on temperature. Considering that PI’s accepted range in permittivity is between ~2.25

at high frequencies and ~3.15 at 1kHz, it is concluded that PF theory inadequately describes

behavior of the material.9

Past work done on PI by Sawa, et al. [120] and Sacher [121] suggest that room temperature

conduction through the material is a result of proton hopping originating from carboxyl groups in

unreacted polyamic acid (PAA) within the bulk of the material. Hopping conduction is described

using equation (5-2) and is more complex than equations (5-1) and (5-3). This equation cannot

be linearized to calculate fit parameters Jo, ϕH, and d. Instead, fitting is performed using the

statistical software R-Studio where a non-linear regression technique optimizes the parameters Jo

and d to minimize the sum of squares between equation (2) and raw data.

In hopping conduction theory, the value of ϕH is taken as a low field activation energy. In

this study, low field activation energy is estimated using the following Arrhenius type equation for

conduction

𝐼 = 𝐼𝑜𝑒𝑥𝑝 (−𝜙𝐻

𝑘𝑏𝑇) (5-6)

where I is measured current, and I0 is a constant associated with conduction as ϕH approaches 0.

Figure 5-2 demonstrates how surface chemical modification reduces leakage current, potentially

impacting the conduction mechanism at high temperatures and fields. For this reason, the PI set is

used to extract a low field activation energy to exclude effects introduced by plasma treatment.

I(V) data for the PI set are plotted as a function of Ln(I) vs. T-1 and presented in Figure 5-3.

Measurements taken at 100V at each temperature were used for low field currents. The

data is described well using the Arrhenius relation in equation (5-6) and returns an activation

energy of 0.25 eV, which is within range reported in studies where PI was processed by solution

9 More information on PF analysis including treatment of data and calculated values of εr,PF are provided in Appendix C

109

Figure 5-3. Arrhenius plot for Pure P1 over the temperature range 25oC – 150oC. Activation energy is extracted

from linearization of equation (5-6) and the slope of the linear fit function.

casting and vapor deposition under AC and DC field conditions [190] [118]. Similarly, ϕH < 1.0

eV is indicative of electronic based conduction in the film, implying electrons may play a role as

charge carriers during DC conduction in the film [190]. This result can be related back to work

done by Ito, et al. [118], Sawa et al. [120], and Sacher [121] where conduction through PI films

was found to be dependent on proton hopping stemming from carboxyl group presence due to

unreacted PAA. In the current study, PI films are obtained from Dupont and are of high quality.

Although the complete absence of proton conduction from carboxyl entities is not guaranteed, the

quality of the films suggests limited proton conduction resulting from unreacted PAA compared

to PI films studied by Sacher [121]. This analysis coincides well with work done by Tu and Kao

[191], where C-V experiments performed on 100% imidized PI suggest conduction is dominated

by an electron transport process, potentially occurring via hopping along acceptor states both along

the polymer chain’s backbone and between adjacent chains.

A combination of physical arguments as well as statistical analysis was used to assess the

validity of the hopping model to explain the J(E) behavior. Due to the form of the function used to

fit J(E) data, calculation of P values should not be implemented to determine parameter estimate

significance. Non-linear models do not have a well-defined relationship between parameter (in this

case d and Jo) and predictor variables (applied field E) which inhibits the creation of a single

hypothesis test that can represent all nonlinear models. A more appropriate method to determine

parameter significance for our purposes would be computation of a confidence interval for each

110

Figure 5-4 Hopping parameters Jo and d estimated using the bootstrapping statistical approach.

parameter estimate. Unfortunately, the distributions of fit parameters describing the sample sets

are unknown and difficult to extract from measurements given the sample size N = 3 in each sample

set. To estimate a distribution for the parameters, bootstrap statistics are employed where variation

of fit parameters that describe the data set can be estimated by sampling with replacement. This

method yields a confidence interval for Jo and d that reflects variation among the samples

comprising PI and PPIDS sample sets.10

Physical arguments concerning the model’s validity begin by examining the hop distance.

Values of d are first considered to assess how well the hopping model describes sample behavior

and are plotted in Figure 5-4 for both sample sets as a function of temperature. Hop distance

estimated for both sample sets ranges between ~10 Å – 30 Å, which is within the range of hop

distances reported in the literature for PI and also BOPP [118] [179] [192] [193]. At room

temperature, d is estimated to be approximately 12 Å, which is quite close to the length of the

chemical repeat unit of PI (~15 Å measured by x-ray diffraction in Ito et al. [118]) which suggests

hopping conduction propagates in the polymer chain direction through the material. At higher

temperatures the hop distance increases in both sample sets: 25 Å in PI at 75oC and 24 Å at 125oC

in PPIDS. This exceeds the chemical repeat unit for the material and may reflect a transition from

intrachain to interchain charge carrier hopping at higher temperatures.

10 A more detailed outline of the bootstrap statistical approach can be found in Chapter 2 section 2.4.1 along with annotated R-Studio script used

for fitting and bootstrap analysis

111

Jo is also analyzed across the measurement’s temperature range. Using the relation Jo =

nfqd, a nf (product of carrier density and vibration frequency) can be calculated from fit estimates.

The product nf ranges from 1.6x1025 to 4.4x1025 m-3s-1 in PI between 25oC – 75oC, and from

5.6x1024 and 8.0x1025 m-3s-1 in the PPIDS set between 25oC – 125oC. These ranges are compared

to previous work done by Ito, et al. [118] that focus on the effect of curing vapor deposited PI

films. Films undergoing 4 hours of curing returned nf values after fitting on the order of 1x1021 m-

3s-1 while uncured films returned 1x1035 m-3s-1. The films used in this study produce a value of nf

within the range reported by Ito, et al. Small differences can be expected considering the difference

in sample preparation, as well as fitting procedures used: Ito, et al. [118] obtains higher activation

energy of 0.34 eV and uses a series of low and high field approximations on equation (5-2) in

fitting.

Statistical interpretation of the fit results was used to comment on the behavior of the

sample set as a function of temperature. At 25oC there is very little change in the estimated values

of either fit parameters between sample sets. This is an expected outcome considering similarity

in behavior between PI and PPIDS sample sets at low temperature reported in Figure 5-2. It is

also noted that the estimates of d and Jo are centered within their respective confidence intervals

computed by bootstrapping which are presented in Table 5-I for PI. This implies that the estimated

parameters follow a symmetric distribution, which is most likely caused by the samples within the

data sets behaving similarly to one another as a function of electric field. As temperature is

increased to 100oC, a significant separation in the values of Jo and d estimated from PI and PPIDS

sets occurs. Both parameters for the PI set exceed values computed for PPIDS. Greater change can

be noted in the 95% confidence intervals for both fit parameters in PI. At 100oC, the confidence

interval pertaining to d ranges a full order of magnitude. Similarly, the estimated value of d is no

longer centered within the confidence interval, indicating an asymmetric distribution for hop

distance. A similar outcome exists for Jo displaying an asymmetric distribution with confidence

interval ranging 7 orders of magnitude at 100oC, indicating a major variation between the samples

comprising the PI data set. These outcomes of fitting d and Jo at high temperature diminish the

significance of their estimated values, indicating a poor fit to the data. Unlike PI, the PPIDS sample

set does not show a pronounced change in fit parameters within 25oC – 100oC. The confidence

intervals for both fit parameters are also significantly tighter and do not display asymmetry, as

shown in Table 5-II, suggesting that samples within the set behaving quite similarly as a function

112

of field within this temperature range, coinciding nicely with small standard deviations calculated

for PPIDS J(E) data in Figure 5-2.11

Table 5-I: parameter fit values and confidence intervals at each temperature for untreated PI sample set. No values

for Jo or d are provided because of the program’s inability to fit the data using equation (5-2).

Temperature

(oC):

25 75 100 125 150 175

Joestimated

: 6.98x104 7.36 x10-4 2.56 x10-3 --- --- ---

2.5% CI 3.66 x10-4 1.03 x10-5 1.67 x10-9 --- --- ---

97.5% CI 1.16 x10-3 2.23 x10-3 8.25 x10-3 --- --- ---

destimated

: 1.26 x10-9 2.50 x10-9 3.18 x10-9 --- --- ---

2.5% CI 9.52 x10-10 1.38 x10-9 1.03 x10-9 --- --- ---

97.5% CI 1.60 x10-9 4.66 x10-9 1.04 x10-8 --- --- ---

Table 5-II: parameter fit values and confidence intervals at each temperature for the plasma treated PPIDS sample

set

Temperature

(oC):

25 75 100 125 150 175

Joestimated

: 7.36 x10-4 1.53 x10-3 7.12 x10-4 3.94 x10-4 2.34 x10-4 2.70 x10-4

2.5% CI 6.17 x10-4 9.09 x10-4 4.24 x10-4 2.45 x10-4 1.61 x10-4 1.84 x10-4

97.5% CI 8.70 x10-4 2.45 x10-3 1.13 x10-3 5.74 x10-4 3.03 x10-4 3.58 x10-4

destimated

: 1.19 x10-9 1.04 x10-9 1.44 x10-9 1.86 x10-9 2.55 x10-9 2.87 x10-9

2.5% CI 1.10 x10-9 7.59 x10-10 1.11 x10-9 1.57 x10-9 2.34 x10-9 2.64 x10-9

97.5% CI 1.27 x10-9 1.32 x10-9 1.75 x10-9 2.18 x10-9 2.84 x10-9 3.18 x10-9

5.3.2.2 Interface Dominated Conduction

Schottky analysis was performed in a similar manner to PF by the linearization of

equation (5-3):

𝐿𝑛(𝐽𝑆) =𝛽𝑆𝐸1/2

𝑘𝑇−

𝜙𝑆

𝑘𝑇+ 𝐿𝑛(𝐴∗𝑇2) (5-7)

In equation (5-7), the J(E) data are plotted in a Shottky plot (Ln(Js) vs. E1/2) where linear fit slope

can be used to calculate material permittivity using the form of βS discussed in section 5.2.2. The

11 Histograms of parameter estimates from which confidence intervals are derived are presented in Appendix D along with raw J(E) data plotted

with superimposed nonlinear fits.

113

data from Figure 5-2 are transformed into Schottky plot format and shown in Figure 5-5 along

with their respective linear fit functions.

Figure 5-5 J(E) data from Figure 5-2 transformed into Schottky plot format. Again, measurements were taken at a)

25 oC, b) 100 oC and c) 150 oC. Here slope of linear fit corresponds to βs/kT in equation (5-7).

114

Both PI and PPIDS data sets behave similarly at 25oC, which is expected given previous

observations, as seen in Figure 5-2. At 100oC a change in the sample sets’ behaviors occurs where

the slope of linear fit corresponding to PI becomes steeper compared to that of PPIDS. As

temperature is increased to 150oC, the difference between these slopes still exists however it is less

dramatic. This implies that the value of permittivity calculated using Schottky theory will change

depending on both temperature and sample processing condition. Calculation of permittivity under

Schottky formalism is done via the following equation:

𝜖𝑟,𝑆 = [(𝑚𝑘𝑇)24𝜋𝜖𝑜

𝑞3]

−1

(5 − 8)

Permittivity values calculated for each sample group as a function of measurement

temperature are shown below in Figure 5-6. At low temperatures, Schottky theory produces

permittivity values within the range of 18 to 4 for PI, indicating that this model inadequately

describes conduction through the material. This outcome coincides well with modeling performed

using hopping theory in section 5.2.1 that confirms that low temperature conduction is better

described by a bulk-dominated process. At elevated temperatures, starting at 100oC, the PI sample

set undergoes a transition in behavior and returns a calculated permittivity that lies within the range

considered acceptable for PI. The value of permittivity calculated using Schottky theory remains

within the range of expected permittivities for the material (determined by the high frequency

permittivity given by refractive index squared (n2) and εr measured at 1kHz) up until 150oC

indicating that high temperature conduction is no longer dominated by hopping but rather injection

through the electrode/dielectric interface.

Unlike the PI, PPIDS samples do not display Schottky type behavior at low and moderate

temperatures. In fact, Schottky theory does not return a permittivity within the expected range of

PI until 150oC and is located at the upper limit of acceptable permittivity for polyimide. At 175oC,

the calculated permittivity for the PPIDS films are well within the expected range for PI, displaying

a value similar to untreated PI at 100oC. This demonstrates that high field conduction in plasma

treated polyimide can be described by a Schottky dominated process only after the film is exposed

to 75oC higher temperature than untreated PI. This result is in good agreement with the results

obtained from section 5.3.2.1 that yielded good fits using hopping theory spanning the entire

temperature range for the PPIDS set.

115

Figure 5-6 Permittivity values calculated from linear fits from Schottky plots between 25oC – 175oC. A shaded region

is marked indicating the range between high frequency permittivity (n2) and permittivity measured between 100Hz –

100kHz.

5.4 DISCUSSION AND CONCLUSIONS

Plasma surface treatment using a mixture of oxygen and helium gas demonstrates the

ability to chemically alter the surface environment of PI, changing both wetting and electrical

properties of the film. Results obtained from XPS measurements on plasma treated PI from the

previous study by Meddeb et al. [13] indicate the increase of hydroxyl groups and suggest the

formation of added carbonyl and carboxyl moieties to the surface of the films.

In the study by Meddeb et al. [13], the addition of these chemical moieties is surmised to

result in high field conduction suppression, suggesting that their presence serves to trap or scatter

charges at the interface. In this present work, it is shown that low temperature conduction through

untreated PI and plasma treated PI is dominated by a hopping type mechanism, governed by the

diffusion of charge carriers through the bulk of the film. PI is shown to diverge from this model at

100oC, exhibiting conduction that is well described by Schottky theory, indicating charge injection

at the electrode/dielectric interface. Calculation of the activation energy in the low field regime

indicates the activation energy for DC conduction through an untreated film is 0.25 eV implying

the presence of electronic charge carriers. This result strengthens the outcome of high temperature

conduction modeling, suggesting electronic injection dominates leakage current through the

material under the combination of sufficiently high electric field and temperatures.

116

Plasma treatment increases the hopping-Schottky conduction transition temperature from

100oC to 175oC. This result indicates that the combination of hydroxyl, carbonyl and carboxyl

groups grafted by plasma treatment could be preventing charge injection at the interface. Previous

mention of the conduction at high temperature dominated by electronic injection at the

electrode/dielectric interface coincides well with this theory: electronegative oxygen containing

moieties create electron trapping centers at the interface and limit current injection at high

temperatures. This finding correlates well with past research that demonstrates conduction is

electronically dominated [194] [191], indicating that the high temperature performance of PI can

be improved by simple surface chemical modification using O2 to suppress charge injection of

electronic carriers. In context of Chapter 4, it seems the carrier type dominant in the material

(holes for P(VDF-TrFE and electrons for PI) plays a significant role in determining the outcome

of plasma surface treatments of a given chemistry. Plasma treatment can potentially limit the

formation of electronic space charges in dielectrics in the context of work done by Locatelli et al.

[186], thereby reducing field enhancements at the electrode/dielectric interface however the

dominant charge carrier must be taken into account prior to surface modification.

Future research concerning PI’s applicability for high temperature dielectrics should

emphasize the role of the electrode/dielectric interface and its potential to be used in tailoring

electrical properties of the material. The outcomes from theoretical analysis of data are used to

provide further insight on how surface chemistry may be used to tailor high field leakage current

in PI, and other materials. Suppressing leakage current by plasma surface treatment will potentially

lead to improved capacitor performance by limiting joule heating, suppressing electronic space

charge development under high fields, and extending the operable temperature range of dielectric

materials for power applications.

ACKNOWLEDGEMENTS

The authors of this publication would like to acknowledge the support of the National

Science Foundation as part of the Center for Dielectrics and Piezoelectrics under Grant Nos. IIP-

1361571 and IIP-1361503. We also would like to acknowledge Adam Walder for his expertise in

R-Studio script writing and input on statistical analysis of parameter estimates from non-linear

regression. Adam is a Ph.D. student in the department of statistics as part of the Eberly College of

Science at Penn State.

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CHAPTER 6

IMPURITY ION AND SPACE CHARGE CONDUCITON AT LOW AND HIGH FIELDS:

ANALYSIS OF IMPURITY ION MIGRATION AND INTERACTION WITH INTERFACES

IN P(VDF-TrFE)

ABSTRACT

Chapter 6 takes concepts from Chapters 3-5 and applies them to the development of a

system in which interfaces in P(VDF-TrFE) can be probed through controlled quantities of

impurity ions. This chapter is broken into two sections: Chapter 6I and 6II. In Chapter 6I an

equivalent circuit model was introduced to describe low frequency polarization mechanisms

dominating ionic conduction through P(VDF-TrFE). An outline for this section is provided below:

Chapter 6-I Outline

Introduction – a short literature review highlighting work which emphasizes the impact of

both injected and ionic space charges on electrical properties, field distribution and material

degradation is presented. The section is completed with statement of Chapter 6-I’s content:

quantification of low frequency ionic charge migration and interaction with P(VDF-TrFE)

polycrystalline morphology.

Materials and Methods – the processes by which LiClO4 doped P(VDF-TrFE) films are

fabricated is explained as well as film structural and electrical characterization methods.

Results and Discussion – raw structural and electrical experimental data is analyzed and

the results discussed prior to the implementation of equivalent circuit modeling techniques.

Equivalent Circuit Modeling – impedance data is fit with an EC descriptive of polarization

mechanisms contributing to the electrical signal. Fit parameter estimation combined with

statistical interpretation using Z-view electrochemical software is used to strengthen the

link between ionic conduction and material structure described by the model.

Conclusions – analysis of data in Chapter 6-I is discussed in context of its impact in

understanding conduction through P(VDF-TrFE) as well as how it will be used in Chapter

6-II.

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Chapter 6-II takes the information on ionic conduction through P(VDF-TrFE) gained in 6-

I and applies it to further knowledge gained in Chapter 3 by controlling space charge interaction

with planar interfaces created by multilayer spin casting. Thermally stimulated depolarization

current (TSDC) is introduced as an experimental technique to compliment low frequency

impedance spectroscopy by capturing electrical depolarization responses at equivalent frequencies

in the quasi DC range. Although 6-I emphasizes low frequency interaction with interfaces in

layered films, the high electric fields and long poling times characteristic of TSDC necessitate

information obtained from Chapter 4 and 5 to accurately interpret results. An outline of Chapter

6-II is provided below:

Chapter 6-II Outline

Introduction – Concepts pertinent to the understanding of conduction obtained from

chapters 3 to 6-I are briefly reviewed in place of the typical literature review. The section

is concluded with the proposed layered dielectric system outlining the mechanism by which

dopant impurities contribute to the understanding of how interfaces impact electrical

properties.

Materials and Methods – processing implemented to create undoped and doped layered

dielectrics along with relevant experimental parameters and techniques are explained.

Results and Discussion – the results of impedance spectroscopy of layered structures as

well as TSDC are presented and discussed in context of relevant literature.

Conclusions – the results of data analysis are discussed to further analysis of the interface

on charge transport through organic dielectrics.

Chapter 6 signifies the end of work done in this dissertation. This chapter is followed by potential

avenues for future work suggested by the author to continue studying charge transport in organic

dielectrics.

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CHAPTER 6I

ANALYSIS OF LOW FIELD IMPURITY ION MIGRATION IN LiClO4 DOPED P(VDF-

TrFE) THIN FILMS

6I.1 INTRODUCTION

In recent work published by Yang, et al. [12] the performance of biaxially oriented PVDF

(BOPVDF) under high electric fields in relation to electrode chemistry is analyzed. Thermally

stimulated depolarization current (TSDC) measurements performed at high fields and long poling

times indicate high ionic polarization in BOPVDF. The amount of ionic polarization observed was

higher than expected considering only impurity ion concentrations associated with sample

fabrication. It was postulated based off research done by Eberle, et al. [85] that HF gas emitted at

high electric fields reacts with Al and Ag electrode metals to produce Ag+ and Al3+ cations, as well

as F- anions which contribute to the large ionic depolarization peak in TSDC. The exact nature of

these ionic species in PVDF are not well understood, however their presence induces space charge

accumulations that interact with the materials polycrystalline structure and can create

heterogeneous field concentrations distributed throughout the material.

Although the effect of space charge migration has not been extensively investigated in

PVDF, the high voltage cable insulation community has placed emphasis on this area of research

in polyethylene (PE) and crosslinked PE (XLPE). Past work by Hozumi et al. [86] demonstrates

via pulsed electroacoustic (PEA) measurements that under electric fields exceeding 0.2 MV/cm

heterocharges related to impurities from crosslinking byproducts (acetophenone) and antioxidant

form within the material. At fields beyond 0.7 MV/cm, the formation of packet charges is observed

and thought to be due to local ionization of impurities assisted by acetophenone through solvation.

Similar observations have been made by Ren et al. [195] where crosslinking byproducts create

non-uniformity in the conductivity across the thickness of XLPE cable insulation. Ultimately,

work by Cao et al. [87] demonstrates that these mobile impurity species contributing to charge

heterogeneity across the film lead to dielectric breakdown in XLPE films at temperatures between

50 – 90oC. Impurity charge migration is also shown to adversely affect the performance of other

material systems such as mineral insulating oil. Gabler et al. [88] demonstrates the impact of

heterogeneous charge build-up due to injected charges as well as intrinsic charge carriers at DC

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frequencies on electric field distribution in mineral oil/paper arrangements. Calculation of field

distributions in the oil/paper arrangements indicate charge separation at the paper/oil interface,

resulting in field drops 7 times larger than the mean field strength through the material. This

ultimately leads to breakdown initiation in the vicinity of charge accumulation.

In this chapter, the effect of ionic charge migration through P(VDF-TrFE) on AC

conductivity at low frequencies and high temperatures is investigated. Films are doped with low

content of LiClO4 to create a model material in which the quantity and species of ionic charge

carrier is well understood and dominates the electric response of the film. This specific ionic

complex is chosen because of past research implementing a combination of transference number

measurements [196] and electrolysis experiments [197] that demonstrate Li+ is the dominant ionic

charge carrier in LiClO4 doped PVDF films. Thus, lightly doping the film enables characterization

of ion migration where the impurity ion is both controlled well defined unlike studies mentioned

in Chapter 1 Table 1-III. and distribution through the bulk of the film without significantly

altering material morphology. Differential scanning calorimetry (DSC) is used to structurally

characterize doped films as a function of LiClO4 wt %. Impedance spectroscopy over a broad

frequency (100 kHz – 0.1 mHz) and temperature (25oC – 110oC) captures the electrical response

of P(VDF-TrFE) due to molecular and space charge polarization mechanisms. Finally, an

equivalent circuit (EC) to model impedance behavior is developed based off the structure of the

material and fit to impedance data using complex nonlinear regression. A combination of results

from DSC, the known structure of P(VDF-TrFE), and statistical outputs from the EC model are

used to enhance the understanding of ionic charge migration and accumulation in P(VDF-TrFE)

thin films.

6I.2 MATERIALS AND METHODS

6I.2.1. Materials

The copolymer P(VDF-TrFE) 70/30 mol% was purchased from Poly K in powder form

with a molecular weight Mn = 205 kg/mol. Battery grade 99.99% metals basis LiClO4 of 106.39

g/mol was purchased from Sigma Aldrich. Both materials were dissolved in N,N-

Dimethylformamids (DMF) purchased from DriSolv® into a solution that was spun onto platinum

coated silicon wafers purchased from Nova Electronic Materials.

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6I.2.2 Thin film Fabrication

Doped copolymer films were fabricated by solution deposition. The weight of LiClO4 was

measured in comparison to solid weight of P(VDF-TrFE) powder: grams(LiCLO4)/gramsP(VDF-

TrFE). This parameter was tuned to create 6 separate batches containing 0% wt (pure copolymer),

0.1%, 0.25%, 0.50%, 0.75%, and 1.0% LiClO4. The total solid wt % of the solution ((wt P(VDF-TrFE)

+ wt LiClO4) / wt solution) was ~7.5%. A degassing procedure to removed trapped air bubbles from

magnetic stirring was performed prior to spin casting onto platinum coated silicon wafers. A KLA-

Tencor P16+ stylus profilometer was used to determine film thickness and uniformity. It was found

600 rpm for 50s yielded a 1μm film of good thickness uniformity. Silver electrodes (50nm thick

by 3 mm diameter) were deposited using a Lab-18 electron beam evaporator provided by Kurt J.

Lesker. The stage temperature was held at 0oC during electrode deposition to prevent sample

damage.

6I.2.3 Structural Characterization

The thermal properties of the spin casted films were measured using a Q2000 differential

scanning calorimeter by TA Instruments. The samples were prepared by scratching 5–7 mg of

copolymer off the wafer into a T-Zero aluminum DSC pan using a carefully cleaned razor blade.

The temperature ramp rate was 10oC/min and spanned a range of -60 – 180oC. Analysis in this

paper used the first heating cycle in order to directly capture the effect of processing and LiClO4

content on copolymer crystal structure. Each film produced three samples and the data for each

film condition is taken to be the average between the three samples from the originating single

film.

6I.2.4 Electrical Measurements

A Cascade Probe Station equipped with DCM 210 series Precision Positioner 20μm probes

were used to capture low field behavior of the samples. Impedance spectroscopy was performed

within the frequency range of 100kHz – 0.1Hz using a Modulab impedance analyzer from

Solartron Analytical. Temperature was swept from 25 – 110oC using a Temptronic TP03000

thermal chuck vacuum wafer probe chiller interfaced with the probe station during measurement.

Values for the real and imaginary parts of impedance were collected with Modulab and converted

to capacitance and loss tangent using the general electrochemistry software Z-view provided by

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Scribner Associates Inc. Impedance fitting and equivalent circuit (EC) modeling was also

performed using Z-View where complex nonlinear regression implemented a calc proportional

data weighting scheme.

6I.3 RESULTS AND DISCUSSION

6I.3.1 Differential Scanning Calorimetry (DSC)

Crystallinity is calculated using a 91.45 J/g melting enthalpy for a theoretically 100%

crystalline sample of P(VDF-TrFE) 70/30 mol% [98] via melting peak integration. The results of

DSC measurement and endotherm integration are presented in Table 6I-I below.

Table 6I-I: DSC results as a function of LiClO4 solid wt% for the first heating cycle. Endothermic peak temperatures

along with integration results are shown and the range in standard deviations of the sample sets are given in italics.

Sample Average Tc

(oC) Int Tc (J/g)

Average

Tm (oC)

Int Tm

(Crystal %)

Pure 110.1 ± 0.6 15.9 ± 0.7 151.3 ± 0.2 32.0 ± 0.6

0.10% 109.3 ± 0.7 16.2 ± 0.9 151.3 ± 0.2 32.5 ± 0.8

0.25% 109.9 ± 0.9 20.1 ± 0.7 152.2 ± 0.3 32.6 ± 1.1

0.50% 107.0 ± 0.5 21.6 ± 1.1 152.7 ± 0.4 33.2 ± 0.7

0.75% 107.0 ± 0.9 21.1 ± 2.0 153.2 ± 0.8 33.6 ± 1.6

1.00% 104.6 ± 0.4 22.7 ± 0.9 153.1 ± 0.3 32.4 ± 1.0

The pure copolymer film shows two peaks a temperatures T1 and T2 in the first heating ramp of

DSC: T1 = 110oC = Tc signifying the -phase crystals transitioning from a ferroelectric phase to

the paraelectric phase [198] and T2 = 151oC = Tm corresponding to polymer crystal melting [160].

As LiClO4 is introduced to the film, changes in Tm and Tc are measured. An increase in Tm occurs

between films containing 0.1% - 1.0% LiClO4, however it is only by 1.85oC. Integration of Tm

reveals a slight increase in % crystallinity of the film as salt content is increased. Similar to Tm,

change in the Tc endotherm is observed which is more pronounced: as LiClO4 % is increased, Tc

peak position decreases from 110.1 – 104.6oC and integrated Tc signal increases from 16.2 – 22.7

J/g. Work by Oliveira et al. [199] that studied P(VDF-TrFE) structure via in-situ X-ray diffraction

(XRD) as a function of temperature shows contributions to both α (2θ = 19.9) and β (2θ = 17.8 )

crystal phases at temperatures below Tc. Above Tc only α remains, indicating the Tm transition

pertains exclusively to α crystal melting in the material. Because of LiClO4 addition’s minimal

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effect on Tm and prominent effect on Tc, it is suggested that salt-ion pair interaction is occurring

predominantly between polar crystal domains associated with the β-phase of the films.

6I.3.2 Dielectric Spectroscopy

Permittivity and loss tangent for each ionic content at room temperature is shown below in

Figures 6I-1a and 1b respectively. The pure copolymer shows a relatively stable permittivity and

loss tangent at room temperature that agrees well with values reported in literature [200]. At high

frequency, a dip in the permittivity can be seen corresponding to the relaxation of the orientational

polarization mechanism associated with permanent C-F dipole rotation [201]. This dip is coupled

by a slight increase in loss tangent and is characteristic of the dipole relaxation mechanism. When

the frequency is between the range of 10Hz – 10kHz, the permittivity and the loss tangent is

Figure 6I-1: a) real part of the permittivity and b) loss tangent measured at 25oC as a function of frequency for ionic

content up to 1.0 wt%.

124

considered stable. At frequencies below 10Hz, an increase in the permittivity and loss tangent is

measured for all samples indicating the onset of space charge migration through the dielectric. An

increase in permittivity and loss tangent within this frequency range occurs as greater quantity of

LiClO4 is introduced into the films suggesting that cation Li+ species serve as the dominant

contributor to space charge in doped films.

Figure 6I-2a and 2b show the permittivity and loss tangent for the same films as seen in

Figure 6I-1, at 100oC. At higher temperatures, dipole mobility increases resulting in larger

permittivity at frequencies related to C-F bond rotation. This increase in dipole mobility also

creates a shift in dipole relaxation to higher temperatures. Temperature’s influence on chain

mobility and free volume also impacts low frequency ionic charge migration by increasing ionic

mobility through the bulk [202, 203]. The pure copolymer film shows an order of magnitude

increase in the permittivity at 0.1Hz at 100oC relative to the 25oC measurement, however change

Figure 6I-2: a) real part of the permittivity and b) loss tangent measured at 100oC as a function of frequency for salt

wt %’s 0 – 1.0%.

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in LiClO4 containing samples are more prominent. The permittivity in the 0.1% doped film

increases from εr = 14 at 25oC to εr = 8.1x103 at 100oC which is coupled by a fully resolved loss

tangent relaxation centered at 10Hz (Figure 6I-2b). Further addition of LiClO4 increases the low

frequency permittivity, reaching a maximum at 1.2x105 for the 0.75% sample, and shifts the

position of the loss tangent peak within the frequency range of 40Hz – 100Hz. The presence of a

fully resolved peak in the loss tangent as well as plateauing in the permittivity give evidence that

Li+ migration through the film interacts with the electrode dielectric interface at the lowest

frequencies of measurement and highest temperatures. The absence of this behavior in the pure

copolymer film suggests that the saturated permittivity in ion containing films is indicative of a

pseudo double layer capacitance between Li+ space charge and the anode.

6I.3.3 AC Conductivity

The real part of the permittivity and loss tangent are used to calculate the AC conductivity

of the films as a function of temperature and ionic content. Permittivity and loss tangent are related

to the AC conductivity of the material via the following relationship:

𝜎𝐴𝐶 = 휀𝑟휀𝑜𝜔𝑇𝑎𝑛(𝛿). (6𝐼 − 1)

The conductivity values for T = 40oC, 80oC, and 100oC using equation (6I-1) are shown in Figure

6I-3a, 3b, and 3c.

Figure 6I-3a represents low temperature behavior of the samples. At 40oC, LiClO4

addition to the polymer has a negligible effect on the conductivity at the highest frequencies. In

this temperature/frequency domain, the dominating conduction mechanism does not depend on

ionic impurities but rather losses due to dipole polarization dominates. LiClO4 begins to have an

effect on the calculated conductivity at frequencies below 10Hz. There is considerable change in

conductivity from low wt% samples, increasing from 2.0x10-11 S/m in the pure film to 5.3x10-11

S/m in the 0.1% doped film at 0.1Hz. An order of magnitude increase is calculated when increasing

from 0.1% wt (5.3x10-11 S/m) to 0.25% wt (2.4x10-10 S/m) in the film. At higher concentrations,

the conductivity saturates at 0.1Hz, where 0.5%, 0.75%, and 1.0% doped films display

conductivities of 1.1x10-9 S/m, 1.1x10-9 S/m, and 1.0x10-9 S/m respectively.

Figure 6I-3b represents sample behavior at moderate temperatures. A plateau in the

conductivity of doped samples occurs at 80oC in ion rich films as a function of frequency,

indicating conduction through the sample is primarily dominated by ionic conductivity due to Li+

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Figure 6I-3: AC conductivity calculated using equation 1 calculated at 100 kHz – 0.1 Hz for each of the measured

LiClO4 wt %. Temperatures measured are a) 40oC, b) 80oC, and c) 100oC.

cation migration. Saturation in the calculated conductivity also takes place at all frequencies for

samples containing 0.50% - 1.0% wt LiClO4, suggesting increased carrier concentration due to

added LiClO4 does not produce large changes in the conductivity of the samples within the range

at the measurement temperature.

Saturation in ion containing samples is less prominent at 100oC than it was at lower

temperatures. A decrease in conductivity is initiated between 1Hz and 0.1Hz in samples containing

LiClO4. This relaxation in the AC conductivity is related to the development of another capacitive

effect in the material caused by the build-up of ionic charges at the electrode/dielectric interface

only observed at high temperatures and low frequencies. Drop in conductivity could arise from the

electrodes blocking ionic charge transport at low frequencies. This interpretation of the response

is supported by no observable change in the conductivity for the pure sample which exhibits

gradual plateauing conductivity as a function of frequency in the absence of Li+ charges.

6I.3.4 Impedance Spectroscopy

The impedance of films containing 0 -1.0% LiClO4 was characterized as a function of

temperature using ac impedance spectroscopy. In this analysis, the imaginary impedance Z” and

real impedance Z’ are measured as a function of frequency. Figure 6I-4 shows the -Z” impedance

as a function of Z’ in Cole-Cole plot format. The ideal impedance response of a capacitor can be

approximated by an RC equivalent circuit which traces a semicircular arc in Z’, Z” space. The

extension of the semicircle in the Z’ direction is representation of the bulk resistivity Rb of the

material while extension into -Z” represents capacitive behavior. In Figure 6I-4, the pure and low

ion containing 0.1% sample extend predominantly into the -Z” direction, indicating a capacitive

response with low leakage and high Rb. This is supported by AC conductivity calculations at low

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Figure 6I-4: Cole-Cole plot of impedance for 0 – 1.0% doped samples at 25oC. The material’s bulk response cannot

be fully resolved however a general trend between LiClO4 addition and conductivity is observed.

temperature in Figure 6I-3a where the pure and 0.1% films display conductivities 1 – 2 orders of

magnitude below their highly doped counterparts. As the doping concentration increases, a greater

portion of the impedance arc is resolved in the Z’ direction indicating the motion of Li+

contributing to the bulk response of the material and lowering the value of Rb.

Higher temperature facilitates the movement of ionic carriers (similar to that seen in the

permittivity and loss tangent results in Figure 6I-2) and yields more informative impedance

diagrams. Figure 6-I-5a, 5b, and 5c show Cole-Cole plots for doped copolymer films at 100oC.

Figure 6I-5a shows the impedance of all samples super imposed on one another. Only the pure

copolymer can be observed at the scale shown in Figure 6I-5a because of its large impedance in

comparison to doped films. Similarly, the pure film only shows a single feature in its impedance

response: a depressed semicircle representing the bulk response of the material under test common

to many polymers and solid polymer electrolyte (SPE) materials [202, 204, 205]. Figure 6I-5b

and 5c show the impedance of the doped copolymer films by progressively decreasing the scales

on the Z’ and -Z” axes. In Figure 6I-5b, the impedance of the 0.1% film shows two features: a

depressed semicircle representing the bulk response of the material and low frequency line that

extends upward in the -Z” direction. This behavior is strong evidence of Li+ blocking at the

electrode/dielectric interface which was interpreted as pseudo double layer capacitance in section

6I.3.2 [205, 206]. The lowest measured impedances are shown in Figure 6I-5c which reveals the

same two features representing bulk and blocking behavior for the 0.25 – 1.0%. This set of films

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display the strongest separation between bulk behavior and blocking and have bulk impedance

responses with a well-defined Z’ magnitude.

Figure 6I-5: Complex impedance Cole-Cole plots at 100oC for a) all tested samples, b) 0.1% – 1.0% samples and c)

0.25 – 1.0% samples.

129

Bulk resistance Rb of the material is taken as the point in which the bulk semicircle touches

down on the Z’ axis, magnitudes marked by open brackets for 0.25 – 1.0% films in Figure 6I-5c.

The bulk conductivity of the material can be calculated by the following equation:

𝜎𝐵 =𝑡

𝑅𝑏𝐴 (6𝐼 − 2)

where t and A are the thickness and area of the film under test. This calculation is used to compute

the bulk conductivity of ion containing film within the temperature range 60oC – 100oC. Only ion

containing films between 0.25 – 1.0% are used because they were the only to consistently exhibit

full resolution of the bulk response.

Arrhenius type behavior of the conductivity is reported in many ion containing systems

with a host polymer matrix such as poly(methyl-methacrylate) (PMMA), poly(vinyl pyrollidone)

(PVP), poly(vinyl acetate) (PVA) and chitosan (CS) [207, 208, 209, 210]. The Arrhenius law

portrays conduction as a thermally activated process and relates the conductivity to the activation

energy via the following relation:

𝜎𝐵 = 𝜎𝑜𝑒−𝐸𝑎𝑘𝑏𝑇 (6𝐼 − 3)

where σo is a constant related to the conductivity at 0K, kb is Boltzmann’s constant, T is the

temperature in K, and Ea is the activation energy. Figure 6I-6 shows the variation of ln(σB) as a

function of T-1 for LiCLO4 0.25% – 1.0%. Linear regression reveals a good fit over the specified

temperature range indicating Li+ migration through the bulk is governed by hopping type

conduction from adjacent trap sites distributed thought the material [207]. As LiClO4 % is

increased, the conductivity is observed to abruptly increase in value at lower temperatures for

concentrations ≥ 0.5%. Conduction through polymer electrolytes is dependent on polymer

chemical structure, crystallinity, free volume, and qualities of the contributing carrier [202]. In

order to address changes in conductivity the activation energy extracted from Figure 6I-6

(embedded in the Arrhenius plot in table format) must be considered. Calculated activation energy

for 0.25% film is 2.32 eV. Following the abrupt low temperature increase in conductivity starting

with the 0.5% samples is a decrease in the calculated Ea to 1.29, 1.59, and 1.52 eV for the 0.50%,

0.75%, and 1.00% samples respectively. In general, high values of Ea is a characteristic feature of

ionic conducting solid polymer electrolytes [202, 211] that are not exhibited by their aqueous

electrolyte counterparts such as tetrabutylammonium triflate (TbaTf) dispersed in propanol. The

aqueous TbaTf system displays

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Figure 6I-6: Arrhenius plot of σb for LiClO4 range of 0.25% – 1.0%. Extracted activation energies from linear fits are

shown in the embedded table.

activation energies in the range of 0.34 – 0.42 eV, which depends on TbaTf concentration

[212]. Values calculated in the P(VDF-TrFE) – LiClO4 system are slightly higher than those

reported for other non-aqueous SPE systems such as in CS: Lithium Triflate (LiTf) [211], however

the level of doping studied in this manuscript is an order of magnitude lower than much of the

literature surrounding SPE ionic conduction. Similarly, P(VDF-TrFE) is unique in the fact it has

polar crystal domains which give the material its piezoelectric nature. The 0.5% LiClO4

concentration serves as a critical point in the conductivity in which the following occurs: 1) a

decrease in the activation energy associated with conduction and 2) a leap upward in low

temperature conductivity and will be discussed in context of EC modeling in the next section.

6I.4 EQUIVALENT CIRCUIT MODELING

The impedance response of P(VDF-TrFE) 1 μm films pure through 1.0% LiClO4 doped

into the polymer matrix was analyzed using a modified Debye like equivalent circuit (EC) shown

in Figure 6I-7a. The EC is broken into 4 main parts: 1) a capacitor element labeled C1 which

accounts for electronic polarization at high frequencies. The value of this element is proportional

to the refractive index squared (n2) of the material and remains constant for each fit at all

temperatures. 2) A constant phase element CPE2 in series with resistor R2. This leg of the circuit

represents the dielectric response attributed to permanent dipole polarization induced by C-F bond

rotation. The element R2 dictates the frequency at which dipole contributions to the impedance

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Figure 6I-7: a) physical model of doped P(VDF-TrFE) with equivalent circuit (EC) model used in fitting impedance

spectra, b) raw impedance data (open symbols) with EC fit (solid lines) at 25oC and c) 100oC.

begin to relax out. 3) A resistor R3 in series with a nested R4/CPE3 element accounts for

predominantly low frequency ionic motion through the bulk of the dielectric. Considering P(VDF-

TrFE) is a semi crystalline material, it is proposed that R3 directly relates to bulk charge carrier

transport through the amorphous region of the material while the nested R4/CPE3 corresponds to

charge carrier transport through the amorphous/crystalline interphase region. A similar model is

proposed by Marzantowicz et al. where a nested CPE/R element is implemented represent the

influence of the crystalline phase on ionic conductivity in poly(ethylene oxide) (PEO) [115]. 4)

The

final element is a stand-alone CPE4 element in series with legs 1 through 3 that represents

low frequency polarization caused by impurity ion build up at the electrode/dielectric interface in

the quasi DC frequency regime. It should be noted that components 1 through 3 describe the bulk

response of the dielectric while component 4 arises in the special case films are doped with LiClO4

and measured at sufficiently high temperatures.12 The quality of fit for each sample at each

temperature was determined by a combination of three ways: 1) how well the fit result matches

raw (Z’, Z”) (M’, M”) (C’, C”) and (|Z|, θ) formalisms, 2) how well parameter estimates reflect

physical properties of the material system and 3) statistically computed parameter estimate

errors.13 Impedance fits using the EC in Figure 6I-7a are shown at 25oC and 100oC in (Z’, Z”)

format as solid lines over raw data.

12 Mathematical interpretation of the EC model used in nonlinear regression is found in Chapter 2 section 2.4.2 13 Parameter estimate error% are compiled for each sample and measurement condition presented in Appendix E.

132

The impedance response of pure and on containing P(VDF-TrFE) films were modeled

using Z-view electrochemical impedance fitting software. In this regard, each circuit element is

regarded as a parameter that is optimized via complex nonlinear regression using a calc-

proportional weighting scheme. All plots concerning individual circuit element contain data points

that are direct outputs of complex nonlinear regression parameter estimation. Statistical

interpretation of the fit results incorporates percent error that is generated by Z-views fitting

statistical report and indicate parameter estimate significance. Each data point shown in fit

parameter estimate figures was taken as the average between fit results extracted from the

responses of three individual samples measured at each temperature and LiClO4 content. The

standard deviations of the fit parameter estimates are also plotted, however in most instances they

are relatively small and covered by the data points.

6I.4.1 Modeling the Capacitive Response

Capacitive elements of the EC are first analyzed to inform how Li cations interact with the

material’s bulk structure. In this section, each capacitive circuit element is discussed in relation to

the polarization or conduction mechanism it describes: electronic polarization, permanent dipole

orientational polarization, ionic / space charge conduction, and blocking polarization.

6I.4.1.1 Electronic Polarization

The ideal capacitor C1 is chosen to represent the dielectric response of the material due to

electron cloud displacement under the applied electric field and has an impedance described by

equation (61-4):

𝑍𝐶1=

1

𝑗𝜔𝐶1 (61 − 4)

Electronic polarization dominates at frequencies on the order of THz, well beyond the

measurement range used to study impedance of P(VDF-TrFE). Thus, the value of C1 is assumed

to remain constant as a function of frequency and temperature for each sample fit. Using the high

frequency approximation εr = n2 and sample electrode area and thickness, C1 was approximated

using the equation C = εrεoA/t and held constant at 1.25x10-11 F.

6I.4.1.2 Permanent Dipole Orientational Polarization

133

Figure 6I-8: Estimated parameter values for a) Q2 from CPE2 as a function of salt wt % and b) approximated material

permittivity. Each film tested is of equivalent thickness. Units for Q are written in terms of conductivity as S sn given

equation 61-5.

The dipolar contributions to the overall bulk impedance response are described by CPE2 in

series with R2. Unlike the ideal capacitor, CPE2 has a more complex definition for impedance

described by equation (6I-5):

𝑍𝐶𝑃𝐸2=

1

(𝑗𝜔)𝑛2𝑄2 (61 − 5)

where the value Q2 is the estimated value of CPE2 acquired by fitting and n2 is the imperfection

factor. In this regard, Q2 must be taken into consideration along with n2 during analysis. Since the

impedance response due to dipole rotation dominates the measured signal within the frequency

range kHz – MHz, CPE2 is defined as an optimizable parameter during fitting.

The values of CPE2 are plotted as a function of LiClO4 wt % in Figure 6I-8a from 25 oC

– 110 oC. The parameter n2 represents a distribution of relaxation times due to heterogeneity of the

molecular environment surrounding permanent dipoles in the material. For all fits, n2 is held

between 0.98 – 0.99, chosen by statistical interpretation of the goodness of fit for the sample being

measured. The value of the circuit element increases as a function of temperature which can be

explained by an increase in dipole mobility due to temperature increase. As LiClO4 content is

increased, there is no significant change in the value of Q2 for any given temperature. Considering

each sample exhibits the same geometry for all salt concentrations, it can be concluded that ionic

inclusions do not have an impact on CPE2 parameter estimation. Because CPE2 describes

polarization associated with dipole orientation, the value of Q2 should correlate to the material

permittivity from Figure 6I-1 and 6I-2 for frequencies that space charge effects are not observed.

134

Figure 6I-9: The behavior of CPE3 as a function of LiClO4 wt % for the temperatures 25 oC – 100 oC. the standard

deviation of parameter estimates in the sample set are reflected by error bars. Fitting between 100oC – 110oC produces

large standard deviations in n3 as well as erratic parameter estimates for n3 and Q3.

Due to the value of n2 being 0.98 – 0.99, the response of CPE2 can considered as that of an ideal

capacitor using equation (6-I-2). Thus, Q2 ≈ C2 and εr ≈ Q2t/εrεo. This approximation uses

parameter estimates of Q2 from Figure 6I-8a to approximate the material permittivity in Figure

6I-8b. The results of permittivity approximation agree with the permittivity calculated from raw

capacitance data in Figures 6I-2 and 6I-3. The orientational polarization is dominant at ~10kHz,

where the permittivity is independent of temperature for all salt ionic contents.

6I.4.1.3 Ionic / Space Charge Conduction

Ionic space charge migration dominates at low frequencies and is described by R3 in series

with the nested CPE3/R4 circuit element. In this portion of the EC, R4 represents conduction of

ionic charge through the amorphous regions of the polymer and CPE3/R4 represents charge

migration through the crystalline/amorphous interphase. Like CPE2, the impedance of CPE3

depends on Q3 and n3. In this scenario, both parameters were estimated by fitting.

The response of CPE3 fit parameters to temperature and LiClO4 solid wt% is plotted in

Figure 6I-9. Parameter estimation of Q3 indicates that salt concentration has an impact on the

behavior of CPE3. As the amount of LiClO4 is increased, Q3 increases in value. At 25 oC, the model

yields a value of 2x10-10 S sn for the pure sample. This increases by two orders of magnitude to

1.21x10-8 S sn in the film containing 1.00% salt. This general trend is seen at each temperature and

can be related to increased interaction between charges and the crystalline regions of the material

as a greater quantity of ionic charge carriers are introduced. P(VDF-TrFE) crystallizes primarily

135

in the polar β-phase, thus interaction of LiClO4 molecules with the crystalline/amorphous

interphase region is anticipated to occur due to internal charge compensation.

The value of n3 is also plotted as a function of LiClO4 % in Figure 6I-9b. In general, the

value of n3 is centered around 0.5. With an n3 of 0.5, the CPE phase angle is constant at 45o and

its magnitude of impedance is proportional to the inverse of the square root of frequency (ω-1/2).

In this scenario, the CPE behaves similar to a Warburg impedance element, which typically models

diffusion-based processes that are characteristic of charge transfer resistance and double layer

capacitance. This outcome of the fit supports that the CPE3 element is descriptive of interaction

between crystalline regions and Li+ cations associated with doping, also described in PEO by

Marzantowicz et al. [115].

It should be noted that the value of n3 becomes erratic as measurement temperature

approaches 110 oC. Table 6I-I from section 6I-3.1 indicates that the Tc for the material ranges

between 104oC – 110oC depending on LiClO4 wt%. At temperatures surrounding the phase

transition temperature of the β-phase, parameter estimation begins returning uncharacteristically

high values of Q3 as well as erratic values of n3 without definable physical meaning. Erratic

parameter estimation of Q3 and n3 is also coupled by large parameter estimate error % (ranging

from 15.6% – 54.8% for Q3 and 8% - 62% for n3 depending on salt concentration)14. Large error

% is indicative of parameter estimate insignificance and inaccuracy when fitting, indicating that

the nested CPE3/R4 circuit element’s contribution to the model breaks around temperatures

associated with the ferroelectric paraelectric phase transition of the crystal. Large standard

deviations within the sample sets of estimated n3 values also occur at high temperature. This

outcome suggests that the nested CPE3/R4 circuit element is unique to polar crystalline sites

through the film and that Li+ transport is significantly impactd by interaction of Li+ with

crystalline/amorphous interphase regions associated with ferroelectric crystals in the material.

6I.4.1.4 Blocking Polarization

The final capacitive circuit element is CPE4 and describes the blocking of ionic space

charges at the lowest, quasi DC frequencies and highest temperatures of measurement. Fit results

for CPE4 are plotted in similar fashion to the others with results of Q4 and n4 parameter estimates

in Figure 6I-10. From T = 25 – 60 oC, the value and n4 for CPE4 are held at n4 = 1. This results in

14 Error % mentioned is presented in Appendix E.

136

Figure 6I-10: Fit results for CPE4 and n4 as a function of salt wt % at temperatures 25 oC – 110 oC. Q4 reflects ionic

charge interaction associated with Li+ and the electrode where 0.5 < n4 < 1.0 estimates indicate electrode/polymer

interfacial roughness and heterogeneous charge distribution at the interface.

impedance of CPE4 to equal that of an ideal capacitor. Similarly, Q4=1F within 25 – 60oC except

for the 0.5% sample at 60oC. This high capacitance indicates the contributing impedance of CPE4

is very low (by equation 6I-4) and does not interfere with the impedance response of the circuit

during fitting within this temperature range. For temperatures beyond 60oC, a value for Q4 is

estimated via fitting. Figure 6I-10a shows these parameter estimates as a function of LiClO4 wt%

and temperature. The pure copolymer samples do not deliver fit results for Q4 until 110oC, however

all LiClO4 containing films return Q4 parameter estimates reflecting charge blocking. The

values of Q4 are within the range of 2x10-7 S sn estimated for 0.1% containing film and gradually

rise to 8x10--6 S sn for the 1.0% containing film. Each sample displays a gradual rise in Q4 as a

function of LiClO4 wt% present in the film which demonstrates the blocking layer capacitance is

proportional to the amount of separated charges at the interface. This follows the traditional

definition of capacitance C = qV where C is capacitance, q is stored charge and V applied voltage.

Values of n4 were also subjected to fitting at temperatures above 60o for all LiClO4

containing samples and are plotted in Figure 6I-10b. The estimated values of n4 range between

0.95 for the 0.25% samples measured at 80oC to 0.72 for the 1.0% samples measured at 100oC.

This n4 range is neither indicative of ideal capacitor behavior, nor charge diffusion. It has been

demonstrated that the impedance response of 2 dimensional systems that show deviation away

from 2D geometry can be modeled using constant phase elements with n = 1/(D-1) where D is the

fractal dimension. In the case that charge accumulation is homogeneous and surface roughness

negligible, D = 2 making n = 1. In the case heterogeneity in charge accumulation occurs and

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surface roughness is non-negligible, 2 < D < 3, causing a range in n between 0.5 and 1 [213].

Fitting of n4 suggests fractal dimensions indicative of heterogeneity and roughness, which reflects

microscopic irregularities suspected to be present at the electrode/dielectric interface.

In order to verify CPE4’s validity in capturing the effect of space charge blocking at low

frequencies, 0.25% samples fabricated 10 μm thick were measured and compared. Increasing the

thickness of the sample had little effect on the behavior of bulk impedance data and related

capacitive circuit elements. At low frequencies however, blocking polarization in the 10 μm film

is comparatively less pronounced than its 1 μm counterpart. This subtle difference is captured by

calculations of error % in parameter estimates for Q4 and n4 which are presented in Table 6I-II.

Table 6I-II: Error % for CPE4 extracted from Q4 and n4 parameter estimates in 1 μm and 10 μm samples.

Q4 Error % n4 Error %

Temperature

(oC) 1 μm 10 μm 1 μm 10 μm

25 --- --- --- ---

40 --- --- --- ---

60 --- --- --- ---

80 4.1 17.8 4.8 19.1

90 3.1 11.7 3.1 13.1

100 5.1 13.7 2.9 9.6

110 2.3 2.3 1.1 1.9

In the case of CPE4 fitting for the 1 μm sample, strong low frequency polarization response seen

in the impedance data is coupled by Q4 and n4 parameter estimates with low error %’s. On the

contrary, error % is an order of magnitude higher in the 10 μm between 80 – 100 oC, indicating

parameter estimates of Q4 and n4 in films with a comparatively weaker low frequency polarization

response are less significant, verifying that CPE4 captures space charge blocking in doped

specimens.

6I.4.2 Modeling the Resistive Response

In this section, parameter estimates of the bulk EC’s purely resistive components R3 and

R4 are analyzed as a function of temperature for salt wt % ranging from the pure material to 1.00%

138

Figure 6I-11: Fit results for resistive EC elements a) R3 associated with amorphous regions of the bulk and b) R4

associate with the crystalline/amorphous interface plotted as a function of LiClO4 solid wt %. R4 is shown to dominate

resistive response at low temperature and LiClO4 wt%.

doped film. R3 and R4 are examined individually as a function of temperature and compared.

During curve fitting of impedance data, both R3 and R4 were set as optimizable parameters at each

temperature and salt %. The values of R3 and R4 obtained from parameter estimation are plotted as

a function of LiClO4 content in Figure 6I-11a and 11b. The R3 circuit element is a standalone

resistor in series with nested CPE3/R4 and is plotted in Figure 6I-11a. Without an associated

parallel capacitor element, R3 is taken to represent energy dissipation due to Li+ cation migration

through the amorphous regions of the material. Unlike R3, R4 exists in parallel with CPE3 and thus

represents resistance associated with the crystalline/amorphous interphase. Both circuit elements

exhibit a reduction in resistance with increasing temperature. Fitting estimates correlate well with

increases in conduction calculated in Figure 6I-4 at mid – low frequency.

Some differences are observed when comparing the values of parameter estimates obtained

by fitting for each resistive component. At 40oC, R4 exceeds R3 by an order of magnitude at all

LiClO4 contents, indicating that the crystalline/amorphous interphase dominates the bulk

resistance of the material especially at low temperature and low doping %.15 At high doping %’s

and low temperatures (40oC), a plateau in both resistive parameter estimates is initiated at 0.5%.

Starting at 60oC, R3 estimates begin to approach estimates of R4, finally showing virtually no

distinction in estimated values of the two parameters at T > 90oC and LiClO4 concentrations

between 0.50% - 1.00%. Within this range, R4 is not considered the dominating parameter,

15 The bulk resistance for the EC model used is equal to the summation R3 + R4 (can be reasoned mathematically by taking the bulk impedance

derived in Chapter 2 section 2.4.2.1 in the limit frequency approaches 0). At low temperatures R4 dominates thus it is considered the

crystalline/amorphous interphase limits conduction.

139

implying that both R3 and R4 contribute equally to bulk conduction and the crystalline/amorphous

interphase no longer limits ionic carrier migration through the bulk after eradication of the β-phase.

Further evidence of this can be concluded by relating fit parameter estimation to the material’s

LiClO4 dependent thermal response discussed in section 6I.3.1. As temperature is increased in the

range of Tc (100 – 110oC) the crystal structure of the material undergoes the ferroelectric to

paraelectric phase transition which disrupts the nature of the crystalline/amorphous interphase

regions within the material. Evidence of this is reflected by fit parameter statistical analysis:

parameter estimates for R4 exhibiting erroneously large error %’s spanning multiple orders of

magnitude in all samples16. The behavior of R3 and R4 coupled with large error % in the model

specifically for CPE3/R4 elements suggests ionic migration is no longer limited by the crystal

phases of the material at high temperature.

6I.5 CONCLUSIONS

Lithium doped P(VDF-TrFE) were successfully fabricated. The impurity Li+ ion migration

through amorphous and amorphous/crystalline interphases played a key role in the electrical

properties. DSC indicated that addition of ions did not have a significant impact on the %

crystallinity but significantly increased -phase integrated signal at Tc. This is surmised to be due

to ions interaction with the polar β-phase by ionic complexation within the crystalline/amorphous

interphase to maintain charge neutrality within the sample.

Dielectric spectroscopy at room temperature indicates an increase in the low frequency

permittivity and loss tangent suggesting added dissipation through space charge polarization in

doped samples. High temperature dielectric spectroscopy measurements of the permittivity

showed a plateau in the low frequency response as well as the formation of a fully resolved peak

in tan(δ). This behavior is evidence of the formation of a pseudo double layer capacitance at the

electrode/dielectric interface in doped films at low frequency, and later verified by high

temperature impedance spectroscopy where linear extension of data along the -Z” axis at low

frequencies clearly indicates blocking.

Increasing ionic content resulted in a reduction in bulk resistance of the films within the 25

– 100oC temperature range. Bulk resistance extracted from (Z’,-Z”) plots showed Arrhenius type

behavior that was governed by Li+ hopping type conduction through the film. The activation

16 Statistical error % reports for all fit parameters can be found in Appendix E.

140

energy abruptly decreased for a LiClO4 content of 0.5%, indicating a transition point in conduction

behavior where that is attributed to combination of polymer morphological change and salt

percolation in the amorphous region of the film.

The EC used to fit impedance spectra captures conduction processes related to the four

polarization mechanisms in the system: electronic, orientational, ionic space charge migration, and

blocking polarization mechanisms. Fit outputs associated with the bulk of the EC highlight

permittivity’s independence from salt concentration at mid – high frequency, indicating that added

Li+ behave as impurity ions and do not interrupt natural polarization processes associated with the

virgin material. The low frequency nested circuit element describing ionic charge migration

reflects space charge diffusion through the crystalline amorphous interfaces of the bulk. Similarly,

at high temperatures the nested CPE3/R4 parameter estimate accuracy and physical meaning begin

to degrade. When compared with DSC results, this degradation between 100 – 110oC of parameters

is tied to the ferroelectric – paraelectric phase transition, reflecting space charge’s dependence on

polar domain interactions associated with the β-phase. At low frequencies, space charge

polarization at the electrode/dielectric interface observed in impedance Cole-Cole plots were fit

using a stand-alone CPE4 element that suggest the formation of an ionic space charge layer. Values

of n4 indicate the non-ideal behavior of the circuit element is attributed to surface roughness effects

at the interface. Ultimately space charge accumulation at DC frequencies at the electrode dielectric

interface creates large field drops at the electrode/dielectric boundary, potentially serving as a point

for breakdown initiation.

In the following section, an outline demonstrating how impedance spectroscopy will be

used in conjunction with TSDC measurements to inform on impurity ion migration and interaction

in layered P(VDF-TrFE) dielectrics will be presented along with preliminary data on copolymer /

polyvinyl alcohol (PVA) multilayered films.

141

CHAPTER 6II

CONDUCTION IN MULTILAYERED LAMINATES: EXPLOITING THE INTERFACE AS

A BARRIER TO CHARGE TRANSPORT

6II.1 INTRODUCTION

In Chapter 6I an equivalent circuit model was introduced to describe low frequency

polarization mechanisms dominating ionic conduction through P(VDF-TrFE). It was found that

the electrode dielectric interface impacts ionic charge transport at low frequencies and high

temperatures (in addition to influencing electronic injection discussed in Chapters 4 and 5). The

crystalline/amorphous interphase regions associated with the material’s β-phase also impacts ionic

charge carrier propagation through the amorphous regions of the material in single layer films. In

this regard, interfaces associated with electrode contact (Chapters 4 and 5) as well as those within

the dielectric (Chapter’s 3 and 6I) impact dielectric performance under DC conditions and must

be understood to improve polymer capacitor performance.

Chapter 6II incorporates results from all subsequent chapters to create a multilayered

composite system in which low frequency charge interaction with bulk distributed interfaces can

be controlled. In this section, a layered composite is fabricated by depositing P(VDF-TrFE) doped

with 0.25% LiClO4 via spin casting, and then adding a thin layer of polyvinyl alcohol (PVA),

which serves as a barrier layer during P(VDF-TrFE) solution re-deposition. This creates a series

of planar interfaces within the material that are in series to the electrode/dielectric boundary. A

schematic of the multilayered test material is displayed in Figure 6II-1 demonstrating PVA

capping layers (interfaces) intended to limit ionic migration at quasi DC frequencies.

Figure 6II-1: schematic of multilayer material system depicting material components and the anticipated results.

142

It should be noted, that the effects of multilayer lamination have been demonstrated in past

work by Mackey et al. [14], where microlayer coextrusion was implemented to create P(VDF-

HFP) / PC layered structures. In this work, the benefits in terms of dielectric performance were

exemplified by large enhancements of breakdown strength (Chapter 1, Figure 1-10) than either

constituent material alone. Similar results were then obtained by related work performed by Zhou

et al. [15] which suggested layered coextruded dielectrics can limit ionic propagation by reducing

the mobility of impurity carriers within interphase regions between layers. Regardless of both

studies, the quantity and species of impurity ions are not well understood or controlled.

The following sections in this chapter present the following: 1) processing techniques for

fabrication of composite multilayer dielectrics thin films. 2) equivalent circuit (EC) modeling of

impedance for layered films. This portion focuses on the development of EC that accounts for the

added effect of PVA charge interacting interfaces distributed throughout the bulk of the film and

will offer greater insight into understanding the impact of layers on low frequency conduction

characteristics. 3) Thermally stimulated depolarization current measurements (TSDC) will be

implemented for both single and multi-layered films. Due to the technique’s high poling fields and

long poling time at DC frequencies (details in Chapter 2 section 2.3.3.3), TSDC offers

information on charge migration due to a) electronic charges associated with charge injection from

electrode into P(VDF-TrFE) and b) ionic charge migration characteristics observed at lower

frequencies than traditional impedance techniques. In this sense, TSDC can be seen as a technique

to characterize space charge interaction with interfaces from multiple contributing charge carrier

types, serving as a framework to apply the technique to similar material systems in which

dominating charge carrier species contributing to conduction is not well known. Finally, the

chapter is concluded with 4) high voltage dielectric breakdown experiments on 1-layer and 4-layer

films to show the impact of interfaces on dielectric breakdown strength and consequentially energy

density.

6II.2 MATERIALS AND METHODS

6II.2.1 Materials

The copolymer P(VDF-TrFE) 70/30 mol% was purchased from Poly K in powder form

with a molecular weight Mn = 205 kg/mol. 87 – 89% hydrolyzed high molecular weight Polyvinyl

alcohol (PVA) was purchased from Alpha Aesar. Battery grade 99.99% metals basis LiClO4 of

143

106.39 g/mol was purchased from sigma Aldrich. P(VDF-TrFE) and LiClO4 were dissolved in

electronic grade 2-Butanone (MEK) purchased from Alfa Aesar while PVA was dissolved into

deionized H2O. Both solutions were spun onto silicon wafers purchased from Nova Electronic

Materials.

6II.2.2 Multilayer Processing

The processing procedure for multilayered dielectrics was an additive spin casting protocol

involving alternating depositions of P(VDF-TrFE) and PVA. Ultimately the ionic content within

the P(VDF-TrFE) is meant to simulate the presence of impurity ions within the material. Due to

their low quantities present in the pure dielectric, it is important to choose a concentration of

LiClO4 that enhances qualities of ionic conduction through the material and does not disturb the

microstructure of the bulk. The 0.25% LiClO4 concentration was chosen over the 0.1% because it

was the lowest amount of added salt that clearly displays space charge polarization during

dielectric spectroscopy (Figure 6I-1 and 6I-2) as well as blocking polarization at high

temperatures in impedance and EC modeling (Figure 6I-5 and 6I-10) relative to the 0.1% sample

set. Also, DSC results from Table 6I-1 indicates that LiClO4 concentrations greater than 0.25%

begin to reduce Tc of the polymer, implying disturbance in its crystal phase. For these reasons,

0.25% was seen as the optimal LiClO4 concentration to use in the study.

Fabrication of pure and 0.25% LiClO4 doped P(VDF-TrFE) was the same as that described

in Chapter 6I section 6I.2.2 with DMF replaced by MEK. PVA was dissolved into deionized H2O

by magnetic stirring in a bath of silicon oil on a hot plate. The oil bath was heated to a temperature

of approximately 85-90oC (measured using a thermocouple) to fully dissolve PVA. Total mixing

time for a 5% solid wt. PVA/H2O solution was 4 hrs. The completely mixed solution was then

Figure 6II-2: SEM image of 5-layer sample depicting PVA interfaces and P(VDF-TrFE) copolymer layers.

144

rested for time spans up to 1 week prior to use. This procedure was determined to be most effective

in the elimination of bubbles from the PVA/H2O solution and yielded best results when spin

casting. Multilayered films of P(VDF-TrFE)/PVA were fabricated by an additive spin cast

procedure. First an 8% solid wt P(VDF-TrFE) solution was deposited onto a silicon wafer at

600rpm for 15s and dried at 100oC plat temperature for 15 min. Next, PVA solution was deposited

using a wafer spin speed of 2000 rpm for 20s and then dried under the same conditions. The process

was repeated a total of 7 times to produce a sample set consisting of 3 layers of PVA 0.56μm thick

and 4-layers of copolymer 2.40μm thick. Samples were freeze fractured in liquid nitrogen so their

cross section may be imaged by SEM. Figure 6II-2 shows the fractured cross section depicting

well defined P(FDF-TrFE) and PVA regions of uniform thickness where interfaces created via

additive spin casting are better defined than those through hot-pressing PVDF in Chapter3,

Figure 3-3.

6II.3 RESULTS AND DISCUSSION

The main purpose of this section is to elucidate the effect of the dielectric interfaces in low

frequency conduction at low and high fields. The experimental results of a layered film are

compared to a 1-Layer control film of equivalent thickness All films are maintained at ~10 micron

thick regardless of layer count and changes in data are compared with maintaining constant device

volume.

6II.3.1 Differential Scanning Calorimetry

Pure P(VDF-TrFE) and 0.25% LiClO4 doped P(VDF-TrFE) samples were measured using

DSC to compare thermal properties to MEK cast films with DMF cast films in Chapter 6I section

6I.3.1. The same measurement parameters as section 6I.3.1 were used. The results of Tc / Tm

location and integration for cast with MEK are presented below in Table 6II-I.

Table 6II-I: DSC results for the first heating of 10 micron P(VDF-TrFE) without (pure) and with 0.25% LiCLO4

included. The solvent used was MEK, dried for 15 min at 100oC and annealed for 24 hrs at 142oC under vacuum.

Sample Average Tc

(oC) Int Tc (J/g)

Average Tm

(oC)

Int Tm

(Crystal %)

Pure 101.6 ± 0.3 23.4 ± 1.4 151.5 ± 0.3 32.8 ± 1.7

0.25% 105.5 ± 0.2 24.6 ± 0.4 152.1 ± 0.2 34.5 ± 0.6

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Both the pure and 0.25% doped films display similar behavior to those cast from DMF; however,

a slightly higher % crystallinity is calculated for the 0.25% film in comparison to those discussed

in Chapter 6I section 6I.3.1. A more noticeable difference is seen in behavior of Tc for the pure

sample. Table 6II-I indicates the Tc of the pure film decreased by 9oC when cast using MEK in

comparison to films cast with DMF. Similarly the integrated signal associated with the beta phase

is stronger (23.4 J/g in comparison to 15.9 J/g). Addition of LiClO4 causes an increase in Tc to

105.5oC however this is below that measured for films cast with DMF (109oC). Considering the

effect of Tc on material impedance behavior and EC model parameter estimation (Chapter 6I)

thermal characteristics of P(VDF-TrFE) cast using MEK will be considered for the remainder of

this section.

6II.3.2 Dielectric and Impedance Spectroscopy

The frequency dependent capacitance and loss of pure 10 μm films were measured in the

range of 10-1 – 105 Hz between 25oC – 110oC in similar fashion to films discussed in Chapter 6I

section 6I.3.2. The permittivity and loss tangent are calculated from real and imaginary

capacitance data and shown in Figure 6II-3. Permittivity of samples cast from MEK are within

the range of those reported for copolymer cast from DMF in section 6I.3.2. In films cast from

MEK, a fully resolved loss tangent peak is observed with 1 – 10 Hz at T = 100oC ≈ Tc of the film

(correlating to Tc in Table 6II-I). This is a similar feature observed in loss tangent data for DMF

cast films within the same frequency range at T = 110oC ≈ Tc. In both materials, features of the

dielectric response depend on transition temperature of the crystalline phase from its ferroelectric

to paraelectric form, signifying the β-phases importance on conduction regardless of solvent

choice.

Impedance spectroscopy is used to analyze the effect of PVA barrier interfaces on ionic

conduction in layered films containing 0.25% LiClO4 in P(VDF-TrFE) layers. Measurements as a

function of temperature are performed on a 0.25% LiClO4 doped 1-layer film and compared to a

4-layer sample set of equivalent total thickness presented in Figure 6II-4a, 4b, and 4c. Addition

of Li+ ionic carriers into the material results in 2 orders of magnitude increase in the low frequency

polarization response as seen in the permittvity between 0.1-1Hz, as well as increase in tan(δ)

relaxation peak magnitude and frequency. This outcome is expected given results reported in

Chapter 6I.3.2 and implies conduction at low frequency is dominated by impurity ion transport

146

Figure 6II-3: permittivity and loss tangent for pure 10μm copolymer cast from MEK. A strong relaxation peak in the

loss tangent is observed between 1-30 Hz in the vicinity of Tc.

Figure 6II-4: a) permittivity and loss tangent for a 0.25% doped 1-layer, b) permittivity and los tangent for 0.25% 4-

layer. Integration of interfaces reduces low frequency polarization as well as lowers relaxation frequency and tan(δ)

peak magnitude. c) M’’ relaxation of doped P(VDF-TrFE) compared with pure PVA.

147

through the material’s bulk. The addition of PVA interfaces into the dielectric impacts the

dielectric response in the following ways:

1) The Composite Effect: PVA contributes to composite polarization at high temperatures and high

frequencies. This effect can be clearly portrayed by observing the imaginary portion of the

complex modulus (M’, M’’) response of a 1-layer 0.25% doped film superimposed on the 1-layer

pure PVA film shown in Figure 6II-4c.

2) The Blocking Effect: at low frequency between 0.1-1Hz, the dominating contributing conduction

mechanism is due to ionic migration through the film. In the 1-layer sample (Figure 6II-4a),

εr=2.5x105 at 110oC and 0.1Hz, indicating polarization due to Li+ accumulation at the electrode

dielectric interface. Layered structures (Figure 6II-4b) exhibit a low frequency εr=4.7x103, which

is two orders of magnitude reduced relative to the 1-layer control sample. A similar phenomenon

is observed in the tan(δ) of layered films where both relaxation peak frequency and magnitude is

lowered. The lower relaxation frequency corresponds to longer ionic relaxation time that suggests

Li+ impurity ion mobility is reduced by the addition of PVA barriers. Similar phenomena are

reported in Zhou et al. [15] that demonstrates lowered tan(δ) relaxation frequency in layered

P(VDF-TrFE)/PMMA/PC fabricated using a multilayer extrusion technique.

The AC conductivity is related to εr and tan(δ) by equation 6I-1 and is used to calculate

the conductivity of 1-layer and 4-layer doped films at 100oC in Figure 6I-5. The conductivity for

the 1-layer sample is in the same range as the 0.25% doped 1-layer film measured in Figure 6I-3.

Figure 6II-5: AC conductivity at 100oC calculated using equation 6I-1 for a doped 1-layer, PVA film, and doped 4-

layer. Conductivity is reduced by two orders of magnitude at low frequency in the layered film relative to the 1-layer

control.

148

The conductivity for the 1-layer pure PVA sample lies beneath that of doped P(VDF-TrFE)

following the same general trend in reduction as a function of frequency. The composite material

behaves very differently than either constituent material alone. There is no difference between 1-

and 4-layered films at high frequency between 104-105Hz because the 4-layer sample is

predominantly P(VDF-TrFE) based (~82% by volume) and loss through the film is dominated by

dipole rotation polarization. At low frequencies where Li+ migration dominates conduction, the

conductivity in layered films is significantly reduced. It is concluded that the interface plays a

significant role in limiting conduction due to impurity ion migration by reducing ionic mobility

and blocking at internal P(VDF-TrFE)/PVA interfaces.

6II.3.3 Equivalent Circuit Modeling

Data analysis from the previous section suggests the presence of PVA interfaces limits Li+

ion conduction through blocking at the interface. In this section, an EC is developed (Figure 6II-

6a) which accounts for the series combination of impedance contributions from bulk P(VDF-

TrFE), bulk PVA, and electrode polarization caused by ionic charge build up. The model is fit to

impedance spectra over the temperature range 40oC – 110oC capturing the evolution from intrinsic

bulk polarization to extrinsic impurity ion transport at low frequency and high temperature. A

similar analysis was done in Chapter 6I. The complex modulus (M’M’’) is considered because of

its sensitivity to both P(VDF-TrFE) and PVA bulk relaxations at high frequency. Figure 6II-6b

shows M’ and M’’ at T=40, 80, and 110oC with EC model fits super imposed on the raw data to

demonstrate the model’s ability to capture the behavior of the composite at all frequencies and

temperatures. Due to the two bulk EC components in series, both P(VDF-TrFE) and PVA

relaxations are represented by the model. To determine the model’s ability to accurately predict

composite behavior, the permittivity of the model is calculated from the series combination of

CPE2 and CPE5 fit estimations. Considering total series capacitance behaves as the reciprocal of

added capacitive responses, and the layer thickness of P(VDF-TrFE) and PVA layers are

equivalent for each material, the total capacitance of the EC can be derived as the following

equation:

𝐶𝐶𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 =휀𝑃𝑉𝐷𝐹휀𝑃𝑉𝐴휀𝑜𝐴

3𝑡𝑃𝑉𝐴휀𝑃𝑉𝐷𝐹 + 4𝑡𝑃𝑉𝐷𝐹휀𝑃𝑉𝐴 (6𝐼𝐼 − 1)

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Figure 6II-6: a) EC used in fitting the composite impedance data. The model takes into account bulk responses from

doped P(VDF-TrFE), pure PVA and electrode/dielectric blocking polarization. b) EC fits to 4-layer M’ data at 40oC,

80oC, and 110oC. Good qualitative fits enforce model accuracy.

where εPVDF and εPVA are computed by taking the estimated values of CPE2 and CPE5 along with

total P(VDF-TrFE) and PVA layer thicknesses (tPVDF and tPVA) respectively and inserting into the

equation εr=Ct/εoA. The composite’s permittivity is then calculated by taking into consideration

CComp and total thickness of the multilayer assembly tComp by the following relationship:

휀𝑟,𝐶𝑜𝑚𝑝 =𝐶𝐶𝑜𝑚𝑝𝑡𝐶𝑜𝑚𝑝

휀𝑜𝐴 (6𝐼𝐼 − 2)

CPE2 and CPE5 estimates from the model are plotted in Figure 6II-7a and permittivity estimates

using Equation 6II-2 are compared to those calculated directly from C’ measurements. It is noted

that estimates for CPE5 corresponding to PVA capacitance contributions are an order of magnitude

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Figure 6II-7: a) CPE2 and CPE5 EC outputs corresponding to P(VDF-TrFE) and PVA bulk capacitances as a function

of temperature are shown (left) and converted to permittivity (right). b) 1-layer blocking CPE estimations (left) and

4-layer blocking CPE estimations (right).

higher than those of CPE2 corresponding to P(VDF-TrFE). This is due to the geometry of PVA

relative to P(VDF-TrFE): total PVA layer thickness is ~1.7μm while P(VDF-TrFE) is ~9.6μm

causing a near order of magnitude disparity of capacitance, considering the relation for capacitance

C= εrεoA/t. The frequency of 10kHz is chosen to compare measured and modeled permittivities

because this frequency showed the most stable measurements of capacitance for P(VDF-TrFE),

PVA, and the composite samples. It is found that the estimated permittivity for the composite is

comparable to that of the measured value, reinforcing the ability of the EC model in Figure 6II-

6a to describe the behavior of the 4-layer system.

The EC element CPE1 represents blocking/interfacial polarization. Figure 6II-7b shows

the behavior of the blocking CPE’s Q value and its imperfection constant n (see equation 6I-5) as

a function of temperature for a 1-layer 0.25% doped control sample and its 0.25% 4-layer

equivalent. In both cases, the value of n is between 0.5 and 1.0 correlates to electrode/polymer

interfacial roughness and heterogeneous charge distribution at the interface. This is similar to

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results reported in Chapter 6I Figure 6I-10. At low temperatures, the blocking CPE is not

required to accurately fit the impedance spectra. At high temperatures, the blocking CPE fit

estimations are required to obtain a good fit to the impedance data and progressively increase as a

function of temperature for the 1-layer film reflecting increased electrode polarization at the

electrode/dielectric interface. The 4-layer films show a similar behavior however Q values are

estimated two orders of magnitude lower in comparison to the 1-layer control. This is consistent

with low frequency permittivity measurements shown in Figure 6II-3 that exhibit two orders of

magnitude reduced low frequency polarization at high temperature. At high temperatures, the

response of the blocking CPE in layered films plateaus. This can be related to a reduced presence

of charge at the dielectric/electrode interface given the fundamental relationship for capacitance

that is charge divided by voltage (C=Q/V). Since the ratio of Li+ carriers to P(VDF-TrFE) is

maintained between the 1- and 4-layer films, reduced charge at the electrode/dielectric interface is

reasoned to be due to charge blocking and deflection at PVA barrier interfaces.

6II.3.4 Thermally Stimulated Depolarization Current Measurements (TSDC)

6II.3.4.1 TSDC on 1-layer P(VDF-TrFE)

Initial measurements focused on understanding 1-layer control sample sets of pure and

0.25% doped films. A parametric study was performed where Ep and the heating rate of the TSDC

experiment were systematically changed between 10 – 30MV/m and 5 – 1oC/min respectively. All

samples tested were spin casted from MEK and were 10μm in total thickness.

The depolarization current as a function of temperature for pure 1-layer P(VDF-TrFE)

films for Ep ranging from 10 – 30MV/m are shown in Figure 6II-8a, 8b, and 8c. Each graph is

plotted on both a linear and logarithmic axis to accentuate low current peaks otherwise not visible

due to scaling. A prominent shoulder in the current density that increases in magnitude with

increasing poling field strength between 30oC < T < 55oC is visible on graphs scaled

logarithmically. The origin of this feature is associated with interfacial polarization at the electrode

during poling due to its dependence on Ep as well as its vicinity to T ≈ Tp = 50oC. For temperatures

between 60oC and 125oC, there are two overlapping current peaks corresponding to separate

depolarization processes. Research by Faria et al. [214] found similar TSDC signals in P(VDF-

TrFE) to those in Figure 6II-8. In this work, the low temperature peak for P(VDF70/TrFE30) is

attributed to a ferroelectric-ferroelectric phase transition and the high temperature peak

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Figure 6II-8: Depolarization current density for pure 1-layer 10μm films at a) Ep=10MV/m, b) Ep=20MV/m, and c)

Ep=30MV/m. All measurements were performed using tp=15min, Tp=50oC and heating rate 5oC/min.

corresponds to a ferroelectric-paraelectric phase transition related to Tc of the material. The origin

of primary and secondary β-phases of copolymer has been investigated in past work by Gregorio

Jr. and Botta [161] where the ratio of each phase developed depends on the vicinity of the

crystallization temperature to the crystallization onset temperature and melt temperature of the

alpha phase To. Although this special temperature To is not well defined for this material system,

Gregorio Jr.’s and Botta’s work suggests 1-layer films have been crystallized above To causing the

development of two β-phases with unique TSDC contributions.

The peaks in Figure 6II-8 do not exhibit repeatable maximum current magnitudes,

however their maximm temperatures (Tm) are unchanging within each sample set. For Ep between

10 and 20 MV/m, a low temperature peak is situated within the range of 83 – 86oC and high

temperature peak around 103 – 105oC (in the vicinity of Tc measured via DSC). Similarities

between the measured data and results from Faria et al. [214] suggest the high temperature TSDC

features in pure copolymer are predominantly due to molecular relaxations associated with

conformational changes within the crystal phase of the material. This is supported when the electric

field is increased to 30 MV/m (approaching coercive field Ec = 50MV/m) causing peak amplitude

increase. [215]. It should be noted that results obtained by Faria et al. [214] involve pellets pressed

at high temperature while samples in this dissertation involve the use of solvent. In this case,

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depolarization from impurity ions cannot be neglected and could account for dissimilarity between

samples.

The heating rate was then reduced by half to 2.5 oC/min for an Ep = 20MV/m. It was found

that the magnitude of depolarization current density was unchanged, however a slight shift in the

high temperature peak occurred from the range of 103-104oC to a range of 107-109oC. Shifting in

the peak allows for greater distinction between low and high temperature features, enabling peak

fitting using peak deconvolution techniques. Peak fitting implemented Bucci-Fieschi theory which

describes depolarization currents in TSDC experiments arising from orientational dipole rotation

events as a function of temperature.17 The fitting procedure to perform peak deconvolution was

performed using a custom R-Studio script by a process described in Chapter 2 section 2.4.3. The

procedure begins by fitting the strongest signal. Parameter estimates of τo (relaxation time), Po

(polarization) and Ψ (activation energy) are then used to generate a function over the entire range

of the convoluted peak from which raw data can be subtracted, leaving the low temperature peak

without contribution from the high temperature signal. This deconvoluted spectrum is then fit and

parameter estimates for both signals are reported.

Figure 6II-9 shows the result of peak fitting for 3 samples along with fit parameter

estimations using the 2.5 oC/min, Ep=20MV/m, Tp=50oC, tp=15min measurement condition. Initial

fitting was performed on the most prominent signal which was the high temperature peak

corresponding to Tc transition (with the exception of sample 2). Fitting on this current peak shows

a good sum of squares residual of 2.1x10-6 A/m2 to 7.0x10-6 A/m2 which is an order of magnitude

below the smallest values present in the TSDC spectrum within the temperature range 60oC –

140oC. The activation energy estimated for high temperature peak associated with the ferroelectric-

paraelectric phase transition ΨF-P was estimated in the range of 1.8eV to 2.1eV with characteristic

relaxation time τo ranging from 7.74x10-28s to 3.51x10-24s, which are in the same range reported

for corona polled P(VDF-TrFE) [216]. Large values of activation energy are typically attributed

to space charge contributions to the TSDC signal and observed in work done by Fedosov et al.

[216], Gaur [126], and Indolia [217], however good fits using Bucci-Feischi theory suggest high

ΨF-F estimates reflect large scale motion associated with crystal phase transition. Similar results

have been recorded for the α relaxation of epoxy in both TSDC and dielectric spectroscopy [218].

17 Specifics regarding Bucci-Fieschi theory including equation and general derivation with annotated assumptions can be found in Chapter 2

section 2.3.3.3 while R-Studio Script used in peak fitting is found in Chapter 2 section 2.4.3.

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Figure 6II-9: Fit TSDC spectrum using Bucci-Fieschi equation along with parameter estimates for entire 1-layer

sample set undergoing TSDC with the following parameters: Ep=20MV/m, Tp=50oC, tp=15min, and scan rate

2.5oC/min. Individual fit components along with total synthetic spectrum are shown.

Peak deconvolution is then performed using parameter estimates generated by fitting the

strongest signal to expose characteristics of the weak signal. The low temperature peak returned

lower parameter estimates for ferro-ferroelectric phase transition ΨF-F and larger estimates on τo

that are closer to the range of those reported for lightly doped PVDF/BaTiO3 nanocomposite

systems reported by Gaur [126]. The sum of squares calculation of the low temperature peak fit

however is calculated to an average of 2.30x10-5 A/m2 +/- 3.36x10-5A/m2 across the sample set

which is larger than the lowest current signals measured within the fit temperature range. This is

indictive that Bucci-Fieschi theory inadequately describes the ferro-ferroelectric phase transition

depolarization process. Characteristics of the ferro-ferroelectric depolarization peak that may

contribute to poor fit results could be a distribution in relaxation times associated with transition

of the crystal phase, or more likely the existence of a third peak not visible in the measured

spectrum that resides within the temperature range associated with space charge depolarization

events.

Addition of 0.25% LiClO4 in 1-layered films has a significant impact on the measured

TSDC and is displayed in Figure 6II-10a-10c for ramp rates 5, 2.5, and 1oC/min at Ep=20 MV/m.

Unlike pure P(VDF-TrFE) the doped films are characterized by a broad depolarization current

peak that dominates the signal spanning 60oC – 115oC. Generally, the peak maximums are

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Figure 6II-10: Depolarization current density for 0.25% doped 1-layer 10μm films at heating rates a) 5oC/min, b)

2.5oC/min, and c) 1oC/min. All measurements were performed using tp=15min, Tp=50oC and Ep=20MV/m.

unchanging in temperature given individual measurement conditions indicating the sample sets are

characteristic of a single relaxation mechanism. The addition of ions produces an order of

magnitude increase in depolarization current density for a scan rate of 5oC/min relative to pure

control films. Reducing the scan rate causes a decrease in the magnitude of the current measured

which is a distinct characteristic of doped films relative to pure. Unlike pure films, there was no

definitive change in measured current density by increasing Ep from 20MV/m to 30MV/m,

indicating the TSDC of doped 1-layered films is dominated by Li+ impurity carrier migration

instead of depolarization events associated with P(VDF-TrFE)’s crystal phase. It should be noted

that irregularity and asymmetry in the TSDC of doped films prevents accurate fitting due to

phenomena pertaining to space charge depolarization in electrets [215], and thus the analysis of

doped 1-layer and 4-layer films in the next section will be done by comparison.

6II.3.4.2 TSDC on 4-layer P(VDF-TrFE)

Incorporation of thin PVA into the P(VDF-TrFE) structure is first analyzed in pure films.

Figure 6II-11a and 11b shows the TSDC of a pure 1-layer sample set compared to a pure 4-layer

sample set of equivalent thickness measured with Ep=20MV/m and heating rate of 2.5C/min.

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Figure 6II-11: Depolarization currents for a) pure 1-layer sample set and b) pure 4-layer sample set. Experimental

TSDC conditions are Ep=20MV/m, Tp=50oC, tp=15min and a heating rate of 2.5oC/min for both sets.

Decrease in the high temperature depolarization current peaks occurs by an order of magnitude in

layered films relative to the pure control sample. The highest temperature peak associated with

ferro-paraelectric phase transition in the material decreases from 1.8x10-4 A/m2 in the pure 1-layer

to 4.0x10-5 A/m2 in the pure 4-layer composite. This can be explained by considering 3 features of

the composite sample. First, P(VDF-TrFE) individual layer thickness is ~2.40 μm and PVA layer

thickness is 0.56 μm, indicating the total volume of the sample is comprised of only 82% P(VDF-

TrFE). This indicates reduced amount of polarizable material present in composites relative to pure

1-layer control films. The second feature takes into consideration field distribution through PVA

relative to P(VDF-TrFE). This can be done conceptually considering the simplified case of a

multilayered dielectric consisting of two materials where the only free charge density contributions

+/-σ occur at the electrodes. Then the displacement can be related to total charge enclosed in the

system via Gauss’s law:

∫ �⃑⃑� ∙ 𝑑𝑎 = 𝑄𝑒𝑛𝑐 (6𝐼𝐼 − 3)

𝐷 = 𝜎 (6𝐼𝐼 − 4)

Equation 6II-4 can then be related to the electric field E in either material via the following

relationship for a linear dielectric:

𝐸 =𝜎

휀𝑟휀𝑜 (6𝐼𝐼 − 5)

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By equation 6II-5 the ratio of field distributed through the P(VDF-TrFE) relative to PVA becomes

the ratio of εPVA/ εP(VDF-TrFE). This was approximated by using εr measured at 10kHz at 25oC for

each constituent material and is calculated to be 0.58 indicating the electric field drop in the PVA

layer is approximately 2 times larger than P(VDF-TrFE). Given depolarization current’s

dependence on Ep observed in pure 1-layer films discussed in section 6II.3.4, field reduction

within P(VDF-TrFE) layers as a result of integrated PVA must be considered as a potential

contributor to reduced currents measured in the TSDC Figure 6II-11. The third feature of the

composite is considered by combining results from impedance spectroscopy to TSDC data in

Figure 6II-11. Current suppression is most extreme for the peak occurring between 86-88oC,

where integration of PVA barrier layers cause the extinction of the ferro-ferroelectric

depolarization peak. TSDC fitting performed in section 6II.3.4.1 indicates that the depolarization

current peak in this temperature range is poorly described using the Bucci-Fieschi equation and is

ultimately linked to the likely hood of a conflicting relaxation process occurring in the same

temperature range. Considering the breadth of Li+ peaks observed in ionically doped samples, as

well as reduced ionic polarization in layered films initiating at T=90oC measured by EC fitting in

section 6II.3.3 Figure 6II-7b, the suppression of TSDC peaks in pure 4-layer composites are

believed to be influenced by the blocking of migrating impurity ions. This is supported by a

prominent peak occurring at low temperatures around Tp=50oC suggesting the presence of

enhanced interfacial polarization in layered samples relative to the 1-layer control.

The effect of interfaces on ionic depolarization in layered films is more thoroughly

investigated by analysis of the doped 4-layer composite sample set. Figure 6II-12a shows 4-layer

doped samples in comparison to the 1-layer doped control sample set for the measurement

conditions Ep=20MV/m and heating rate 2.5C/min. The current in doped layered films is reduced

by nearly an order of magnitude relative to their 1-layer control group, displaying current densities

in the same range of the low temperature peak measured for pure 1-layer films. It is also noted that

signals spanning a broad temperature range characteristic of doped 1-layer films is not featured by

layered films suggesting Li+ contributions to the depolarization current are suppressed in layered

films. Figure 6II-12b shows a single sample characteristic of the 1-layer pure film set in

comparison to a characteristic sample from the 4-layer doped sample set. Unlike the pure 1-layer

sample set that exhibits two depolarization features, doped layered films exhibit a single well-

defined peak centered at 95oC caused by Li+ ion migration. This comparison reveals impurity ion

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Figure 6II-12: Depolarization currents for a) 1-layer doped sample set compared to 4-layered doped sample set and

b) 1-layer pure sample compared with 4-layer doped sample. Experimental TSDC conditions are Ep=20MV/m,

Tp=50oC, tp=15min and a heating rate of 2.5oC/min for both sets.

contributions to the TSDC is centered between the ferro-ferroelectric and ferro-paraelectric

depolarization peaks in the pure material. This observation explains Bucci-Fieschi theory’s

inadequate representation of low current peaks in the TSDC of pure copolymer: interference from

impurity ion depolarization.

6II.3.5 High Voltage Dielectric Breakdown

Breakdown experiments of pure 1-layer P(VDF-TrFE) film and a pure 4-layer samples

done using the procedure described in Chapter 2 section 2.3.3.4. F Dielectric breakdown results

are dependent on the total thickness of the sample tested [136] [139], thus the thickness of 1-layer

and 4-layer samples used were spin cast to near equivalent thicknesses of 9.6μm and 11.0μm

respectively. The total number of breakdown events was n=30 for both films and the results are

plotted in the Weibull plot in Figure 6II-13a. Both the 1-layer and 4-layer films display a bimodal

Weibull distribution, suggesting the presence of defect-controlled breakdown events at low electric

field and breakdown events associated with the material’s intrinsic behavior at higher fields. This

is a phenomenon observed in the similar material P(VDF-TrFE-CTFE) in both electroded and

unelectroded samples undergoing ball and plate dielectric breakdown under the same IEEE

standards [128]. In the case of layered films,

159

Figure 6II-13: High voltage dielectric breakdown Weibull analysis for a) all breakdown fields exhibiting bi-modal

Weibull distributions separating defect and intrinsic type breakdown mechanisms and b) 7 lowest Ebd events analyzed

under IEEE standards for small sample sizes.

the dielectric breakdown at the lower tail of the distribution is most significantly impacted where

a substantial gap in ln(Ebd) occurs. Linear regression was performed on the first 7 data points in

each distribution and plotted in Figure 6II-13b. The R2 values for pure and layered films were

0.91 and 0.95 respectively, which satisfies the minimum R2 criteria of 0.91 for a sample population

of 7 as defined by IEEE standards. This indicates that the low field values can be described

sufficiently using Weibull statistics for analysis. Analysis was performed using a procedure

outlined for small data sets of singly censored data found in IEEE standards for statistical analysis

of dielectric breakdown [127]. The estimated modulus (β) and characteristic breakdown strength

(α) for the 1-layer and 4-layer defect driven distribution are listed adjacent to Figure 6II-13b in

table format. With the addition of interfaces, estimated β is calculated to increase by 59% from 23

(1-layer) to 37 (4-layer). Similarly, a 27% increase in α is also calculated from 394MV/m (1-layer)

to 501MV/m (4-layer). The increase in modulus and characteristic breakdown strength indicate

interfaces have a significant effect on defect driven breakdown events. In the context of impurity

ion blocking observed in impedance spectroscopy and TSDC in sections 6II.3.2-6II.3.4, layers

can be viewed as barriers to defect propagation through the dielectric, limiting the effect of defects

160

on high field performance by their deflection at barrier interfaces. It should be noted that field

intensity reduction in P(VDF-TrFE) afforded by the presence of PVA should also be considered

in the analysis of breakdown results (briefly discussed in section 6II.3.4.2) and should be

addressed in future work.

6II.4 CONCLUSIONS

An additive spin casting procedure was developed to fabricate P(VDF-TrFE)/PVA

multilayered laminates with reproducible layer thickness. SEM cross sections of P(VDF-

TrFE)/PVA layered dielectrics exhibit a more definitive interface than hot-pressed laminates

(Chapter 3). Thermal analysis of P(VDF-TrFE) films cast from MEK measure a decrease in the

Tc of 9oC in the pure material and 4oC in the doped films indicating the ferroelectric phase is

affected by solvent used to cast films.

Impedance spectroscopy captures the effect of the interface on low frequency conduction

in two ways: 1) blocking polarization at low frequency is decreased by 2 orders of magnitude and

2) tan(δ) relaxation frequency is lowered reflecting reduced ionic mobility in layered films. AC

conductivity is also impacted in layered films, exhibiting a two order of magnitude reduction in a

doped layered film relative to the 1-layer control. An EC model is developed that captures the

impedance response of both doped P(VDF-TrFE) as well as PVA interface layers and can be used

to predict material properties with high accuracy. Analysis of blocking circuit element estimates

reveal that 4-layered films reduce electrode polarization by two orders of magnitude, reinforcing

observations made on dielectric permittivity and loss data at high temperature and low frequencies.

TSDC on pure P(VDF-TrFE) revealed depolarization events associated with two β-phase

transitions: ferro-ferroelectric transition at 84oC<T<86oC and ferro-paraelectric transition in the

vicinity of the material’s Tc measured by DSC. High temperature peaks at Tc were described well

using Bucci-Fieschi theory, coinciding well with the assumption this signal occurs due to dipole

depolarization associated with the ferroelectric crystal. The low temperature peak was separated

from the raw signal implementing a peak deconvolution technique however ultimately returned

poor fits using the Bucci-Fieschi equation. TSDC on pure 4-layer films show significantly

suppressed depolarization current densities which is through to be due to a combination of 1) the

blocking of low levels of impurity species distributed thought the material and 2) composite effects

including reduced volume% of polarizable P(VDF-TrFE) and increased electric field drop in the

161

PVA layers during poling. The addition of Li+ impurity carriers enable more effective comparison

between 1-layer and 4-layer composites. Depolarization currents in doped 4-layer films were

measured to be an order of magnitude lower than the doped 1-layer control indicating Li+ blocking

at PVA interfaces.

Comparison to pure 1-layer films with the 4-layer doped group show a depolarization peak

situated between the ferro-ferroelectric and ferro-paraelectric peak caused by Li+ migration. This

demonstrates that high temperature depolarization in P(VDF-TrFE) TSDC is caused by a mixture

of β-phase crystal transitions combined with impurity ion depolarization contributions. This is in

good agreement with fitting results that show poor results when Bucci-Fieschi theory is applied to

low current level broad peaks at 84oC-86oC.

Finally, dielectric breakdown on pure 1-layer and pure 4-layer films of equivalent thickness

was performed. Results show bimodal Weibull distributions for both films indicating defect and

intrinsic type behavior mechanisms at play in both films. The defect dominated breakdown

mechanism showed most significant effect due to layering and is described well using Weibull

statistics. Statistical Analysis intended for small sample sizes indicate increased Weibull modulus

and characteristic breakdown strength increase by 27%, suggesting that internal barrier layers

within the dielectric mainly block and deflect defect propagation. This conclusion agrees well with

results from impedance spectroscopy, EC modeling and TSDC which demonstrate strong impurity

ion species blocking at internal PVA interfaces.

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CHAPTER 7

CONCLUSIONS AND FUTURE WORK

7.1 CONCLUSIONS

In Chapter 1 of this dissertation, a brief history of capacitor technology is presented and

the performance criteria for polymer-based capacitors are reviewed. Various attempts at achieving

high energy density in polymer-based dielectrics by targeting their low permittivity are discussed.

Alternative approaches for improving dielectric breakdown strength in polar organics are also

reviewed. The chapter concludes with a description of the research goals and a general outline of

the thesis document.

Chapter 2 provides an in-depth description of material processing, characterization

equipment, and analytical techniques used in this research. Multilayered laminates were fabricated

via hot-pressing and spin casting techniques. Spin casting was found to produce films with greater

repeatability, control, and uniformity. The material processing section is concluded with an

overview of plasma surface modification and electrode deposition techniques. Each piece of

equipment used in chemical, structural, and electrical analysis is listed with a cursory explanation

of underlying fundamental physics required to understand its purpose. Greater detail is provided

for equipment that this dissertation relies on most heavily. The last section of this chapter provides

a description of analytical techniques used in impedance spectroscopy and thermally stimulated

current discharge data analysis.

In Chapter 3, hot-pressing pure PVDF multilayered laminates was explored. SEM

imaging of the cross section of layered films verified the existence of interfaces between hot

pressed films. High voltage dielectric breakdown using IEEE experimental and statistical analysis

standards were usedn. 1-layer samples exhibited a 415 MV/m breakdown while 2- and 3-layers

increase to 480 and 490 MV/m, respectively. The higher dielectric breakdown strength for

laminates were attributed to barrier effects at internal interfaces and processing defect reduction in

multilayer films with thinner individual layers. It was concluded that in order to continue the study

of role of interfaces on charge transport, total thickness of the dielectric must be reduced while

layer count must be increased. This motivated the start of spin cast film fabrication discussed in

Chapter 4.

163

Chapter 4 presents a plasma surface modification procedure (describes in Chapter 2) for

altering the electrode/dielectric contact chemistry. The intent was to study the impact of electrode

contact properties on high field charge injection of thin films. A considerable amount of surface

chemical and structural characterization is performed as a function of plasma treatment and

annealing. First, polymer surface chemistry is analyzed using XPS for untreated and

50%CF4/50%O2 gas plasma treated thin films. Synthetic peak fitting of the XPS C1s spectrum

indicated the addition of carbonyl C=O groups on treated films. Fitting of the O1s spectrum also

indicated the uptake of CF-O and C-O moieties. It was determined that the treatment time duration

had no effect on the quantity of chemical species detected by XPS; however, annealing after

plasma treatment did affect the ratio of F/C detected. Annealing also impacted surface topology:

films annealed after plasma treatment resulted in a surface roughness equivalent to an untreated

film. This is seen as a procedure that can repair damage done to the surface of the film during

plasma treatment, allowing the surface chemistry to dominate during contact angle and electrical

measurements.

Water contact angle experiments showed a near constant contact angle for various plasma

treatment durations in the post-anneal set, corresponding with constant surface chemistry after

treatment as well as uniform surface roughness measured via profilometry. With copolymer

surface chemistry and structure well understood, electrical analysis involved low field

spectroscopy and I(V) measurements. Plasma treatment had no significant impact on dielectric

constant; however, the resistivity decreased from 8x1011 Ω-m to 0.8x1011 Ω-m after plasma

treatment. The reduced contact resistance was attributed to grafted chemical species. The results

for high field I(V) were similar: leakage current increased after plasma treatment. Electronic

conduction models (Poole-Frenkel theory and Schottky theory) were considered and the dominant

high field conduction mechanism is Schottky emission. Finally, similar work performed by Reddy

[173] were applied to develop a comparative mathematical technique used to extract approximate

barrier height change due to grafted chemical species. The barrier height was lowered by 0.05eV,

causing enhanced emission in plasma treated films. It is posited that the inclusion of acceptor type

states (F and O) to the surface of P(VDF-TrFE) increase hole density at the electrode dielectric

contact, likely causing enhanced hole transport at the electrode dielectric contact.

164

Chapter 518 investigates similar phenomenon as Chapter 4, however using PI as the

material system. Unlike PVDF copolymer, PI is a non-polar high glass transition temperature

material typically considered for high temperature dielectrics. Thus I(V) measurements were

performed as a function of temperature beginning at 25oC and ending at 150oC. I(V) data was

analyzed using a combination of PF, Hopping, and Schottky theories. PF-theory returned

unrealistic estimations of the materials permittivity based on spectroscopy data recorded in

Meddeb et al.[1], suggesting Hopping is more appropriate mechanism for bulk limited conduction

analysis. Hopping analysis was performed by using a bootstrap statistical procedure by which the

behavior of the sample set itself imparts the framework for statistical analysis. It was found that

Hopping theory describes the conduction characteristics well to 100oC, at which point the model

breaks down. TUnlike P(VDF-TrFE), PI has been observed to undergo predominantly electronic

dominated [194] [191] conduction processes. It is determined that the conduction properties of the

material under test play an intimate role in determining the effect of surface chemical modification

on high field conduction.

Chapter 6 is broken into two separate studies: 1) Chapter 6I which focuses on the role of

Li+ impurity ion transport in P(VDF-TrFE) and 2) Chapter 6II which exploits concepts developed

in 6I to study impurity ion transport in Li+ impregnated layered dielectrics.

In Chapter 6I, copolymer films are spin cast with varying wt% of LiClO4 ranging from

0% – 1.0%. DSC measurement indicate that the β-phase is significantly impacted by LiClO4

inclusion into the material, resulting in reduction of Tc from 110oC in the pure film to 104oC in the

1.0% doped sample. Impedance spectroscopy was then used to study dissolved Li+ ion transport

through the film as a function of frequency between 25oC – 110oC. The high frequency behavior

of the samples remained constant as a function of salt% in the film while low frequency

polarization and dissipation increased indicating that ionic contributions to the permittivity are

only active at low frequency. High temperature impedance analysis showed saturation in the

permittivity and fully resolved tan(δ) relaxations, implying the presence of Li+ impurity ion

blocking at the electrode dielectric interface. Observations in the behavior of the impedance as a

function of temperature and frequency along with the known P(VDF-TrFE) material structure were

used to develop an EC model to describe the doped system. Analysis of capacitive circuit elements

18 Data acquisition for LI I(V) analysis provided in Chapter 5 was performed in a separate study by Meddeb et al. [13] independent of the

mathematical analysis provided in this dissertation.

165

as well as resistive circuit elements determines that Li+ interactions with the crystalline/amorphous

interphase region limit bulk transport at low frequency. In the quasi DC regime at high

temperatures, the impedance is dominated by Li+ polarization at the electrode dielectric interface.

In this regard, low frequency and high temperature conduction in doped P(VDF-TrFE) films are

found to: 1) show space charge conduction mechanisms similar to those reported in literature for

a wide variety of polymer dielectric materials (Table 1-III), 2) be controlled by quantity of LiClO4

introduced into the films and 3) be dominated by interfaces in the bulk of the film

(amorphous/crystalline interphase) as well as the electrode/dielectric contact interface.

Chapter 6II begins with the establishment of processing protocol used to fabricate

multilayer copolymer films with PVA barriers. SEM imaging of the film’s demonstrates superior

uniformity as well as repeatability in layer geometry relative to the hot-pressing technique

discussed in Chapter 3. Impedance spectroscopy captured the effect of PVA interfaces on low

frequency conduction in two ways: 1) decreasing electrode/dielectric blocking polarization by two

orders of magnitude and 2) lowering tan(δ) relaxation frequency. Both outcomes suggest the

deflection of Li+ carriers at low frequencies prevent substantial charge build up at the

electrode/dielectric interface. An EC model is developed that captures the impedance response of

both doped P(VDF-TrFE) as well as PVA interface layers. Analysis of blocking circuit element

estimates reveal that 4-layered films reduce electrode polarization by two orders of magnitude,

reinforcing observations made on dielectric permittivity and loss data at high temperature and low

frequencies. TSDC measurements were introduced as a method to investigate charge transport at

elevated electric fields and effective DC frequencies. The TSDC of pure 4-layer films result in

reduced depolarization currents at high temperatures and show an additional low temperature peak

centered around Tp=50oC indicating interfacial polarization in layered films. Addition of Li+

increases the depolarization current by an order of magnitude in 1-layered doped films, however

similarly doped 4-layer films display current densities on the order of pure 1-layer films. Finally,

dielectric breakdown reveals both intrinsic and defect breakdown behavior in 1 and 4-layer

samples. Weibull analysis for small sample sizes 5<n<15 is performed on the defect related

distribution, reporting an increase in Weibull modulus by 60% and characteristic breakdown field

by 27% in layered films. The analysis suggests that internal barrier layers within the dielectric

mainly block and deflect extrinsic related conduction mechanisms and reduces their impact on the

dielectric’s electrical performance.

166

7.2 SIGNIFICANT CONTRIBUTIONS

Throughout the completion of this work, the following contributions were made to the field

of dielectrics for high energy storage high powered electrical insulation:

1) Effect of Plasma Treatment on High Field Performance: A significant contribution of this

work was to systematically investigate the effect of chemical surface modification on

polymer surface structure and on high field properties. In this study, it was found that both

polymer surface chemistry and surface texture are altered by the application of plasma

treatment. The application of a thermal anneal at 142oC for 24 hr post plasma treatment

restored the surface roughness to that of the untreated control while maintaining the

modified surface chemistry. To the best of my knowledge, this processing procedure has

not been implemented in other investigations studying interfacial dominated charge

emission. Also, this study compares the behavior of PI to P(VDF-TrFE). Unlike

copolymer, PI is a non-polar low permittivity polymer thought to exhibit conduction of

predominantly electronic carriers instead of holes. Grafting acceptor type O species to the

surface of PI results in suppressed leakage current which contradicts the behavior of plasma

modified copolymer. These findings agree with arguments linking the combination of the

material’s primary charge carrier and surface chemistry to high field interface-dominated

injection.

2) Data Analysis for Surface Modified Thin Films: A considerable effort was put forth in the

development of data analytical techniques to quantify high field leakage current behavior

in polymer dielectrics. One contribution was the development of a mathematical technique

to comparatively quantify material property change in plasma treated thin films using

Schottky theory. In this method, results from ToF-SIMS on plasma treated P(VDF-TrFE)

that approximate the chemically modified surface of the film to be ~1-3nm thick was used

to justify an unchanged Richardson constant for the material. This enabled the derivation

of Schottky barrier height change from two linearized Schottky plots of an untreated film

and plasma treated equivalent. Although this method is not used in any other literature, I

have encountered, similar assumptions were made by Reddy [173] who investigated the

effect of 30nm coatings of PVDF on charge injection properties of InP. Other contributions

have been made on the analysis of high field conduction using non-linearizable conduction

167

theories such as hopping. The hopping equation implemented to describe bulk limited

transport in PI depends on the hyperbolic function, preventing linearization that enables

simple linear regression for fitting. Non-linear regression is required, complicating the fit

parameter estimations. Non-linear models do not have a well-defined relationship between

parameter (in this case d and Jo for hopping theory) and predictor variables (applied field

E) which inhibits the creation of a single hypothesis test that can represent all nonlinear

models. This eliminates the ability to use the “P-values” for statistical interpretation of

goodness of fit. In this work, bootstrap statistics were employed where the behavior of the

sample set itself was used to effectively create the statistics involved in parameter

estimation analysis. Although a widely accepted technique, boot strapping has not been

rigorously implemented to describe nonlinear leakage current behavior in the current

standing body of literature. Introducing this technique can improve how non-linear

processes to small sample sets are treated and improve methodology used to determine

transitions between conduction mechanisms in dielectric materials over broad temperature

ranges in future research.

3) Impurity ion transport in P(VDF-TrFE): As discussed in Chapter 6I, the migration of

impurity ion species in PVDF and in other materials such as XLPE contribute to

degradation at high electric fields at long time scales. This work provides an in-depth

investigation of impurity ion transport through P(VDF-TrFE) which is achieved by doping

with low concentrations of LiClO4.Two unique contributions that stand out relative to other

publications investigating similar phenomena: 1) Ionic concentrations are kept low enough

that the structure of the material remains unaltered, enabling quantification of their

interaction with amorphous and crystalline regions of the bulk. Most literature focuses on

improving the ability to ionically conductors with high ionic concentrations, which causes

structural irregularities unassociated with the pristine material. These changes in

microstructure, including increased porosity or integration of aqueous electrolytes, mask

the response of impurity species on the material’s natural structure. Eliminating this effect

by keeping impurity concentration low allows for an accurate portrayal of how ionic charge

carriers impact electrical performance in dielectrics used for capacitor applications. 2) The

dominant ionic charge carrier is well known both in quantity and chemical species. The

nature of impurity ion species in polymers contributing to extrinsic conduction is

168

ambiguous and dependent on the material and its processing. In the case of solution cast

films, residual solvent is typically assumed to contribute to the response; however,

literature studying conduction through PVDF also cites the possibility that electrochemical

interactions between the electrode and dielectric surface contribute to the available ionic

carriers at high fields [12]. By controlling the quantity of LiClO4 added to the material, the

available quantity of Li+ carriers contributing to conduction can be tailored such that they

dominate low frequency conduction at high temperature. In this sense, I have created a

model material in which impurity ionic conduction can be fundamentally studied to

understand the effect of interfaces on impurity ion transport in layered films.

4) Creation of a Model Material to Understand the Role of Interfaces: the study of interfaces

on high and low field conduction PC/P(VDF-HFP) composites wasinvestigated by

Mackey and Zhou et al. [14] [15]. Mackey et al. hypothesized that increases in dielectric

breakdown strength in layered structures are caused by blocked ionic charge interfaces.

The local electric field is influence by planar discharge and breakdown channel deflection.

Zhou et al. continued this work and reports similar enhancements of dielectric breakdown

strength in layered films, and also notes slower ion migration behavior in films containing

a ‘tie layer” of PMMA between the PC/P(VDF-HFP) interface. My work creates a PVDF

matrix with controlled Li+ dopant concentration of, enabling direct investigation of charge

interaction with PVA interfaces. Unlike either work produced by Mackey et al. or Zhou et

al., this dissertation implements TSDC to bridge results obtained by low field impedance

spectroscopy measurements to results of high voltage dielectric breakdown experiments.

Poling at fields in the range of 20-30MV/m introduces depolarization current from dipole

orientation, electronic charge injection (Chapter 4 and 5), and Li+ impurity ion

migration/interfacial polarization (Chapter 6I and 6II). Simultaneous contribution of these

mechanisms provides a complete picture of how interfaces impact both intrinsic and

extrinsic aspects of low frequency conduction in layered composites. This is the first time

a model system has been developed which controls extrinsic conduction for understanding

charge blocking within a multilayered dielectric. A definitive charge blocking mechanism

was discovered for multilayering with increased resilience to defect driven breakdown

processes.

169

7.3 FUTURE WORK

7.3.1 Tailoring the Electrode/Dielectric Interface for Limited Current Injection

In this dissertation, I showed how electrode/dielectric contact chemistry impacts both low

and high field leakage current in Chapter 4. Grafting of O and F acceptor type chemical moieties

to the surface of the films via reactive plasma treatment causes a reduction in the Schottky barrier

height. It is posited that the introduction of acceptor states promotes the accumulation of carriers

in the valence band near the electrode/dielectric interface and enhances current emission due to

P(VDF-TrFE)’s tendency to conduct holes. This hypothesis is supported by observations found in

PI which is dominated by electronic conduction and had leakage current suppressed by the

introduction of acceptor type chemical moieties at the surface of the film. In order to reduce charge

emission in P(VDF-TrFE) via chemical surface modification, the following should be taken into

consideration:

1) Plasma gas Chemistry: The gas chemistry was limited to a 50/50 mixture of CF4/O2. and

other plasma chemistries were not considered due to the availability of gasses offered in

our facilities. Both O and F have relatively high electron negativities of 3.44 and 3.98

respectively. To move away from electron accepting states, gas plasmas with low electron

negativity elements should be considered, such as hydrogen-based plasma. Similarly, inert

gasses including He and Ar should also be considered to investigate their effect on material

structure in comparison to what was reported in Chapter 4.

2) Additional Surface Coating Techniques: This dissertation limits surface chemical

modification to the use of reactive ion plasma treatments, however other avenues to

achieving thin surface coatings should be considered. Both molecular layer deposition

(MLD) and atomic layer deposition (ALD) processes yield high quality thin film growth

with excellent thickness control. Ultimately this technique can be optimized to produce

high quality thin films of acceptor or donor type materials (such as B or Al doped Si vs. Bi

or P doped Si) at the surface where the effect of surface chemical state on P(VDF-TrFE)

injection can be more rigorously investigated.

7.3.2 Multilayer Dielectric Processing

A major hurdle that needed to be overcome in the processing of multilayer dielectrics was

solvent from consecutive solution depositions destroying the surface of preexisting films. This was

addressed by spin casting a thin film of PVA/H2O on top of P(VDF-TrFE) as a capping layer.

170

PVA’s chemical resistance to the solvent MEK enabled the capping layer to serve as protection to

the P(VDF-TrFE) residing underneath. Despite the practicality afforded by PVA’s chemical

resistance to most solvents, certain aspects of the material should be addressed in future work to

bolster the significance of claims made referring to the “composite effect” in Chapter 6II:

1) Processing P(VDF-TrFE) Thin Films Using MEK: Multilayer laminates cast using MEK

as the solvent for copolymer show porosity in the bulk microstructure. It is believed that

the volatility of MEK causes a rapid dry time that impedes the’s ability to form a dense

copolymer film. Future work should address this issue by re-visiting processing conditions

used to fabricate thin films of copolymer using MEK specifically 1) hot plate temperature,

2) solution weight%, and 3) solvent drying time.

2) Integration of New Barrier Layers: multilayer laminates were realized via a solution

casting technique, however similar to suggestions made in Section 7.2.1, other methods to

creating internal interfaces should be explored. ALD and MLD provide an avenue to create

ultra-thin interfaces on the order of 10’s-1nm thick. Other techniques such as vapor

deposition can also be used to create multilayered dielectrics. For example, Perylene

coating is a common and viable option for interface layer deposition, however it was not

tried in this dissertation. It should be noted that a barrier layer of different chemistry could

support P(VDF-TrFE)/DMF solution deposition, which would reduce copolymer porosity

through solvent selection.

3) Field Distribution in Composites: a conceptual derivation using Gauss’s law and the

equation for electric field in a linear dielectric is used to approximate field drop across the

PVA relative to P(VDF-TrFE) layers. This derivation makes the assumption that 1) the

permittivity of the material is taken at room temperature, 2) free charges do not contribute

to free charge density at the PVA/copolymer internal interface and 3) both PVA and

P(VDF-TrFE) behave linearly with a poling field of 20MV/m and 220V applied across the

composite sample. In order to accurately portray the field distribution, modeling

implementing either COMSOL or ABAQUS should be implemented. In this study, the

geometry and permittivity of P(VDF-TrFE) and PVA layers can be controlled.

Conductivity of the PVDF layer in relation to PVA can also be considered. Similarly, free

charge density at the PVA/copolymer interface can be added in accordance with the amount

of charge introduced by controlled LiClO4 doping. The free charge state on the electrodes

171

can be controlled by a user defined function empirically derived from TSDC results of

layered films as a function of temperature and ramp rate. From this the model can predict

field distribution and as a function of temperature during TSDC, giving an internal “in-

situ” view of laminate depolarization.

7.3.3 Composite Characterization Using High Voltage Techniques

TSDC is able to capture a gamut of charge injection, conduction, and polarization events

simultaneously including injected electronic polarization, interfacial polarization, dipole

orientational polarization, and defect ion polarization. These conduction processes are all captured

using quasi DC frequencies and high poling electric fields, making TSDC a powerful link between

low and high field experiments (in this case linking Spectroscopy to I(V) and dielectric

breakdown). Future work should focus on implementation of TSDC to develop greater

understanding in layered dielectrics, as well as incorporate other high voltage techniques via the

following suggestions:

1) Thorough Investigation of TSDC Experimental Conditions: Depolarization processes in

polled electrets are strongly influenced by the experimental conditions during TSDC. In

this dissertation, heating rate and electric field intensity were varied to understand the

origins of TSDC features for 1-layer and 4-layer films. More work can be done

investigating the effect of Tp and tp. Measuring impedance data as a function of temperature

could capture the conditions that ionic space charge contribution dominates. Then, Tp and

tp can be adjusted to explore the TSDC of the material on time scales above and below the

ionic relaxation as a function of polling temperature.

2) Comparison to Pulsed Electric Acoustic Measurements: In the case of studying the effect

of barrier layers on charge blocking, pulsed electroacoustic measurements (PEA) would

enhance analysis by providing an internal depiction charge distribution of a poled, unpoled,

and de-poled layered composite. Typically, PEA measurements are performed on bulk

films ~100μm in thickness. From a processing point of view, this is easily achievable with

careful selection of solution deposition parameters during spin casting. PEA will capture

the distribution of charges through the films as a function of poling condition. Given

features found in TSDC that give good indication of carrier type (peak location and shape)

and relative quantity (through TSDC peak integration), features measured in PEA can be

easily identified based on location and relative charge quantity. Another attribute of PEA

172

Figure 7-1: Space charge distribution between cathode and anode of INS3-SC1 cable insulation under

60kV/mm stress as a function of measurement time. Packets of positive and negative charge are clearly

resolved [16].

measurement is for the technique’s ability to capture both charge location as well as charge

sign simultaneously. This is exemplified in Figure 7-1 which shows a map of distributed

charge recorded by PEA measurement through the thickness of high voltage cable

insulation exposed to constant 60kV/mm as a function of measurement time. Regions of

positive and negative charge are easily resolved by the technique, and can be applied to

LiClO4 doped PVDF specimens as a method to determine if Li+ ions are the dominating

ionic carrier (as suggested by Tsuchida et al. [197]) or if ClO4- anions are also mobile. It is

expected that significant charge proportional to the quantity of Li+ introduced by doping

will be located at the interface of P(VDF-TrFE) and PVA, however PEA is necessary to

verify the accuracy of the model presented in Chapter 6II Figure 6II-1.

3) Transference Number Measurements: In this dissertation, it is assumed that the main

contributor to low frequency conduction at high temperatures is dominated by the passage

of impurity ions through the bulk of the dielectric. This assumption is made by interpreting

features present in dielectric data and comparing to literature that makes similar claims (see

Table 1-III). The possibility that conduction through the material could be a mixture of

both cations, anions and electronic carriers has not been scientifically tested. In order to

prove conduction under low frequency and high temperature is predominantly ionic,

transference number measurements should be performed in both doped and undoped

dielectric films. Similar analysis has been performed in P(VDF-TrFE) gel electrolytes by

173

Saikia and Kumar [219] that calculates transference numbers within 0.90-0.98 which imply

the conductivity is due to a single ionic carrier. A number of acceptable methods used to

calculate transference numbers in aqueous electrolyte solutions already exist [220] [221]

[222], however measurement in lithium salt doped non-aqueous systems are not well

documented [223]. Currently used methods such as potentiostatic polarization and nuclear

magnetic resonance are typically implemented [224] [225] [226] however reported results

need be interpreted cautiously due to the measurements inherent difficulty. This

measurement will be a powerful tool when combined with PEA measurements, enabling

visual representation of the space charge distribution throughout the dielectric film as a

function of time, but also conclusive evidence the measured charges are purely due to a

single ionic species: Li+ cations or CLO- anions.

4) High Field P-E Loops: Although the dielectric breakdown strength can be related to stored

energy density of the material via equation (1-2), a major assumption that the material is

a linear dielectric in the derivation of this formula renders its use inappropriate for our co-

polymer. Polarization/electric field (P-E) loops are a better way to characterize energy

density of nonlinear dielectrics and P-E can be controlled. In context of this work, these

experiments should be done as a function of both temperature and frequency (related to

Figure 6II-4a and 4b). The ferroelectric hysteresis of doped and undoped 1-layer and 4-

layer films should be measured initially at temperatures and frequencies space charge

polarization is not featured in the dielectric spectrum. This can then be compared to

equivalent measurements under experimental conditions where it is known space charge

dominates the impedance response. Integration of the polarization with respect to field will

return the effect blocking layers have on recoverable energy density and inform on how

charge blocking can be implemented to improve dielectric performance.

174

APPENDIX A

Annotated Code for I(V) Nonlinear Regression

The following script was used in the fitting and bootstrap procedure for all hopping

nonlinear analysis. Annotations in the code explaining non-trivial steps are written in green font

and initiated by the # symbol in the code. Comments are not observed by the program when fitting.

R function definitions imperative to the operation of the code are also presented in the comments.

Definitions are taken from a combination of R Documentation, a “Table of Useful R Commands”

found on www.calvin.edu, and user-based forums that were referenced when creating the script.

Procedures are explained in context of PI and PI* explained in the Bootstrap Procedure section

of this document.

Annotated Code

#Loaded Library:

library(nlstools)

#Defined physical constants associated with hopping theory:

q = 1

kb = 8.617*10^-5

t = 298.15

Phi = 0.25

#Compiling raw data:

#vect_E1 – vect_E3 are vectors containing electric fields associated with current measurement in the J(E)

experiments using the function c(a1, a2,…, an). This stores data a1,…,an as a vector of length n. These are considered

“independent variables”

vect_E1 = c(7692307.692, 15384615.38, 23076923.08, 30769230.77, 38461538.46, 46153846.15, 53846153.85,

61538461.54, 69230769.23, 76923076.92, 84615384.62,

92307692.31, 100000000, 107692307.7, 115384615.4)

vect_E2 = c(7692307.692, 15384615.38, 23076923.08, 30769230.77, 38461538.46, 46153846.15, 53846153.85,

61538461.54, 69230769.23, 76923076.92, 84615384.62,

92307692.31, 100000000, 107692307.7, 115384615.4)

vect_E3 = c(7692307.692, 15384615.38, 23076923.08, 30769230.77, 38461538.46, 46153846.15, 53846153.85,

61538461.54, 69230769.23, 76923076.92, 84615384.62,

92307692.31, 100000000, 107692307.7, 115384615.4)

vect_E = c(vect_E1, vect_E2, vect_E3) #creates a vector representing PI set’s independent variables

#y_PI1 – y_PI3 are vectors containing current densities at each field value for samples 1, 2, and 3 respectively. These

#are considered “dependent variables”.

y_PI1 = c(1.30E-08, 1.45E-07, 2.71E-07, 4.05E-07, 5.72E-07, 7.06E-07,

8.84E-07, 1.05E-06, 1.27E-06, 1.54E-06, 1.86E-06, 2.22E-06,

2.74E-06, 3.27E-06, 4.03E-06)

y_PI2 = c(6.74E-08, 1.46E-07, 2.27E-07, 3.25E-07, 4.08E-07, 5.38E-07,

6.13E-07, 7.73E-07, 9.68E-07, 1.16E-06, 1.41E-06, 1.75E-06,

2.10E-06, 2.62E-06, 3.22E-06)

175

y_PI3 = c(1.35E-07, 3.04E-07, 4.75E-07, 6.46E-07, 8.43E-07, 9.92E-07,

1.24E-06, 1.48E-06, 1.77E-06, 2.06E-06, 2.48E-06, 3.07E-06,

3.78E-06, 4.65E-06, 5.71E-06)

y_PI = c(y_PI1, y_PI2, y_PI3) # creates a vector representing PI set’s dependent variables

df = data.frame(y=y_PI,x=vect_E) #creates a data frame that is set PI. The data.frame() function is used to store the

#data as a table with their associated properties intact.

#Hopping theory function used to fit raw data:

JPI_nonlin = nls(y~(Jo*exp(-Phi/(kb*t))*sinh((q*d*vect_E)/(2*kb*t))),

start = list(Jo = 0.007,

d = 1*10^-9), data = df

) #The nls(f(x, Pn)) function determines the nonlinear least-squares estimates of a parameter or set

of #parameters Pn, using a nonlinear model f(x, Pn). Here, Jo and d are parameters being fit to equation (2) in this

#documents associated manuscript.

#Plotting raw data and fit function (used in the creation of nonlinear regression fits in the sextion “Raw Data with

#Non-linear Fits”)

plot(vect_E,y_PI,pch=19,col="black",main="Polyimide 25C", xlab="E (V/m)", ylab="J (A/m^2)",ylim=c(0,6*10^-

6))

lines(vect_E,predict(JPI_nonlin),col = "green") #The predict(f(x, Pn)) function yields the predicted values as a

#function of x, of the model function f(x, Pn).

#Bootstrap procedure to acquire confidence interval on parameter estimates:

iters = 10000

bs.samples = matrix(0,ncol=2,nrow=iters) #a defined unfilled matrix of 2 columns and 10,000 rows

#initiation of loop used fit 10,000 distributions formed by sampling with replacement.

#for(i in 1:γ) {procedure} – a flow control statement initiating a loop. It indicates to perform the ith iteration of the

#outlined procedure for a total of γ iterations spanning from 1 to γ.

for(i in 1:iters){

bs.inds = sample(45,45,replace=T) #sample(α, β, replace = T/F) – takes a sample from a vector. α represents total

#number of possible indices to select from a matrix, β represents number of elements to choose (in this situation,

#number of indices), replace = T/F indicates sampling with replacement yes or no, respectively.

bs.y = y_PI[bs.inds] #samples with replacement from vector y_PI to create PI* set’s dependent variables

bs.x = vect_E[bs.inds] #samples with replacement from vector vect_E to create PI* set’s independent variables

bs.df = data.frame(y=bs.y, x=bs.x ) #creates PI* set

#performs non-linear regression using hopping theory to PI*

bs_fit = nls(y~(Jo*exp(-Phi/(kb*t))*sinh((q*d*x)/(2*kb*t))),

start = list(Jo = 0.007,

d = 1*10^-9), data = bs.df

)

bs.samples[i,] = as.vector( summary(bs_fit)$coefficients[,1] ) #defines bs.samples matrix as vector containing

#10,000 non-linear regression outputs of fit parameters Jo and d. The The summary(object) – produces a result

#summary of various model fitting functions represented by “object”.

}

#Extraction of statistical parameter estimates

Jo_est = mean(bs.samples[,1])

d_est = mean(bs.samples[,2]) #obtains the mean for the indicated fit parameters

Jo_CI = quantile(bs.samples[,1], probs=c(0.025,0.975))

d_CI = quantile(bs.samples[,2], probs=c(0.025, 0.975)) #obtains the 95% confidence interval for the indicated fit

#parameters where quantile(α, prob = c(β,γ)) yields sample quantiles of an object or vector α. The quantile produced

#corresponds to probabilities defined by β (lower range) and γ (upper range).

176

Jo_hist = hist(bs.samples[,1], freq = TRUE, breaks = 500, main="Jo Histogram 25C",xlab="Range of

Jo",ylab="Counts")

d_hist = hist(bs.samples[,2], freq = TRUE, breaks = 500, main="d Histogram 25C",xlab="Range of

d",ylab="Counts")#displays the indicated fit parameter’s empirically derived probability distribution for visual

#representation.

177

APPENDIX B

Annotated Code for TSDC Peak Fitting

The following script was used in the fitting peak deconvolution procedure for pure 1-layer

P(VDF-TrFE) TSDC analysis. Annotations in the code explaining non-trivial steps are written in

green font and initiated by the # symbol in the code. Comments are not observed by the program

when fitting. Definitions are taken from a combination of R Documentation, a “Table of Useful R

Commands” found on www.calvin.edu, and user-based forums that were referenced when creating

the script.

Annotated Code

## Performs peak fitting (Bucci Theory) on initial TSDC peak. estimated fit parameters are then used to generate a

function over the entire temperature range data is collected (via a second input file) which is then subtracted from the

data to deconvolute peaks within the T range selected. ##

install.packages("cubature")

install.packages("nnet")

install.packages("stringi")

install.packages("fit.models")

install.packages("seewave")

install.packages("gdata")

library(cubature) #package cubature

library(nnet) #package nnet

library(seewave) #package seewave

library(stringi)

library(fit.models)

library(gdata)

data <- read.csv(file.choose()) # Input csv file location, Temperature should be in Kelvin, strongest peak

chosen

T <- na.omit(data$T) # Need to tailor data range to peak of interest

J <- na.omit(data$J)

Ea <- seq(1, 3, by=0.005) # Activation energies vector [eV]

P <- exp(seq(log(1e-3), log(2e-0), length.out=length(Ea))) # Polarization vector

kb <- 8.165656e-05 # Boltzmann constant [eV]

Tm <- T[which.max(J)] # Current peak temperature

b <- 2.5/60 # Heating rate [deg/s]

Tau <- c(1:length(Ea)) # Relaxation time

result <- c(1:length(T)) # Fitting vector

err <- matrix(nrow = length(P), ncol = length(Ea)) # Error matrix

#Peak fitting for loops using equation 2-43

for (j in seq(from=1, to=length(Ea), by=1)) {

Tau[j] <- kb*(Tm^2)/(b*Ea[j]*exp(Ea[j]/(kb*Tm)))

for (k in seq(from=1, to=length(P), by=1)) {

for(i in seq(from=1, to=length(T), by=1)){

result[i] <- P[k]/Tau[j]*exp(-Ea[j]/(kb*T[i]))*exp(-kb*T[i]^2/(b*Tau[j]*Ea[j])*exp(-Ea[j]/(kb*T[i])))

}

178

err[j,k] <- rms(result-J)

}

}

I = which(err == min(err), arr.ind = TRUE)

E = Ea[I[1]] # Fitted Best value for Ea

P0 = P[I[2]] # Fitted Best value for P

Tau0 = kb*(Tm^2)/(b*E*exp(E/(kb*Tm))) # Relaxation time using E

##### CHECK POINT: fit check (make sure it fits well visually and call out min(err)) #####

for(i in seq(from=1, to=length(T), by=1)){

result[i] <- P0/Tau0*exp(-E/(kb*T[i]))*exp(-kb*T[i]^2/(b*Tau0*E)*exp(-E/(kb*T[i])))

}

plot(T,J, type="b", ylim=c(0, 2e-4),xlab="",ylab="")

par(new = TRUE)

plot(T,result, ylim=c(0,2e-4), type="l", col="red",xlab="Temperature (K)", ylab="J (A / m2)")

####### fit check (make sure it fits well visually) ########

###### Import New Data set (Spans full TSDC T range ) ######

data <- read.csv(file.choose())

T <- na.omit(data$T)

J <- na.omit(data$J)

#generates fit function for data subtraction over TSDC temperature range

fit1 <- function(t){

fit1_1 <- P0/Tau0*exp(-E/(kb*t))*exp(-kb*t^2/(b*Tau0*E)*exp(-E/(kb*t)))

return(fit1_1)

}

df_fit1 <- data.frame(T, fit1(T))

plot(df_fit1, type="l", col="blue")

#exports fit function data points into its own file

x_name <- "fit T (K)"

y_name <- "fit J (A/m2)"

df_fit <- data.frame(T,fit1(T))

colnames(df_fit) <- c(x_name, y_name)

setwd(choose.dir())

write.csv(df_fit,file="S10 High T Peak Fit Function")

#subtracts data from fit function

df_raw <- data.frame(T, J)

plot(df_raw, type="b", col="black")

df_merged <- data.frame(within(merge(df_raw, df_fit1, by = "T"), J_sub <- J - fit1.T.))

df_subtracted <- data.frame(T, df_merged$J_sub)

plot(df_subtracted, type="b", ylim=c(0,2e-4)) # VISUAL CHECK: Make sure filtered data is clean

#exports subtracted data

x_name <- "T"

y_name <- "J"

df <- data.frame(T, df_merged$J_sub)

colnames(df) <- c(x_name, y_name)

179

setwd(choose.dir())

write.csv(df,file="0.25% Subtracted dat_function generated")

############ END creation of subtracted data set #############

### USER REQUIRED STEP: Select T range for Subtracted Peak ###

############ START fitting of subtracted data set ############

#import subtracted data set and undergo same fitting procedure

data <- read.csv(file.choose())

T <- na.omit(data$T)

J <- na.omit(data$J)

Ea2 <- seq(0.001, 2, by=0.002)

P2 <- exp(seq(log(1e-5), log(1e1), length.out=length(Ea2)))

kb <- 8.165656e-05

Tm2 <- T[which.max(J)]

b <- 5/60

Tau2 <- c(1:length(Ea2))

result2 <- c(1:length(T))

err2 <- matrix(nrow = length(P2), ncol = length(Ea2))

for (l in seq(from=1, to=length(Ea2), by=1)) {

Tau2[l] <- kb*(Tm2^2)/(b*Ea2[l]*exp(Ea2[l]/(kb*Tm2)))

for(m in seq(from=1, to=length(P2), by=1)) {

for(i in seq(from=1, to=length(T), by=1)){

result2[i] <- P2[m]/Tau2[l]*exp(-Ea2[l]/(kb*T[i]))*exp(-kb*T[i]^2/(b*Tau2[l]*Ea2[l])*exp(-

Ea2[l]/(kb*T[i])))

}

err2[l,m] <- rms(result2-J)

}

}

I = which(err2 == min(err2), arr.ind = TRUE)

E2 = Ea2[I[1]]

P02 = P2[I[2]]

Tau02 = kb*(Tm2^2)/(b*E2*exp(E2/(kb*Tm2)))

for(i in seq(from=1, to=length(T), by=1)){

result2[i] <- P02/Tau02*exp(-E2/(kb*T[i]))*exp(-kb*T[i]^2/(b*Tau02*E2)*exp(-E2/(kb*T[i])))

}

#plots deconvoluted peak with fitted function

plot(T,J, type="b", ylim=c(0, 1.5e-4), xlab="", ylab="")

par(new = TRUE)

plot(T,result2, ylim=c(0, 1.5e-4), type="l", col="red",xlab="Temperature (K)", ylab="J (A / m2)")

legend("topleft",

legend = c("Exp", "Fit"),

col = c(rgb(0.1,0,0),

rgb(0.9,0,0.1)),

pch = c(19,NA_integer_),

bty = "n",

pt.cex = 2,

cex = 1.2,

text.col = "black",

horiz = F ,

inset = c(0.1, 0.1))

180

APPENDIX C

P(VDF-TrFE) Poole-Frenkel Analysis

C.1 Poole-Frenkel Analysis

Both PI, and PPIDS sample sets are considered using Poole-Frenkel theory. The linear regression

is performed on the mean of the three measurements in each sample set at the temperatures of

25oC, 75oC, 100oC, 125oC, 150oC, and 175oC. The PF plots for data taken at 25oC, 100oC, and

Figure C-1: Linearized J(E) data into Poole-Frenkel plots for PI and PPIDS. Data is shown for measurements at a)

25oC, b) 100oC, and c) 150oC

181

150oC are shown in Figure C-1 to illustrate the plasma treatment’s effect on raw data through at

the indicated temperatures using PF theory. At low temperatures the effect of the plasma treatment

is not observable which is similar to what is seen during Schottky analysis. Unlike linearization

performed using Schottky theory, linearization using PF theory yields non-linear data at 25oC

indicating poor description of sample behavior in both sets at room temperature. At higher

temperatures, linearization produces a linear relationship between Ln(J/E) vs E1/2. To assess

accuracy of PF theory in describing conduction in the samples, material permittivity is calculated

using the slope of linear fit functions pertaining to the data. The slope of the fit can be converted

to permittivity under PF theory by equation (A-1) in the manuscript and reproduced below:

𝜖𝑟,𝑃𝐹 = [(𝑚𝑘𝑇)2𝜋𝜖𝑜

𝑞3]

−1

(A − 1)

Permittivity values calculated from the linear regression as a function of measurement

temperature are shown below in Figure C-2. Calculation of the permittivity from PF plots returns

values that are greater than the acceptable range defined by the limits n2 and εr at 1 kHz by at least

an order of magnitude at all temperatures. This indicates that PF theory is insufficient to describe

conduction through the material for either processing condition at all measurement temperatures.

Fig C-2: Permittivity values calculated from linear fits in PF plots. A shaded region is marked in both plots that

indicates the range between high frequency permittivity defined by polyimide’s refractive index squared (n2) and

permittivity measured at 1kHz.

182

APPENDIX D

Polyimide I(V) Nonlinear Regression Parameter Estimates

The following sections show parameter estimates as well as estimated model fits using the

procedure and code outlined in Chapter 2 section 2.4.1 for data discussed in Chapter 5 section

5.3.2.1 Figure 5-2.

D.1 Hopping Conduction Parameter Estimate Histograms

Figure D-1: Histograms of parameter estimates from PI* after 10,000 iterations for Jo and d at 25oC, 75oC, and 100oC.

183

Figure D-2: Histograms of parameter estimates from PPIDS* after 10,000 iterations for Jo and d at 25oC, 75oC, 100oC,

125oC, and 150oC.

184

Figure D-3: raw data from the PI data set (black points) displaying the converged fit result using nonlinear

regression (blue solid line) superimposed.

Figure D-4: Raw data from the PPIDS data set (red points) displaying the converged fit result using nonlinear

regression (blue solid line) superimposed.

185

APPENDIX E

Equivalent Circuit Estimate Error Reports

E.1 Capacitive EC Element Error Percent

The error percent of all parameter estimates for capacitive circuit elements at each

temperature and LiClO4 quantity is listed below in Tables E-I through E-III.

Table C-I: Error percent associated with CPE2 parameter estimates out-put from the model

Table C-2: Error percent associated with CPE3 parameter estimates out-put from the model

Table C-3: Error percent associated with CPE3 parameter estimates out-put from the model

186

E.2 Resistive EC Element Error Percent

The error percent of all parameter estimates at each temperature and LiClO4 quantity is

listed below in Tables E-IV.

Table E-IV: Error percent associated with R3 and R4 parameter estimates out-put from the model

187

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206

VITA

Michael Anthony Vecchio

Michael Anthony Vecchio was born in New York City, ESA in 1991, and was raised in

Long Valley New Jersey. Inspired by his father’s passion for science, Michael pursued a degree in

Physics and Mathematics at Dickinson College in Carlisle Pennsylvania, where he obtained his

Bachelor’s of Science in 2014. Unsatisfied, he enrolled at the Pennsylvania State University to

pursue a Ph.D. in Materials Science and Engineering in Fall of 2014. He served as a Graduate

Assistant in both the Electroactive Materials Characterization Laboratory lead by Dr. Zoubeida

Ounaies and the High Energy Capacitor Group by Dr. Michael T. Lanagan, which he is

particularly proud of.

Listed below are his publications during his tenure at Penn State University:

Journal Manuscripts

1. *“Conduction through Plasma Treated Polyimide: Analysis of High-Field Conduction by

Hopping and Schottky Theory” Michael A. Vecchio, Amira Barhoumi Meddeb, Michael

T. Lanagan, and Zoubeida Ounaies. Journal of Materials Science 54. 14 (2019): 10548-

10559.

2. *“Plasma Surface Modification of P(VDF-TrFE): Influence of Surface Chemistry and

Structure on Electronic Charge Injection.” Michael A. Vecchio, Amira Barhoumi Meddeb,

Michael T. Lanagan, Zoubeida Ounaies, and Jeff Shallenberger. Journal of Applied Physics

124, 114102 (2018); doi: 10.1063/1.5042751.

3. “Fabrication of Solid-State Multilayer Glass Capacitors.” Rudeger H. T. Wilke, Harlan

Brown-Shaklee, Adrian Casias, Billy Cunningham, Jr., Amanda Dean, Michael A.

Vecchio, and Rohith Vudatha. IEEE Transactions on Components, Packaging and

Manufacturing Technology 7.11 (2017): 1906-1910.

Conference Proceeding Papers

4. *“Schottky Barrier Height Quantification of P(VDF-TrFE) Thin Films” Michael A.

Vecchio, Amira Barhoumi Meddeb, Michael T. Lanagan, Zoubeida Ounaies, and Jeff

Shallenberger. (2018) IEEE Conference on Electrical Insulation and Dielectric

Phenomena, Cancun Mexico.

5. *“Plasma Surface Modification of P(VDF-TrFE) Dielectrics.” Michael A. Vecchio, Amira

Barhoumi Meddeb, Michael T. Lanagan, Zoubeida Ounaies, and Jeff Shallenberger. (2017)

18th US-Japan Seminar on Dielectric and Piezoelectric Materials, Santa Fe NM.

6. *“Polymer Laminates for High Energy Density and Low Loss.” Michael A. Vecchio,

Zoubeida Ounaies, Michael T. Lanagan, and Amira Barhoumi Meddeb. (2016) IEEE

Conference on Electrical Insulation and Dielectric Phenomena, Toronto Canada.