electrical conductivity, electromagnetic interference

University of Calgary

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Graduate Studies The Vault: Electronic Theses and Dissertations

2014-02-14

Electrical Conductivity, Electromagnetic Interference

Shielding and Dielectric Properties of Multi-walled

Carbon Nanotube/Polymer Composites

Arjmand, Mohammad

Arjmand, M. (2014). Electrical Conductivity, Electromagnetic Interference Shielding and Dielectric

Properties of Multi-walled Carbon Nanotube/Polymer Composites (Unpublished doctoral thesis).

University of Calgary, Calgary, AB. doi:10.11575/PRISM/25855

http://hdl.handle.net/11023/1379

doctoral thesis

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UNIVERSITY OF CALGARY

Electrical Conductivity, Electromagnetic Interference Shielding and Dielectric Properties of

Multi-walled Carbon Nanotube/Polymer Composites

by

Mohammad Arjmand

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF CHEMICAL AND PETROLEUM ENGINEERING

CALGARY, ALBERTA

FEBRUARY 2014

© Mohammad Arjmand 2014

ii

To:

My Parents, Spouse and Siblings

for their heartfelt supports

iii

They did not know it was impossible, so they did it!

Mark Twain

iv

Acknowledgment

Back in September 2009, my great supervisor, Dr. Uttandaraman Sundararaj, and I were new

to the University of Calgary. At that time, Dr. Sundararaj had just moved to the University of

Calgary as the Head of the Department of Chemical and Petroleum Engineering and his

postdoctoral fellows were still at University of Alberta, who moved to Calgary a few months

later. Being my supervisor’s first graduate student at University of Calgary along with the

difficulties of occupying and organizing new laboratories depicted a challenging PhD career

towards me. Nonetheless, my supervisor was a tremendous source of management, unconditional

support and encouragement. I am truly indebted to his support during the last four years, not only

as a prominent supervisor, but also as an elder friend who guided me with academic and real

lives.

I would like to convey my wholehearted gratitude to the members of Polymer Processing

Group, particularly, Dr. Genaro Gelves and Mr. Ali Sarvi, who assisted me with my graduate life

in Calgary. I would like to thank the supervisory committee members for their insight and

comments, namely: Dr. Nader Mahinpei and Dr. Maen Husein. I express my warmest

appreciation to Dr. Simon Park and Dr. Mehdi Mahmoodi for their collaboration in

manufacturing the mold and injection molding of the composites (chapters 4 and 6). Special

thanks go to Dr. Michal Okoniewski and Mr. Thomas Apperley for their contributions to the

analysis of electrical properties data (chapter 5). A sincere appreciation goes to Dr. Rosario

Bretas and Dr. Aline Silva for their cooperation with producing the copper nanowire composites

and their characterization (chapter 8).

v

The financial supports from the Natural Science and Engineering Research Council (NSERC)

of Canada and Alberta Innovates Technology Futures (AITF) are highly appreciated. I also owe

a great deal of appreciation to Dr. Tieqi Li and Ms. Jeri-Lynn Bellamy in Nova Chemicals®,

Calgary, AB, Canada for the polymer extrusion/blending. I would like to thank Dr. Samaneh

Abbasi of Ecole Polytechnique (Montreal, Canada) for assistance with Raman spectroscopy. My

appreciation and thanks to Dr. Michael Schoel and Dr. Tobias Furstenhaupt who contributed me

with microscopy imaging. I am also very grateful to Americas Styrenics LLC, who generously

provided me with the neat polystyrene.

The deepest gratitude goes to my parents, spouse and siblings who though have been

geographically far away from me during my PhD career, but have always been in my heart.

vi

Abstract

Driven by the ever-growing demand for versatile electronics with increased functionality,

high performance, light weight, low cost and improved design options, conductive filler/polymer

composites (CPCs) have emerged as a distinctive solution. Manipulating the conductive network

formation in CPCs allows them to be employed in a wide range of applications, such as charge

storage, electrostatic discharge dissipation and electromagnetic interference (EMI) shielding.

In this dissertation, controlling the conductive network formation was the key aspect in

designing the morphology of CPCs for electrical applications. Multi-walled carbon nanotube

(MWCNT) was chosen as conductive filler due to its surprising electronic structure and growing

industrial usage. We employed two distinct techniques to improve or deteriorate conductive

network formation to improve the electrical properties in MWCNT/polymer composites, i.e.

electrical conductivity, EMI shielding and dielectric properties. These techniques comprise (1)

aligning MWCNTs using an injection molding machine, and (2) replacing MWCNTs with

copper nanowires (CuNWs).

Prior to exploring the influence of the above-mentioned techniques on the electrical properties

of CPCs, a series of studies were implemented on MWCNT/polymer composites to obtain a

general understanding from the electrical behaviors of CPCs as a function of MWCNT content.

The results over the X-band (8.2 – 12.4 GHz) showed that the electrical conductivity, EMI

shielding and dielectric properties rose with MWCNT content. The increase in electrical

conductivity with MWCNT loading was attributed to the formation of conductive paths across

the composite. Increase in EMI shielding with MWCNT content was related to a greater number

of interacting nomadic charges and also higher real permittivity (polarization loss) and imaginary

vii

permittivity (Ohmic loss). Moreover, the broadband dielectric spectroscopy (10-1

– 10+6

Hz)

showed that both real permittivity and imaginary permittivity increased drastically as the

MWCNT concentration approached the percolation threshold. Increase in real permittivity was

related to the formation of a large number of nanocapacitor structures, MWCNTs as electrodes

and polymer matrix as dielectric material, and increase in imaginary permittivity was ascribed to

greater number of dissipating charges, enhanced conductive network formation and boosted

polarization loss arising from interfacial polarization.

MWCNT alignment, induced by an injection molding machine, was observed to deteriorate

the conductive network formation. As inferior conductive network formation reduces imaginary

permittivity, this technique was introduced as an innovative technique to improve the dielectric

properties of MWCNT/polymer composites. Nonetheless, MWCNT alignment indicated an

adverse influence on the percolation threshold, electrical conductivity and EMI shielding due to

its negative influence on conductive network formation. In brief, unavoidable flow-induced

alignment of MWCNTs in injection molding process was presented as an opportunity to improve

the dielectric properties for charge storage or as a challenge to be avoided for producing

conductive CPCs.

CuNWs were creatively displayed to be competent substitutions for MWCNTs for charge

storage applications. Unavoidable oxide layer formation on the surface of CuNWs, which has

always been a disadvantage for electronics applications, was employed as a benefit to decay the

conductive network formation and reduce the imaginary permittivity. Moreover, higher

conductivity of fresh core of CuNWs relative to MWCNTs provided the composites with more

free charges contributing to real permittivity. In conclusion, high conductivity of fresh core of

viii

CuNWs combined with the presence of the oxide layer on CuNW surfaces depict a promising

future for CuNW/polymer composites as charge storage materials.

ix

Table of Contents

Dedication…………………………………………………………………………………………ii

Citation…………………………………………………………………………………………...iii

Acknowledgement………………………………………………………………………………..iv

Abstract…………………………………………………………………………………………...vi

Table of Contents………………………………………………………………..……..…………ix

List of Tables……………………………………………………………...…………………….xiv

List of Figures…………………………………………………………………………………...xv

List of Symbols and Abbreviations…………………………………………………………...….xx

Chapter 1 – Introduction………………………………………………………………………..1

1.1. General Background ................................................................................................................ 1

1.2. State-of-the-Art ........................................................................................................................ 2

1.3. References ................................................................................................................................ 5

Chapter 2 – Literature Review………………………………………………………………….6

2.1. Conductive Filler/Polymer Composites (CPCs): Structure, Applications and Market............ 6

2.2. Electrical Conductivity .......................................................................................................... 10

2.3. Electrostatic Discharge (ESD) ............................................................................................... 12

2.4. Electromagnetic Interference (EMI) Shielding ...................................................................... 16

2.4.1. General Background ....................................................................................................... 16

2.4.2. Magic of Shielding .......................................................................................................... 17

2.4.3. Shielding Effectiveness ................................................................................................... 20

2.4.4. Reflection, Absorption and Multiple-reflection for Conductive Monolithic Materials .. 22

2.4.4.1. Shielding by Reflection ............................................................................................ 22

2.4.4.2. Shielding by Absorption ........................................................................................... 24

2.4.5. Effect of Real Permittivity on Shielding of Conductive Monolithic Materials .............. 27

2.5. Dielectric Theory ................................................................................................................... 28

2.5.1. Dielectric Material .......................................................................................................... 28

2.5.2. Permittivity ..................................................................................................................... 29

2.5.3. Dielectric Mechanisms.................................................................................................... 31

2.5.4. The Electrical Current of Dielectrics under a Step DC Voltage ..................................... 35

2.6. Electrical Properties of Conductive Filler/Polymer Composites (CPCs) .............................. 38

x

2.6.1. Electrical Conductivity of CPCs ..................................................................................... 38

2.6.2. EMI Shielding of CPCs .................................................................................................. 43

2.6.3. The Mechanisms Behind the Broadband Dielectric Spectroscopy of CPCs .................. 49

2.7. Effects of Conductive Filler Type (MWCNT versus CuNW) on Electrical Properties of

CPCs ............................................................................................................................................. 51

2.7.1. Carbon Nanotubes ........................................................................................................... 53

2.7.1.1. Structure and Electrical Properties ........................................................................... 53

2.7.1.2. Carbon Nanotube Synthesis...................................................................................... 56

2.7.1.3. Carbon Nanotube Market ......................................................................................... 57

2.7.2. Copper Nanowire (CuNW) ............................................................................................. 58

2.8. MWCNT Alignment, Induced by Injection Molding, and Electrical Properties of CPCs .... 59

2.8.1. Flow Conditions in Injection molding and its Effect on Filler Alignment ..................... 60

2.8.2. A Brief Review on Electrical Conductivity of Injection Molded CPCs ......................... 62

2.9. Project Motivation and Objectives......................................................................................... 64

2.10. References ............................................................................................................................ 67

Chapter 3 – Materials, Processing and Characterization………………………...………….78

3.1. Methodology .......................................................................................................................... 78

3.2. Materials ................................................................................................................................ 79

3.3. Sample Preparation, Processing and Molding ....................................................................... 82

3.3.1. Phase I ............................................................................................................................. 82

3.3.2. Phase II............................................................................................................................ 83

3.3.2.1. Materials Preparation ................................................................................................ 83

3.3.2.2. Experimental Design and Composite Molding ........................................................ 84

3.3.3. Phase III .......................................................................................................................... 89

3.3.4. Phase IV .......................................................................................................................... 90

3.4. Electrical Properties Measurement Setups............................................................................. 91

3.4.1. Surface/Volume Resistivity Measurement ..................................................................... 91

3.4.2. EMI Shielding Setup ....................................................................................................... 95

3.4.3. Dielectric Spectroscopy Setup ........................................................................................ 98

3.5. References .............................................................................................................................. 99

Chapter 4 – Electrical and Electromagnetic Interference Shielding Properties of Flow-

induced Oriented Carbon Nanotubes in Polycarbonate…………………………...……….101

4.1. Presentation of the Article ................................................................................................... 101

xi

4.2. Abstract ................................................................................................................................ 102

4.3. Introduction .......................................................................................................................... 103

4.4. Experimental ........................................................................................................................ 106

4.4.1. Composite Preparation and Molding ............................................................................ 106

4.4.2. Electrical and EMI Shielding Measurements ............................................................... 108

4.4.3. Morphological Characterization ................................................................................... 109

4.4.4. Raman Spectroscopy ..................................................................................................... 110

4.5. Results and Discussion ........................................................................................................ 110

4.5.1 Electrical Conductivity of MWCNT/PC Composites .................................................... 110

4.5.2. Morphological Analysis ................................................................................................ 119


4.5.4. Electromagnetic Interference Shielding Measurements and Mechanism ..................... 124

4.6. Conclusions .......................................................................................................................... 129

4.7. References ............................................................................................................................ 130

Chapter 5 – Comparative Study of Electromagnetic Interference Shielding Properties of

Injection Molded versus Compression Molded Multi-walled Carbon Nanotube/Polystyrene

Composites………………………………………………………………………………...…...134


5.2. Abstract ................................................................................................................................ 136

5.3. Introduction .......................................................................................................................... 137

5.4. Experimental ........................................................................................................................ 139

5.4.1. Composite Preparation .................................................................................................. 139

5.4.2. Experimental Design and Composite Molding ............................................................. 140

5.4.3. EMI Shielding Properties Measurements ..................................................................... 142

5.4.4. Morphological Characterization and Raman Spectroscopy .......................................... 144


5.5.1. Morphological Analysis and Raman Spectroscopy ...................................................... 144

5.5.2. Comparison of Electrical Conductivity and EMI SE of Injection Molded versus

Compression Molded MWCNT/PS Composites .................................................................... 146

5.5.3. Effects of MWCNT Alignment on Shielding Mechanisms in MWCNT/PS Composites

................................................................................................................................................. 152

5.6. Conclusions .......................................................................................................................... 157

5.7. References ............................................................................................................................ 158

xii

Chapter 6 – An Innovative Method to reduce the Energy loss of Conductive Filler/Polymer

Composites for Charge Storage Applications……………………………...………………. 163


6.2. Abstract ................................................................................................................................ 164

6.3. Introduction .......................................................................................................................... 165

6.4. Material and Methods .......................................................................................................... 166

6.4.1. Materials ....................................................................................................................... 166

6.4.2. Composite Molding ...................................................................................................... 167


6.4.4. Determination of Carbon Nanotube Length Distribution ............................................. 169


6.4.6. Electrical and Dielectric Properties Measurements ...................................................... 170


6.5.1. Morphological Analysis and Raman Spectroscopy ...................................................... 171

6.5.2. The Effects of Processing and Molding on MWCNT Length Distribution .................. 173

6.5.3. The Effects of MWCNT Alignment and Length on the Dielectric Properties ............. 174

6.6. Conclusions .......................................................................................................................... 182

6.7. References ............................................................................................................................ 183

Chapter 7 – Broadband Dielectric Properties of Multi-walled Carbon

Nanotube/Polystyrene Composites…………………………………………………………...186


7.2. Abstract ................................................................................................................................ 187

7.3. Introduction .......................................................................................................................... 188

7.4. Experimental ........................................................................................................................ 189

7.4.1. Materials and Composite Preparation ........................................................................... 189

7.4.2. Electrical and Dielectric Properties Measurements ...................................................... 191

7.4.3. Morphological Characterization ................................................................................... 191



7.5.2. DC Conductivity ........................................................................................................... 195

7.5.3. AC Conductivity ........................................................................................................... 196

7.5.4. Charge Polarization Mechanisms in MWCNT/Polymer Composites .......................... 199

7.5.5. The Broadband Behavior of Real Permittivity ............................................................. 200

7.5.6. The Broadband Behavior of Imaginary Permittivity .................................................... 203

xiii

7.6. Conclusions .......................................................................................................................... 205

7.7. References ............................................................................................................................ 206

Chapter 8 – Novel Composites of Copper Nanowire/PVDF with Superior Dielectric

Properties………………………………...…………………………………………………….210


8.2. Abstract ................................................................................................................................ 211

8.3. Introduction .......................................................................................................................... 212

8.4. Experimental ........................................................................................................................ 214

8.4.1. Materials ....................................................................................................................... 214

8.4.2. Mixture Preparation ...................................................................................................... 215

8.4.3. Characterization ............................................................................................................ 216


8.5.1. Oxidation of CuNWs .................................................................................................... 217

8.5.2. Morphological Characterization of the Nanocomposites ............................................. 218

8.5.3. DC and AC Conductivity .............................................................................................. 220

8.5.4. Dielectric Permittivity and Dielectric Loss ................................................................... 224

8.6. Conclusions .......................................................................................................................... 231

8.7. References ............................................................................................................................ 232

Chapter 9 – Summary, Conclusions and Future Work…………………………….………236

9.1. General Background and Project Objectives ....................................................................... 236

9.2. Electrical Behaviors of CPCs and the Mechanisms Behind ................................................ 238

9.2.1. Volume Resistivity........................................................................................................ 238

9.2.2. EMI Shielding ............................................................................................................... 239

9.2.3. Broadband Dielectric Spectroscopy of CPC ................................................................. 242

9.3. Effects of MWCNT Alignment, Induced by Injection Molding, on Volume Resistivity and

EMI Shielding ............................................................................................................................. 244

9.4. Effects of MWCNT Alignment, Induced by Injection Molding, on Dielectric Properties .. 248

9.5. Novel CuNW/PVDF Nanocomposites for Charge Storage: Comparison of its Dielectric

Properties with MWCNT/PVDF Nanocomposite ...................................................................... 250

9.6. Recommendations ................................................................................................................ 251

9.7. References ............................................................................................................................ 255

xiv

List of Tables

Table 2-1: CPC applications with their required range of electrical conductivity [8]. ................... 7

Table 2-2: Classifications of materials in terms of surface resistivity [31]. ................................. 14

Table 2-3: Electrical conductivity and magnetic permeability of common materials used in

shielding barriers [33, 34]. ............................................................................................................ 27

Table 3-1: Physical properties of MWCNT (NC7000) [1]. .......................................................... 81

Table 3-2: The concentrations of the prepared MWCNT/PS nanocomposites in terms of weight

percent and volume percent. ......................................................................................................... 83

Table 3-3: Experimental design showing the two-level, four factor factorial design. The factors

are mold temperature (C1), melt temperature (C2), injection/holding pressure (C3) and injection

velocity (C4). ................................................................................................................................. 85

Table 3-4: Levels (set points) of the processing parameters used in the injection molding

experiments. The processing parameters are mold temperature (C1), melt temperature (C2),

injection/holding pressure (C3) and injection velocity (C4). ......................................................... 85

Table 3-5: Dimensions of the designed mold. .............................................................................. 86

Table 4-1: Percolation thresholds, critical exponents and correlation factors for compression-

molded samples and injection-molded samples at different areas, corresponding to different

alignments. .................................................................................................................................. 119

Table 4-2: Raman intensity ratios parallel/perpendicular to the flow direction of compression-

molded and injection-molded samples of PC/MWCNT. ............................................................ 124

Table 5-1: The concentrations of the prepared nanocomposites in terms of weight percent and

volume percent. ........................................................................................................................... 140


experiments (EXPs). The processing parameters are mold temperature (C1), melt temperature

(C2), injection/holding pressure (C3) and injection velocity (C4). .............................................. 141

Table 5-3: Dimensions of the designed mold. ............................................................................ 142

Table 5-4: Raman intensity ratios parallel/perpendicular to the flow direction of the compression

molded and injection molded samples of 5.00 wt% MWCNT/PS composites. ......................... 146


volume percent. ........................................................................................................................... 167

xv

List of Figures

Figure 2-1: Schematic of conductive network formation in a CPC [5]. ......................................... 6

Figure 2-2: The approximate range of electrical conductivity covered by CPCs [7]. .................... 7

Figure 2-3: Some important applications of CPCs. From left to right: Capacitors (charge

storage); airplane tire (antistatic dissipation); circuit board carrier (ESD protection); cell phone

enclosure (EMI shielding) [6, 12]. .................................................................................................. 8

Figure 2-4: Global market for CPCs in 2010-2016 [22]. ................................................................ 9

Figure 2-5: Simplified diagram of the electronic band structure in the Band Theory. ................. 11

Figure 2-6: Costs due to ESD damage at various incremental levels [30]. .................................. 13

Figure 2-7: The diagram of a typical static-safe workbench [32]. ................................................ 15

Figure 2-8: Illustration of the use of shielded enclosure (a) to contain radiated emission, (b) to

exclude radiated emission [34]. .................................................................................................... 16

Figure 2-9: Illustration of interaction between incident plane wave and conductive barrier [34].19

Figure 2-10: Schematic of the effects of multiple-reflection in a conductive shield: (a) combining

multiple transmissions, (b) calculations in terms of intrinsic impedance and reflection and

transmission coefficients [34]. ...................................................................................................... 26

Figure 2-11: Charges on a parallel-plate capacitor with (a) air between the plates, and (b) a

dielectric between the plates [25]. ................................................................................................ 28

Figure 2-12: (a) Circuit diagram of a dielectric under an AC field, (b) Argand diagram of

complex current-voltage relationship [25]. ................................................................................... 31

Figure 2-13: Frequency response of dielectric mechanisms [49, 54]. .......................................... 32

Figure 2-14: Typical DC response of a dielectric to a step voltage application [46]. .................. 36

Figure 2-15: Percolation curve of compression molded MWCNT/PS composite (A typical

percolation curve of CPCs) [41]. .................................................................................................. 41

Figure 2-16: Diagram of electron-transfer mechanisms between adjacent sites separated by a

potential energy barrier [77]. ........................................................................................................ 42

Figure 2-17: EMI SE of compression molded MWCNT/PS composite as a function of MWCNT

concentration and shielding plate thickness. ................................................................................. 44

Figure 2-18: Schematic of resistor and capacitor structures in a CPC. ........................................ 45

xvi

Figure 2-19: Contributions of (a) reflection and (b) absorption to the overall EMI SE for the

compression molded MWCNT/PS composites as a function of MWCNT concentration. The

thickness of all the samples is 2.0 mm [41]. ................................................................................. 47

Figure 2-20: Real permittivity and imaginary permittivity of MWCNT/PS composites over the

broadband frequency range [41] ................................................................................................... 48

Figure 2-21: The equivalent-circuit model of MWCNT/polymer composites. ............................ 50

Figure 2-22: TEM images of different CNTs : (a) SWCNT, (b) MWCNT with different layers of

5, 2 and 7 [112, 114]. .................................................................................................................... 53

Figure 2-23: Schematic diagram showing how a hexagonal sheet of graphene is rolled to form a

CNT with different chiralities; (a) Armchair; (B) Zigzag; (C) Chiral [68, 115]. ......................... 54

Figure 2-24: Basic hexagonal bonding structure for a graphite sheet; carbon nuclei shown as

filled circles, out-of-plane bonds represented as delocalized (dotted line), and bonds connect

the nuclei in-plane [119]. .............................................................................................................. 56

Figure 2-25: Global market for CNT grades based on committed production, (2011-2016),

($ Million) [125]. .......................................................................................................................... 58

Figure 2-26: Comparison between isothermal and non-isothermal velocity and shear rate

distributions for a non-Newtonian melt in thickness direction [126]. .......................................... 61

Figure 2-27: Influence of (a) convergent channel and (b) divergent channel on filler alignment in

a small element of polymer melt. (c) Schematic of fountain flow at the melt front [126]. .......... 62

Figure 2-28: Schematics showing (a) randomly distributed MWCNT/polymer composites, (b)

aligned MWCNT/polymer composites, and (c) CuNW/polymer composites. ............................. 65

Figure 3-1: Experimental Strategy. ............................................................................................... 79

Figure 3-2: Consecutive steps of nanowires synthesis [2, 3]. ....................................................... 82

Figure 3-3: An image of Coperion ZSK co-rotating intermeshing twin-screw extruder employed

for diluting the MWCNT/PS masterbatch. ................................................................................... 84

Figure 3-4: A schematic view of the designed mold. ................................................................... 86

Figure 3-5: Volume resistivities of the injection molded MWCNT/PS composites with 5.00 wt%

MWCNT loading at different molding conditions in the thickness direction [4]. ........................ 87

Figure 3-6: Minitab main effect plot of the volume resistivity mean of the injection molded

samples [4]. ................................................................................................................................... 88

Figure 3-7: The equivalent circuit for 8009 Test Fixture used to measure volume resistivity [6].

....................................................................................................................................................... 92

xvii

Figure 3-8: The equivalent circuit for 8009 Test Fixture used to measure surface resistivity [6].93

Figure 3-9: (a) Electrode construction, (b) equivalent circuit for 4-point probe technique [7]. ... 94

Figure 3-10: (a) Schematic of network analyzer diagram, (b) S-parameters diagram in a network

analyzer [8, 9]. .............................................................................................................................. 97

Figure 3-11: Electrode arrangement of 12962A sample holder [10] ............................................ 98

Figure 4-1: (a) Schematic of the dog-bone sample. The three different areas studied in the

specimens are indicated, (b) Experimental setup. ....................................................................... 108

Figure 4-2: Percolation curve for rectangular (compression-molded) samples of MWCNT/PC

composite. ................................................................................................................................... 111

Figure 4-3: Percolation curve for rectangular (compression-molded) samples and injection-

molded samples (parallel and perpendicular to the flow direction) at (a) area 1, (b) area 2 and (c)

area 3. .......................................................................................................................................... 115

Figure 4-4: Current-voltage characteristics of a) compression-molded sample, b) injection-

molded sample (area 3) in thickness direction. 1The measured current of composites holding 0.5

wt% of MWCNT in Fig. 3(a) and 1.5 wt% of MWCNT in Fig. 3(b) have been multiplied by 50

to enable its visualization in the plot........................................................................................... 117

Figure 4-5: SEM images of PC+1.5 wt% MWCNT. (a) compression-molded sample; (b) aligned

injection-molded sample (area 3), parallel to the flow direction; (c) aligned injection-molded

sample (area 3), perpendicular to the flow direction. ................................................................. 120

Figure 4-6: TEM micrograph of aligned injection-molded sample (area 3): a) Parallel to the flow

direction, b) Perpendicular to the flow direction. ....................................................................... 122

Figure 4-7: Raman spectra of PC/5 wt% MWCNT nanocomposites. ........................................ 123

Figure 4-8: EMI SE of MWCNT/PC compression-molded samples as a function of MWCNT

concentration and shielding plate thickness. ............................................................................... 127

Figure 4-9: (a) Contribution of absorption, (b) Contribution of reflection to the overall EMI SE

for compression-molded samples as a function of shielding material thickness and MWCNT

concentration. .............................................................................................................................. 128

Figure 5-1: A schematic view of the designed mold. ................................................................. 142

Figure 5-2: TEM micrographs of (a) an injection molded sample (EXP #1), and (b) a

compression molded sample. Both are 5.00 wt% MWCNT/PS composite. The white arrow in (a)

indicates the flow direction. ........................................................................................................ 145

Figure 5-3: (a) Electrical conductivity and (b) EMI SE for the compression molded and injection

molded samples of the MWCNT/PS composites as a function of MWCNT concentration. The

xviii

data related to the electrical conductivity of the injection molded samples were achieved in

parallel to the flow direction. The thickness of all the samples was 2.0 mm. ............................ 148

Figure 5-4: EMI SE, as a function of electromagnetic wave frequency, of (a) the compression

molded samples and (b) injection molded (EXP #1) samples. The thickness of all the samples

was 2.0 mm. ................................................................................................................................ 151


compression molded and injection molded samples of the MWCNT/PS composites as a function

of MWCNT concentration. The thickness of all the samples was 2.0 mm. ............................... 154

Figure 5-6: (a) Real permittivity and (b) imaginary permittivity for the compression molded and

injection molded samples of the MWCNT/PS composites as a function of MWCNT

concentration. .............................................................................................................................. 156

Figure 6-1: TEM micrographs of (a) an injection molded sample, and (b) a compression molded

sample. Both are 5.00 wt% MWCNT/PS composite. The white arrow in (a) indicates the flow

direction. ..................................................................................................................................... 172

Figure 6-2: Effects of molding on length distribution of MWCNTs in 2.00 wt% MWCNT/PS

composites................................................................................................................................... 174

Figure 6-3: Volume resistivity for the compression molded and injection molded samples of the

MWCNT/PS composites as a function of MWCNT concentration. ........................................... 176

Figure 6-4: (a) Imaginary permittivity and (b) real permittivity, as a function of MWCNT

concentration, for the compression molded and injection molded samples of the MWCNT/PS

composites in the X-band............................................................................................................ 179

Figure 6-5: Dissipation factors for the compression molded and injection molded samples of the

MWCNT/PS composites as a function of MWCNT concentration in the X-band. .................... 182

Figure 7-1: LM micrograph of MWCNT/PS composites with 1.00 wt% loading...................... 193

Figure 7-2: TEM micrographs of the solution-mixed samples at (a) low magnification, (b) high

magnification (polymer-rich area) and (c) high magnification (agglomerated area). ................ 194

Figure 7-3: The percolation curve (DC conductivity) of the solution-mixed samples of the

MWCNT/PS composites. ............................................................................................................ 196

Figure 7-4: AC conductivity of the solution-mixed MWCNT/PS composites. .......................... 198

Figure 7-5: Real permittivity, as a function of frequency, of the solution-mixed samples at

different MWCNT concentrations. ............................................................................................. 201

Figure 7-6: Imaginary permittivity, as a function of frequency, of the solution-mixed samples at

different MWCNT concentrations. ............................................................................................. 205

xix

Figure 8-1: TEM micrographs of (a) as-received MWCNT (NC7000), (b) synthesized CuNW.

..................................................................................................................................................... 215

Figure 8-2: WAXD diffractogram of the CuNW. ....................................................................... 218

Figure 8-3: SEM images: a) MWCNT/PVDF nanocomposites; b) CuNW/PVDF nanocomposites,

both with 1.5v% of filler. ............................................................................................................ 219

Figure 8-4: TEM images of: a) MWCNT/PVDF nanocomposites; b) CuNW/PVDF

nanocomposites, both with 1.5v% of filler. ................................................................................ 220

Figure 8-5: a) DC conductivity as a function of volume concentration, and linear fitting of the

data to the power law equation for electrical conductivity; b) AC conductivity of the

MWCNT/PVDF nanocomposites as a function of frequency. ................................................... 223



CuNW/PVDF nanocomposites as a function of frequency. ....................................................... 224

Figure 8-7: Dielectric permittivity (ɛ´): (a) MWCNT/PVDF nanocomposite; (b) CuNW/PVDF

nanocomposites. .......................................................................................................................... 226

Figure 8-8: Dielectric loss (ɛ) :(a) MWCNT/PVDF; (b) CuNW/PVDF nanocomposites. ....... 227

Figure 8-9: Dissipation factor (tanδ) as function of the frequency: (a) MWCNT/PVDF

nanocomposites; (b) CuNW/PVDF nanocomposites. ................................................................. 230

Figure 8-10: Scheme of core-shell structured CuNW, composed of a non-conductive shell (oxide

layer) and a conductive core (fresh copper), showing the blocking of the charge carriers at

internal interfaces of the individual CuNW…………………………………………………….230

xx

List of Symbols and Abbreviations

Abbreviations

AC Alternating current

ASTM American society for testing and material

CISPR Comité International Spécial des Perturbations Radioélectriques

CNT Carbon nanotube

CPC Conductive filler/polymer composites

CuNW Copper nanowire

CVD Chemical vapor deposition

DC Direct current

DMF N,N-Dimethylformamide

EMI Electromagnetic interference

ESD Electrostatic discharge

hr Hour

LED Light-emitting diode

LFD Low-frequency dispersion

LM Light microscopy

MeOH Methanol

min Minute

MUT Material under test

MWCNT Multi-walled carbon nanotube

MWS Maxwell-Wagner-Sillars

NIR Near-infrared

PAO Porous aluminum oxide

PC Polycarbonate

PCB Printed circuit board

PNA Programmable network analyzer

PPG Polymer Processing Group

PVDF Poly(vinylidene fluoride)

xxi

PS Polystyrene

RC Resistance/capacitance

SiP System-in-package

SE Shielding effectiveness

SEM Scanning electron microscopy

SWCNT Single-walled carbon nanotube

TEM Transmission electron microscopy

VGCNF Vapor grown carbon nanofiber

VNA Vector network analyzer

WAXD Wide angle x-ray diffraction

3-D Three dimensional

Symbols

A

Area of sample

Electric or magnetic field strength unit vector

C0 Capacitance of free space

C1 Mold temperature

C2 Melt temperature

C3 Injection/holding pressure

C4 Injection velocity

d Thickness of sample

dB Decibel (unit of shielding effectiveness)

e Charge of an electron

E Electric field

EI Incident electric field

ET Transmitted electric field

f Electromagnetic wave frequency

H Magnetic field

HI Incident magnetic field

HT Transmitted magnetic field

I Electric current

IR Resistive current

xxii

IC Capacitive current

J Current density

M Ratio of conducting aggregate to average gap width

Ne Number of electrons

P Power density

PI Incident power

PT Transmitted power

Q Stored charge

q Charge of particle

R Resistance

r1 Contact resistance

r2 Resistance of cable

Rx Resistance of sample

S Siemens (unit of electrical conductivity)

SEOA Overall shielding effectiveness

SER Shielding by reflection

SEA Shielding by absorption

SEMR Shielding by multiple-reflection

S11 Ratio of reflected power to incident power in port 1

S12 Ratio of transmitted power from port 1 to port 2 to incident

power in port 1

S21 Ratio of transmitted power from port 2 to port 1 to incident

power in port 1

S22 Ratio of reflected power to incident power in port 2

t Critical exponent of percolation threshold

T Torque

tanδ Dissipation factor

V Voltage

W Watt (Unit of power)

VC Percolation threshold

Z Real impedance

Z" Imaginary impedance

xxiii

Greek Letters

α Attenuation constant

β Phase constant

γ Propagation constant

δ Skin depth

ε' Dielectric (real) permittivity

ε" Dielectric loss (Imaginary permittivity)

ε0 Dielectric permittivity of free space

εr Relative dielectric permittivity

η Intrinsic Impedance of shielding materials

η0 Intrinsic impedance EM wave in free space

μ Magnetic permeability

μ0 Magnetic permeability of free space

μr Relative magnetic permeability

ρ0 Volume resistivity of conductive filler

ρs Surface resistivity

ρv Volume resistivity

σ Electrical conductivity

σ0 Electrical conductivity of copper

σr Relative electrical conductivity

τ Time constant

Ω Ohm (unit of resistance)

ω Angular frequency

1

Chapter 1

Introduction

1.1. General Background

In today’s marketplace, consumers are demanding lighter weight and smaller electronic devices

with improved functionality and design options. Accordingly, conductive filler/polymer composites

(CPCs) have recently drawn great interest to be employed in electronics, due their superior

properties such as tunable electrical conductivity, light weight, low cost, corrosion resistance,

processability, etc. Tunable electrical conductivity of CPCs allows them to be used in a broad range

of applications, such as charge storage, antistatic dissipation, electrostatic discharge (ESD)

protection and electromagnetic interference (EMI) shielding [1-3].

The significance of CPCs can be illustrated by the applications of these materials in a cell phone.

In a typical printed circuit board (PCB) of a cell phone, the discrete passives dominate the active

integrated circuits in terms of number and occupied surface area [4]. Therefore, the passive

components are the major challenge in the development and miniaturization of PCBs. Embedded

passive components have, thus, been introduced as a breakthrough in the size reduction and

performance enhancement of PCBs. CPCs, due to their unique features, have shown as promising

materials for producing embedded passive components, which are meritorious substitutions for the

surface-mounted passive components [5]. In terms of EMI shielding, by using CPCs, manufacturers

are able to produce lighter and smaller cell phone enclosures with improved design options and

2

dramatically reduced electromagnetic emissions having direct impact on peoples’ health.

Employing CPCs as packaging materials of cell phones is useful to dissipate the electrostatic

discharge, which can horribly damage the cell phones during shipping. Annually, the electronics

industry incurs great losses due to lack of proper packaging for electronics, which are sensitive to

electrostatic discharge.

1.2. State-of-the-Art

The main objective of this dissertation is to determine how unique morphologies of

nanocomposites can be created by manipulating mixing methods and processing conditions using

various nanofillers, and how that morphology relates to the final electrical properties, i.e., electrical

conductivity, EMI shielding and dielectric properties. In order to carry out the objectives, multi-

walled carbon nanotube (MWCNT) was selected as the conductive filler, due to its great electrical

properties and growing industrial usage; and polycarbonate (PC), polystyrene (PS) and

poly(vinylidene fluoride) (PVDF) were used as the polymer matrices.

In this dissertation, controlling the conductive network formation is the key aspect in designing

the morphology of CPCs for electrical applications. Improving the conductive network formation

enhances electrical conductivity and EMI shielding; whereas, deteriorating the conductive network

formation reduces the leakage current, thus developing dielectric properties [6-8]. Having a

comprehensive understanding how to manipulate the conductive network formation enables the

manufacturers to employ cost-effective materials and appropriate processing conditions to obtain

3

the desired electrical properties. In this dissertation, two different techniques were employed to

control the conductive network formation including:

Aligning the conductive filler (MWCNT) using an injection molding machine

Changing the type of conductive filler (substituting MWCNTs with copper nanowires

(CuNWs))

Employing the above-mentioned techniques to regulate the conductive network formation is quite

novel and introduced for the first time in the area tailoring the electrical properties. Accordingly,

this thesis is composed of the following sections:

1. Literature review, which mainly details the mechanisms behind the electrical properties of

conductive monolithic materials and CPCs.

2. Materials, processing and characterization section, which provides further information about

the used matrices and conductive fillers, experimental design, composite preparation

methodologies and electrical setups.

3. The main achievements of the thesis given in the format of five scientific papers as follows:

First paper: “Electrical and electromagnetic interference shielding properties of

flow-induced oriented carbon nanotubes in polycarbonate”; investigating the effects of

alignment on electrical conductivity of MWCNT/PC composites and also providing

useful information about the shielding mechanisms of CPCs.

Second paper: “Comparative study of electromagnetic interference shielding properties

of injection molded versus compression molded multi-walled carbon

4

nanotube/polystyrene composites”; exploring the impacts of MWCNT alignment on

EMI shielding properties of MWCNT/PS composites over the X-band frequency range

(8.2 – 12.4 GHz) and inspecting the mechanisms behind.

Third paper: “An innovative method to reduce the energy loss of conductive

filler/polymer composites for charge storage applications”; creatively introducing

MWCNT alignment as a novel technique to improve the dielectric properties of

MWCNT/PS composites.

Fourth paper: “Broadband dielectric properties of multi-walled carbon

nanotube/polystyrene composites”; detailing the broadband dielectric behaviors of

MWCNT/polymer composites, i.e., 10-1

– 10+6

Hz. This paper is a decent introductory

section for comparing the broadband dielectric properties of CPCs holding MWCNTs

and CuNWs.

Fifth paper: “Novel composites of copper nanowire/PVDF with superior dielectric

properties”; innovatively presenting CuNW, as a competent substitution for MWCNT,

with enhanced broadband dielectric properties.

4. Finally, a general discussion, including the obtained achievements and brief summary of

results, is given followed by conclusions, recommendations and proposed future work.

5

1.3. References

[1] Al-Saleh MH, Sundararaj U. Electromagnetic interference (EMI) shielding effectiveness of

PP/PS polymer blends containing high structure carbon black. Macromolecular Materials

and Engineering. 2008;293(7):621-30.

[2] Yang SY, Lozano K, Lomeli A, Foltz HD, Jones R. Electromagnetic interference shielding

effectiveness of carbon nanofiber/LCP composites. Composites Part a-Applied Science and

Manufacturing. 2005;36(5):691-7.

[3] Strumpler R, Glatz-Reichenbach J. Conducting polymer composites. Journal of

Electroceramics. 1999;3(4):329-46.

[4] Kakimoto MA, Takahashi A, Tsurumi TA, Hao J, Li L, Kikuchi R, et al. Polymer-ceramic

nanocomposites based on new concepts for embedded capacitor. Materials Science and

Engineering B-Solid State Materials for Advanced Technology. 2006;132(1-2):74-8.

[5] Lu JX, Moon KS, Xu JW, Wong CP. Synthesis and dielectric properties of novel high-K

polymer composites containing in-situ formed silver nanoparticles for embedded capacitor

applications. Journal of Materials Chemistry. 2006;16(16):1543-8.

[6] Arjmand M, Apperley T, Okoniewski M, Sundararaj U. Comparative study of

electromagnetic interference shielding properties of injection molded versus compression

molded multi-walled carbon nanotube/polystyrene composites. Carbon. 2012;50(14):5126-

34.

[7] Chung DDL. Electromagnetic interference shielding effectiveness of carbon materials.

Carbon. 2001;39(2):279-85.

[8] Al-Saleh MH, Sundararaj U. Electromagnetic interference shielding mechanisms of

CNT/polymer composites. Carbon. 2009;47(7):1738-46.

6

Chapter 2

Literature Review

2.1. Conductive Filler/Polymer Composites (CPCs): Structure, Applications and Market

The rapid growth in portable electronics market has accelerated the demand for electronics with

(1) reduced PCB size, (2) light-weight conductive enclosures to decrease EMI pollution, and (3)

appropriate packaging presenting ESD protection [1-4]. CPCs have drawn great interest to meet

these requirements, due to their tunable electrical conductivity, light weight, low cost, corrosion

resistance and easy processability [5, 6]. CPCs are produced by incorporating conductive filler into

a polymer matrix. Conventional polymers such as PC, PS and PVDF are insulative; however,

adding conductive fillers to these polymer matrices can give them broad range of conductivities

through the formation of two- or three-dimensional conductive network. Figure 2-1 shows a

schematic of conductive network formation in a CPC.

Figure 2-1: Schematic of conductive network formation in a CPC [5].

7

The ability to manipulate the conductive network formation in CPCs entitles them to present

wide spectrum of conductivity, and to perform as insulative, semi-conductive or conductive

materials (Figure 2-2). The level of electrical conductivity determines the applications in which

CPCs can be employed. Charge storage, ESD protection and EMI shielding are the major

applications of CPCs, requiring low, medium and high electrical conductivity, respectively. Table

2-1 lists the required range of electrical conductivity for each application.

Figure 2-2: The approximate range of electrical conductivity covered by CPCs [7].

Table 2-1: CPC applications with their required range of electrical conductivity [8].

Application Electrical Conductivity (Sm-1

)

Charge Storage < 10-11

Antistatic Dissipation 10-7 – 10

-10

ESD Protection 10-3 – 10

-6

EMI Shielding > 10+1

8

Figure 2-3 depicts some applications of CPCs requiring different ranges of electrical

conductivity. CPCs with low electrical conductivity present desirable dielectric properties for

charge storage applications. This is due to their unique structure holding a large number of

nanocapacitor structures, i.e., conductive filler as nanoelectrode and polymer matrix as

nanodielectric [9-14]. CPCs with medium electrical conductivity can be used for antistatic

dissipation and ESD protection. Antistatic dissipation is required where relative motion between

dissimilar materials takes place, such as conveyor belts and airplane tires. ESD protection is used to

bleed off charge on the surface to avert harmful arcing discharges. ESD protection applications

comprise chip or circuit board carriers for shipping of electronic equipments [6].

Figure 2-3: Some important applications of CPCs. From left to right: Capacitors (charge storage);

airplane tire (antistatic dissipation); circuit board carrier (ESD protection); cell phone enclosure

(EMI shielding) [6, 12].

EMI shielding is the most demanding application of CPCs in terms of required electrical

conductivity [15-19]. Electronic devices innately emit electromagnetic (EM) waves. Since these

waves can interfere with the operation of other electronic devices, related agencies have applied

regulations for electromagnetic compatibility (EMC) of electronics housings [20]. EMC means that

a device does not affect itself or other devices by emitted emissions. In order to comply with EMC

regulations, electronics should be enclosed with appropriate conductive shields. Conventional

polymers, due to their insulative nature, are inherently transparent to incident EM waves. However,

9

CPCs due to presence of interacting mobile charge carriers in conductive filler can attenuate the EM

wave efficiently. The CPCs used in EMI shielding applications typically have electrical

conductivity more than 10+1

S·m-1

[21]. Highly electrical conductive CPCs, i.e. CPCs holding large

number of interacting mobile charge carriers, can shield the EMI effectively.

The ever-increasing demands of high-performance electronic devices has led to flourishing

market for CPCs. Figure 2-4 demonstrates the global market for CPCs in 2010-2016 [22]. The

global market for CPCs was $1.7 billion and $1.8 billion in 2010 and 2011, respectively, and is

expected to reach $2.4 billion by 2016 at a compound annual growth rate of 5.9%. The market for

CPCs includes those for EMI shielding, ESD/antistatic packaging, electrostatic painting, printed

circuit board components, etc. EMI shielding comprises stationary and mobile enclosures. ESD

technologies include those used for packaging, furniture, apparel, flooring and electronics; whereas,

PCB components comprise batteries, transistors, capacitors, corrosion-resistant coating products,

etc [23]. This huge competitive market has stimulated companies to perform intense research to

develop novel high-performance CPCs.

Figure 2-4: Global market for CPCs in 2010-2016 [22].

10

2.2. Electrical Conductivity

Electrical conductivity originates from the ordered movement of charges (electric current). In the

absence of electric field, the conduction electrons are scattered freely in a solid due to their thermal

energy. If an electric field, E, is applied, the force on an electron, e, is –eE and the electron is

accelerated in the opposite direction to the electric field due to its negative charge. Then, there is a

net velocity and the current density is given by

J=Ne e E (2-1)

where J the current density, Ne the number of electrons, e charge of electron, the electron

mobility, and E the applied electric field [24]. The applied electric field equals to applied voltage

over the thickness of a sample. Then, the electrical conductivity can be defined as

(2-2)

where is the electrical conductivity and its SI unit is Siemens per meter (S·m-1

). Electrical

conductivity of materials is a property, which spans a very wide range. The conductivity of

insulators is typically less than 10-12

Sm-1

, that of semi-conductive materials covers the range 10-12

to around 10+2

Sm-1

, and for semi-metals and metals is more than 10+2

Sm-1

.

The conductivity of materials can be explained using the Band Theory [25]. In the Band Theory,

the energy level of each electron is considered as a horizontal line. As any solid has a large number

of electrons with different energy levels, the sets of energy levels form two continuous energy

bands, called the valence band and the conduction band. The energy gap between two bands

represents the forbidden zone for electrons. Electrons restricted to individual atoms or interatomic

bonds are, in the Band Theory, said to be in the valence band. Those electrons that have sufficient

11

energy to be delocalized by an applied electric field lie in the conduction band. Figure 2-5 shows a

schematic of the bands in a solid identifying three main types of materials: insulators,

semiconductors and metals.

Figure 2-5: Simplified diagram of the electronic band structure in the Band Theory [24].

The energy gap between valence and conduction bands in metals is negligible and they mostly

overlap each other; therefore, metals show very high conductivity. In intrinsic semiconductors, the

valence-conduction gap is larger than metals, but small enough so that the electrons in valence band

can be excited to conduction band by thermal energy. Among the three types of materials shown in

Figure 2-5, insulators show the largest valence-conduction band gap and; therefore, fewer electrons

can be found in or excited to their conduction band by an applied electric field. This leads to very

low conductivity in insulators.

12

2.3. Electrostatic Discharge (ESD)

All people know static electricity as the static cling of clothing or arcing when touching a

doorknob or metallic object. Static electricity is a surface phenomenon and static charges just exist

on the surface and not in the bulk of materials [26, 27]. Static electricity can be produced in various

ways, but the most common method is triboelectric charging, which is the charge production by

contact and separation of materials [28]. Upon contact of materials, some materials tend to absorb

free charges, while some others are prone to give up free charges. Thus, the material with higher

affinity to absorb electrons will be charged negatively and the other material will acquire positive

charges. The magnitude of charge transfer depends on the difference in the affinity of two materials

to absorb electrons, surface tidiness, the pressure of contact, surface smoothness, speed of

separation, amount of rubbing, etc.

Triboelectric charging occurs only when two insulators or one insulator and one conductor

contact each other and then get separated. In these cases, some charges will be transferred from one

material to another. As the charges in an insulator are not nomadic, the transferred charges will not

return to their original position after separation and two materials will remain charged. If two

conductors contact each other, upon their separation the charges will return to their original

position, since the mobility of charges is high in conductors, and the conductors become neutral.

The science of static electricity has been employed to design many useful devices, such as

electrostatic copier, air purifier and dust precipitators. Nevertheless, uncontrolled ESD has appeared

as a threat to the industry of electronics. ESD costs the electronics industry millions of dollars

annually in damaged and degraded parts at different incremental levels (Figure 2-6). Accordingly,

13

related agencies have adjusted standards, under the overall subject of EMC, to protect the

electronics from ESD. Usually, the same techniques as EMI shielding regulations have been utilized

to satisfy the ESD protection standards [29].

Figure 2-6: Costs due to ESD damage at various incremental levels [30].

A charged insulator by itself is not an ESD threat, since the charges are not nomadic in an

insulator, and is not able to generate ESD. The danger will emerge when this charge is transferred

to a conductor, by contact or induction, which is capable of discharging. Charges stored on an

insulator leave it in two ways, leakage or arcing. Arcing is an electrical breakdown of a

nonconductive media such as air, leading to intense current through the media. Arcing is avoided

due to damage from intense current; therefore, leakage is the preferred way of discharging

materials.

14

As rapid discharge may result in large peak current that can damage electronic components, it is

of great significance to leak off the charges over a period of time. The leak off time for an object is

proportional to its surface resistivity. Hence, it is very important to select a material with an

appropriate surface resistivity to avert large peak current. If a charge exists on a surface, it should

be discharged slowly to limit the current and avoid harm [28].

DOD-HDBK-263 categorizes the material into four classifications in terms of surface resistivity,

which are listed in Table 2-2 [31]. Conductive materials, due to their high electrical conductivity,

are the rapidest to discharge the free charges. Grounded conductive materials may damage

electronics if they come in contact with electronic devices, since they will leak free charges off over

a short time with a large peak current.

Table 2-2: Classifications of materials in terms of surface resistivity [31].

Grounded static dissipative and antistatic materials, with the range of surface resistivity shown

in Table 2-2, are the desirable candidates to dissipate accumulated charges on sensitive electronics.

Static dissipative materials dissipate free charges at a slower rate relative to conductive materials

due to higher surface resistivity. Grounded static dissipative materials can be employed to prevent

charge buildup and dissipate safely the charges already stored. Antistatic materials are the slowest

Material Surface Resistivity (ohmsq-1

)

Conductive < 105

Static Dissipative 105 – 10

9

Antistatic 109 – 10

14

Insulative > 1014

15

to dissipate charge. Nonetheless, they are useful since they are able to dissipate charges faster than

it is generated and thus they can preclude materials from accumulating charges. Insulators, due to

their high surface resistivity, hold whatever charge they have and they should not be employed in

ESD-sensitive environment alone. Figure 2-7 shows a schematic of static-safe workbench, which

should be used for handling electronic setups. The tabletop, floor mat and wrist strap are made or

covered by ESD protective or static dissipative materials which are grounded through 1 M

resistor. This configuration can reduce the damages arising from ESD tremendously.

Figure 2-7: The diagram of a typical static-safe workbench [32].

16

2.4. Electromagnetic Interference (EMI) Shielding

2.4.1. General Background

Many electronic devices inherently irradiate electromagnetic signals. EMI occurs when emitted

signals from a device interfere with its operation or operation of other electronic devices. EMI

effects can range from interruption of operation to degradation of electronics or electrical

equipments [21]. Therefore, developing appropriate EMI shields has emerged as an important

technical challenge considering the upward market of electronic devices, such as laptops, cell

phones, weather radars, TV picture transmitters, etc [1-3, 16, 33]. Figure 2-8 depicts the usage of

shielded enclosures to contain or exclude radiated emissions.

Figure 2-8: Illustration of the use of shielded enclosure (a) to contain radiated emission, (b) to

exclude radiated emission [34].

To reduce EMI issues, appropriate agencies such as CISPR (Comité International Spécial des

Perturbations Radioélectriques) have adjusted regulations for electromagnetic compatibility (EMC)

of electronic enclosures. EMC means that a device does not affect itself or other devices by its

radiations and these regulations must be satisfied or exceeded for commercial electronics.

Considering EMC regulations, an EMI shielding effectiveness (EMI SE) of at least 30 dB, which

corresponds to shielding of 99.9% of incident radiation, i.e., 0.1% is transmitted, is considered

17

commercially as a sufficient level of shielding for many applications [33, 35]. In order to meet these

extremely large values for EMI SE, the electronics must be entirely enclosed by the shield. Any

penetration into the shield, unless appropriately treated, can significantly reduce the EMI SE [8].

Metals are definitely the most commonly employed materials for the EMI shielding of

electronics. Nevertheless, when metal sheets are used as shields, poor quality seams can form slots,

which lead to leakage of radiation reducing the EMI shielding. In addition, there are some other

serious deficiencies in metal-coated polymers, such as recyclability and delamination that

necessitate the development of versatile substitutions for the future [4]. CPCs have, thus, recently

drawn great attention, due to their light weight and processability which aids to reduce or omit the

seams and penetrations in electronics’ enclosures.

2.4.2. Magic of Shielding

To design a shield (CPC or metal-coated polymer) appropriately, an understanding of the

shielding mechanisms is critical, so that both overshielding, which results in higher product cost,

and undershielding, which may cause failure in the final material application, can be avoided [17,

36-39].

Based on the distance between EMI source and the shielding enclosure, the radiation can be

classified as near field or far field [33, 35]. The transition point is the wavelength divided by 2.

The EMI setup employed in this dissertation for EMI shielding measurements operated in the far

field; accordingly, all the equations and shielding mechanisms will be presented for the far field. In

the far field, the EM wave is considered a plane wave. In a plane wave, the electric and magnetic

18

fields are perpendicular to each other and these fields are transverse to the direction of wave

propagation. In the near field, however, the fields are often much more complex.

When an EM wave strikes a shield, the electrons in the shield respond to the electric and

magnetic fields according to Lorentz’s force law [33, 34]:

(2-3)

where q is the charge of each particle of velocity, ; is the magnetic permeability of free space

equal to 4π×10-7

H·m-1

; and, and are the electric and magnetic fields, respectively. The charged

particles actually diminish the incident EM wave in two ways: (1) the charges absorb energy from

the incident wave and move in response to the EM wave; and, (2) these moving charges also

generate an electromagnetic field, called an induced field, which decreases the power of the

transmitted EM wave.

As schematically illustrated in Figure 2-9, three mechanisms are generally involved in EMI

shielding, namely: reflection, absorption and multiple-reflection [16, 33, 40-42]. When an EM wave

strikes a conductive material, a fraction of the wave is reflected from the shield due to interaction

with surface charges and a fraction is transmitted through the shield with its energy dissipated via

absorption. The amplitude of the wave that penetrates through the conductive material is attenuated

by a factor of

, where z is the distance that EM wave penetrates into the shield and δ is the skin

depth of the conductive material. The skin depth is the distance inside the conductive material at

which the wave power decreases to of its incident value and is defined as √ ,

where f is the wave frequency, μ is shield’s magnetic permeability and σ is the shield’s electrical

conductivity [43]. The greater the amount of mobile charge carriers in the shield, the greater is the

19

ability of the shield to attenuate the EM wave through reflection and absorption mechanisms [3,

18]. When the EM wave strikes the backside of the shield (shield-to-air interface), a fraction of the

wave is transmitted through the interface; and, a fraction is reflected off the interface. This reflected

wave from the second interface is also a part of the reflection mechanism. The final mechanism of

shielding is multiple-reflection, which usually occurs in materials with large interfacial areas, such

as filler-added polymers. Multiple-reflection is actually re-reflection of waves already reflected

inside the shield. Multiple-reflection has a negative effect on the overall EMI shielding and it can be

ignored if the shield’s thickness is larger than the shield’s skin depth [16].

Figure 2-9: Illustration of interaction between incident plane wave and conductive barrier [34].

20

2.4.3. Shielding Effectiveness

An EM wave is composed of two fields: electric field and magnetic field. The ratio of electric

field to magnetic field of a propagating wave in any media is called intrinsic impedance [33]. This

ratio is extremely important in the degree of shielding and prevailing shielding mechanisms in

conductive shields. The unit of intrinsic impedance is E/H = (V/m)/(A/m) = ; where E is electric

field and H is magnetic field. The intrinsic impedance of a material can be defined as following:

√

(2-4)

where is intrinsic impedance, is electrical conductivity, is angular frequency and and are

permeability and permittivity, respectively. The permittivity and permeability of free space are

equal to 8.85×10-12

F·m-1

and 4×10-7

H·m-1

, respectively. Considering low conductivity of free

space, the intrinsic impedance of free space is equal to 377 . As an incident EM wave penetrates

into a conductive shield, the intrinsic impedance decreases tremendously and, therefore, electric

field transforms partially to magnetic field. The degree of transformation depends on the degree of

impedance mismatch between two media.

The EM wave expressions can be written with the same analogy of the power expressions with

the circuit variables [33, 34]. For an electrical circuit, the instantaneous power dissipated by resistor

is given by

( ) ( ) ( ) (2-5)

where v(t) and i(t) are instantaneous voltage and current, respectively. Analogously, the

instantaneous power density P(t) for a plane wave, with the electric and magnetic field

perpendicular to each other, is given by

21

( ) ( ) ( ) (2-6)

Due to time-changing nature of EM wave, the average power Pave is typically used:

( )

( )

(2-7)

where Ex and Hy are the root means square of electric and magnetic fields in x and y directions,

respectively, and is the intrinsic impedance of conductive material. Equation 2-7 shows that

power is proportional to square of amplitude of electric field or magnetic field.

The ability of conductive materials to attenuate EM wave is stated as EMI shielding

effectiveness (EMI SE). EMI SE is expressed in dB and defined as logarithm of incident electric

(magnetic) field to transmitted electric (magnetic) field

( ⁄ ) (2-8)

or considering that the power is proportional to square of amplitude of electric field or magnetic

field leads to

( ⁄ ) ( ⁄ ) (2-9)

where PI is the incident power, PT is the transmitted power and EI and ET are the root mean square

of incident and transmitted electric fields, respectively, and HI and HT are the root mean square of

incident and transmitted magnetic fields, respectively. It should be mentioned that second and third

parts in Equation 2-9 are equivalent when the media on both sides of the shield are the same.

Equation 2-8 says that the lower the transmitted EM power to free space, the higher the EMI SE of

the shielding material. Equations 2-8 and 2-9 can also be used to calculate the contributions of

reflection and absorption to overall EMI SE considering relevant incident and transmitted fields.

22

2.4.4. Reflection, Absorption and Multiple-reflection for Conductive Monolithic Materials

The shielding mechanisms presented in the following sections are developed for conductive

monolithic materials, such as bulk of metals. The presented equations need to be modified for

heterogeneous structures, such as CPCs.

2.4.4.1. Shielding by Reflection

As shown in Figure 2-9, an incident EM wave interacts with the conductive shield through

reflection, absorption and multiple-reflection mechanisms. For an incident EM wave, the reflection

and transmission coefficients from the first and second interfaces, in the absence of absorption, can

be defined as follows:

(2-10)

(2-11)

where η0 is the impedance of free space and η1 is the intrinsic impedance of shielding material.

Considering impedance as the ratio of electric field to magnetic field gives

(2-12)

(2-13)

In view of the above equations and lower intrinsic impedance of conductive shield relative to

free space, it can be claimed that the primary transmission of magnetic field takes place at the first

interface; whereas, the primary transmission of electric field occurs at the second interface. As a

23

matter of fact, at the first interface the transmitted magnetic field may have greater strength than

incident magnetic field due to electric field-magnetic field transformation. The same scenario is true

for the electric field at the second interface. However, it is notable that the transmitted power is

always smaller than incident power.

Therefore, effective shields for the attenuation of electric field can be constructed from thin

shield with very high conductivity to short out the electric field at the first interface; whereas, the

shields for the attenuation of magnetic field can be constructed from thick shields with high

electrical conductivity and magnetic permeability [33].

In the absence of absorption and using Equations 2-9 to 2-11, shielding by reflection can be

defined as:

(

) (

)

( ) (2-14)

In a conductive material, the conduction current is much greater than the displacement current, i.e.,

. Thus, substituting the approximate formula for intrinsic impedance of a conductive shield

into Equation 2-14 gives

(2-15)

where is magnetic permeability of conductive shield relative to that of free space and is the

conductivity of shield relative to the conductivity of copper. For the permittivity and permeability

of metals, it is customary to refer to that of free space, while for the conductivity of metals, it is

usually referred to that of copper:

= Permeability = r0 = r (4 10-7

H·m-1

)

24

= Permittivity = r0 = r (8.85 10-12

F·m-1

)

= Conductivity = r0 = r (5.8 10+7

Sm-1

)

Equation 2-15 gives a good idea to select appropriate materials to present a high reflection loss.

According to Equation 2-15, the reflection loss is proportional to

, i.e., the materials with higher

conductivity present higher reflection loss, while the magnetic materials degrade the reflection loss.

2.4.4.2. Shielding by Absorption

Absorption attenuates EM wave through interaction with mobile charge carriers and

electric/magnetic dipoles [16]. The amplitude of EM wave that penetrates through a conductive

material is attenuated by factor , where = √ ( ) and z is the distance

inside the shield. γ, α and β are called propagation constant, attenuation constant and phase constant,

respectively. For the conductive materials, the amplitude of the wave is attenuated by factor

and =1/, where is the skin depth of conductive shield. Therefore, for the conductive shield

shown in Figure 2-9 with a thickness of t, shielding by absorption can be defined as following:

(

)

√

(2

(2-16)

Equation 2-16 elucidates that a material with high conductivity and magnetic permeability can

absorb the EM wave efficiently. In addition, there is a linear relationship between shielding by

absorption and thickness of shielding material. As a matter of fact, the higher the thickness of a

conductive material, the greater is the amount of interacting mobile charge carriers and/or

electric/magnetic dipoles.

25

2.4.4.3. Shielding by Multiple-Reflection

Multiple-reflection represents internal reflections inside a conductive barrier. As the resultant of

multiple-reflection is an increment in transmitted wave, it has a negative influence on overall EMI

shielding. Figure 2-10 illustrates the effect of multiple-reflection inside a conductive shield with the

calculations in terms of intrinsic impedance and reflection and transmission coefficients.

Considering multiple-reflection effect, the overall transmitted electric field can be defined as

( ) and ( )

( ) (2-17)

If | | as is the case for conductive shield, the shielding by multiple-reflection can be defined as

| | | (

)

| (2-18)

As in conductive monolithic materials, the propagation constant is almost equal to attenuation

constant or inverse of skin depth; therefore, multiple-reflection is negligible when the thickness of a

material is much greater than its skin depth ( √ ).

Given the equations for shieldings by reflection, absorption and multiple-reflection, the overall

EMI SE, SEOA, can be defined as

]+ [ √ ] | (

)

| (2-19)

26

Figure 2-10: Schematic of the effects of multiple-reflection in a conductive shield: (a) combining

multiple transmissions, (b) calculations in terms of intrinsic impedance and reflection and

transmission coefficients [34].

Table 2-3 presents a list of common materials employed in shielding barriers with their electrical

conductivity and magnetic permeability. This table can give a good idea for choosing proper

materials to shield an EM wave with specific features. As mentioned before, the reflection loss is a

function of

, whereas the absorption loss is a function of rr; and reflection is more important

for the electric field while absorption is of more consequence for the magnetic field. Thus, having

27

the knowledge of the nature of field and limitations for conductive shield in terms of weight and

cost, an efficient and cost-effective shielding material can be selected to shield an EM wave.

Table 2-3: Electrical conductivity and magnetic permeability of common materials used in shielding

barriers [33, 34].

Material r r A rr R r /r

Silver 1.05 1 1.05 1.05

Copper 1 1 1 1

Gold 0.7 1 0.7 0.7

Aluminum 0.61 1 0.61 0.61

Nickel 0.2 600 120 3.3×10-4

Stainless Steel 0.02 500 10 4×10-5

2.4.5. Effect of Real Permittivity on Shielding of Conductive Monolithic Materials

Effect of real permittivity on EMI shielding in conductive monolithic materials is negligible

since the ratio of conduction current to displacement current is small. If a known alternating voltage

is applied to a conductive monolithic material, the resultant current is almost in phase with the

applied voltage. The real permittivity of conductive monolithic materials is small and is presumed

to be equal to that of free space. Therefore, shielding arising from polarization loss in conductive

monolithic materials is negligible and permittivity does not play any role in the equations developed

in the preceding sections. However, CPCs due to their unique structure holding a large number of

nanocapacitors present a high real permittivity. Hence, there is a phase difference between the

applied alternating voltage and measured current in CPCs. Due to high real permittivity of CPCs,

there is a considerable shielding originating from polarization loss. Accordingly, the formulas

28

developed for conductive monolithic materials must be modified for CPCs in order to consider the

effect of polarization loss and real permittivity.

2.5. Dielectric Theory

2.5.1. Dielectric Material

A material is classified as “dielectric” if it has the ability to store energy when an external

electric field is applied. The degree to which a dielectric responds to an applied electric field can be

acknowledged by parallel-plate capacitor configuration. If a DC voltage of V is applied to such a

capacitor, where the plates are separated by the distance d, the electric field between the plates is

uniform and equal to E=V/d. This electric field leads to charge polarization within the dielectric

material, i.e., separation of positive and negative charges. In other words, dielectric material

increases the storage capacity of capacitor by neutralizing charges at the electrodes (Figure 2-11).

Figure 2-11: Charges on a parallel-plate capacitor with (a) air between the plates, and (b) a

dielectric between the plates [25]. (Reprinted with the Permission of Cambridge University Press)

29

When the dielectric material is free space, the charges per area stored on the surface of plates is

equal to , where 0 is real permittivity of free space. However, if free space is replaced with

a dielectric material, an extra charge (denoted as P) is stored on the surface of capacitor originating

from higher polarisability of dielectric material relative to free space. This extra charge is defined as

following:

( ) (2-20)

where r is real permittivity of dielectric material relative to free space. The higher the real

permittivity of a dielectric material and the greater the applied electric field, the higher is the stored

energy on surface of a capacitor.

2.5.2. Permittivity

Permittivity has two components; namely real permittivity (ε´) and imaginary permittivity (ε˝).

Real permittivity shows how much energy from an external field is stored in a material, however,

imaginary permittivity shows how dissipative a material is to an external electric field. Therefore,

permittivity can be defined as a complex quantity as below

(2-21)

where ɛ´ and ɛ˝ are real permittivity and imaginary permittivity, respectively. It is worth noting

that in literature real permittivity is also called dielectric permittivity or dielectric constant; whereas,

imaginary permittivity has other names such as dielectric loss or loss factor.

As no perfect dielectric material exists, all dielectric materials can be modeled in terms of an

equivalent circuit of a resistor in parallel with an ideal capacitor [25, 44-46]. When an AC voltage

30

source “V” is applied to a dielectric material, two different electrical currents are induced within the

dielectric, i.e., conduction current and displacement current (Figure 2-12). The former arises from

free electrons and will give rise to electric loss (imaginary permittivity) while the latter is due to

charge polarization (real permittivity).

The current I that flows through such a circuit after applying an alternating voltage

can be calculated as follows

( )

(

) (2-22)

where Q, t, ω and C0 are stored charge, time, angular frequency and the capacitance of free space,

respectively. Equation 2-22 shows that the induced current has two components; i.e. IC (capacitive

component) which leads the voltage by 90° and IR (resistive component) which is in phase with

voltage. The resistive current passes through the capacitor (leakage current), whereas the capacitive

current does not pass through the capacitor; but flows in the circuit to compensate for the charges

stored on the surface of capacitor.

(2

(2-23)

(2-24)

The real and imaginary permittivities or capacitive and resistive currents are linked together with

the term dissipation factor, which is of great importance in industry.

(2-25)

Notice that when , the material is considered as a good conductor, and when ,

the material is regarded as a good insulator.

31

Figure 2-12: (a) Circuit diagram of a dielectric under an AC field, (b) Argand diagram of complex

current-voltage relationship [25]. (Reprinted with the Permission of Cambridge University Press)

2.5.3. Dielectric Mechanisms

A dielectric material has an arrangement of electric charge carriers that can be reorganized by

applying an electric field, i.e., the charges get polarized to compensate for the applied electric field.

As illustrated in Figure 2-13, there are several dielectric mechanisms that contribute to overall real

permittivity, namely: interfacial, dipolar, atomic and electronic. All or some of these polarization

mechanisms may occur in a material depending on morphology and frequency range [46-48].

Interfacial polarization is broadly observed in heterogeneous systems with phases with different

conductivities or real permittivities, such as suspension of colloids, blends and CPCs [45, 49, 50].

This polarization is referred to as Maxwell-Wagner-Sillars (MWS) after the study of Maxwell who

first recognized the mechanism for DC field [51] and Wagner and Sillars who extended the theory

for AC field [52-54]. Interfacial polarization occurs due to the accumulation of mobile charges, on a

mesoscopic scale, at the interface of dissimilar phases with different electrical conductivities or

32

permittivities. As interfacial polarization takes place at large scale (mesoscopic scale), it has usually

been observed at low frequencies, due to its large relaxation time with respect to electric field

frequency at high frequencies [9, 11].

Figure 2-13: Frequency response of dielectric mechanisms [49, 54].

Dipolar (Orientational) polarization happens in polar materials, which contain permanent dipoles

in their structure, such as molecule of water [46, 49, 55]. The dipole moments are oriented in a

random manner in the absence of electric field. By applying an electric field, electric dipoles

experience a torque T and rotate in response to applied field. The friction due to orientation of

dipoles in an AC field is used in many applications, such as warming foods up in microwave ovens.

The frequency range over which dipolar polarization occurs depends on the size of molecule, from

105 Hz for large molecules such as a protein in solution to around 10

9 Hz for smaller molecules

33

such as amino acids [49]. Above these frequencies, the dipolar polarization diminishes due to

relaxation phenomenon.

Atomic polarization process originates from displacement of charged ions with respect to each

other in a crystal lattice. An applied field leads to separation of positive and negative ions, inducing

a dipole moment. This type of polarization is the predominant form of polarization in inorganic

crystals, glasses and ceramics, while in organic compounds, where ions are absent; this type of

polarization does not contribute to total polarization. The high real permittivity in conventional

ferroelectric ceramics originates from atomic polarization, where polarization happens collectively

in domains [46]. Atomic polarization extends from DC up through infrared frequencies.

Electronic polarization takes place inside atoms when an electric field displaces the nucleus with

respect to the electrons that surround it. For many dry solids, this is the dominant polarization

mechanism. Electronic polarization continues over the whole frequency range from DC up through

optical frequency. The reason that electronic polarization has the largest frequency coverage among

all polarization mechanisms is its smallest scale of charge polarization, i.e., intra-atomic scale.

The electric dipole has a magnitude equals to strength of each charge times the separation

between charges. Considering the scale at which charges are polarized at different polarization

mechanisms, the degree of contribution of polarization mechanisms to real permittivity has the

following order: interfacial, dipolar, atomic and electronic. Therefore, at low frequencies, all the

mechanisms may contribute to real permittivity; however, the role of the ones with larger

polarization scale is more significant than the others. With frequency increase, the sluggish

34

mechanisms drop out in turn, leaving the faster ones to contribute to real permittivity. This leads to

a descending trend for real permittivity as a function of frequency.

The imaginary permittivity (dielectric loss) is the part of energy of an AC field in a dielectric

material which is dissipated into heat. The dielectric loss is composed of two components; namely

Ohmic loss and polarization loss. Ohmic loss arises from DC conduction and represents the

dissipation of electrical energy by mobile charge carriers moving through the dielectric material. In

fact, the nomadic charges dissipate the electrical energy via collision with other particles. The

dissipation by Ohmic loss weakens with frequency due to the reduced available times for free

electrons to sweep the network in each half cycle of alternating field. It is notable to declare that DC

conduction is independent of frequency.

The polarization loss in a dielectric material includes: interfacial, dipolar, atomic and electronic.

As the magnitude and direction of electric field vary in an AC field, the polarized charges also

change in magnitude and direction. It was explained that the polarized charges contribute to real

permittivity by generating a momentum arising from separation of positive and negative charges.

Simultaneously, the friction accompanying the orientation of electric dipoles in each half cycle of

an AC field raises the dielectric loss. Therefore, it can be said that the polarization loss, as a portion

of imaginary permittivity, has a direct relationship with real permittivity. In other words, the higher

the real permittivity of a dielectric, the greater is the momentum generated by the charge

polarization, and thus the higher is the dissipation of energy to come over the momentum to reorient

the dipoles in each half cycle of alternating field. Thus, the order of magnitude of polarization loss

mechanisms is: interfacial, dipolar, atomic and electronic.

35

If a dipole is oriented due to an applied electric field, the orientation of dipole requires a certain

amount of time (relaxation time). Relaxation time is a measure of mobility of dipoles within a

dielectric [47]. At frequencies below relaxation time, the electric field is slow enough that the

dipoles keep pace with alternating field. Thus, the imaginary permittivity demonstrates a direct

relationship with frequency at frequencies below relaxation. In fact, at frequencies below relaxation

time, increasing frequency facilitates more frequent occurrence of fully reorientation of dipoles in a

time frame. Thus, imaginary permittivity ascends with frequency till reaching to a maximum where

dielectric relaxation or resonant occurs (Figure 2-13). The relaxation or resonant frequency is the

maximum frequency in which the dipoles can adapt themselves to an alternating electric field.

Above the relaxation or resonant frequency, both real and imaginary permittivities diminish since

the electric field is too fast to affect the dipole rotation, and charge polarization disappears.

A resonant effect is usually engaged with electronic and atomic polarizations and relaxation

effect is linked to interfacial and atomic polarizations [47]. The resonant frequency and relaxation

frequency are defined by a peak of maximum absorption in and a response in (Figure 2-13).

Above the resonance and relaxation, the contributions of charge polarization mechanisms to real

and imaginary permittivities vanish [47].

2.5.4. The Electrical Current of Dielectrics under a Step DC Voltage

It is easier to understand the frequency dependence of AC conductivity by exploring the current

response of a dielectric under a step DC voltage. The spectra of currents, depicted in Figure 2-14,

36

are generated to compensate for the charges stored on the surface of dielectric due to step DC

voltage. The stored charges arise from polarization mechanisms within the dielectric material.

Figure 2-14: Typical DC response of a dielectric to a step voltage application [46].

By applying a DC voltage, a pulse of initial current with very short duration is generated. This

current is associated with electronic (IElectronic) or atomic (IAtomic) polarization, which develops in

times of the order of a half cycle of optical or infrared frequencies, respectively. Although the

amount of stored charges due to atomic and electronic polarization is very small, but due to their

very short time of occurrence, the generated current is quite large. Next, if dielectric is inherently

polar, another high level of current (IDipolar) is generated, which is related to dipolar polarization.

IDipolar is smaller than IElectronic or Iatomic due to longer time frame of occurrence. Then, there is a

current related to interfacial polarization (IInterfacial), which diminishes more slowly than IDipolar, due

to its larger time constant. Finally, the insulation current levels off to long time DC conductivity.

The electrical currents from electronic, atomic, dipolar and interfacial polarizations are capacitive or

37

out-of-phase, which do not pass through the insulator but are generated to compensate for the

charges stored on the surface of capacitor. The DC current is in-phase or resistive and is real flow of

charges through the dielectric under an applied electric field.

2.5.5. DC and AC Conductivity

The electrical conductivity of a material is proportional to induced electrical current over the

applied voltage (

), where electrical conductivity, I electrical current and V applied voltage.

The electrical current is defined as the amount of charges passes a cross section in a time frame.

This definition is the basis to illuminate the difference between DC and AC conductivities.

The frequency responses of electrical current in DC and AC fields are different. In an AC field,

at low frequencies, the electrical current is just due to DC conductivity. With increase in frequency,

the role of capacitive current highlights, since high-frequency voltage facilitates frequent

development of capacitive currents in a time frame. For instance, for an AC voltage with optical

frequency, the role of Ielectronic is significant since it can be generated at each half cycle of optical

frequency. Although the amount of capacitive charges are smaller than resistive charges; however,

due to very short occurrence time of polarization mechanisms, the magnitude of capacitive current

is much higher than DC current. Hence, AC conductivity, which is proportional to sum of resistive

and capacitive currents, shows a strong ascending trend with frequency. Of interest to note, DC

conductivity, which originates from resistive current, is usually independent of frequency and is

industrially measured under a low-frequency AC voltage, where the influence of capacitive currents

is negligible [56].

38

AC conductivity can be obtained using the real permittivity and imaginary permittivity

(capacitive currents and resistive current, respectively) data. Real permittivity corresponds to

currents arising from charge polarization and is out-of-phase with voltage; whereas imaginary

permittivity corresponds to leakage current through a capacitor, which is in-phase with voltage.

Thus, combining Equations 2-2 and 2-22 gives

( ) ( )

(2

(2-26)

where AC is AC conductivity, 0 is permittivity of free space, is angular frequency and ´and

ʺare real and imaginary permittivities, respectively. This equation shows that the real part of AC

conductivity is proportional to imaginary permittivity and occurs due to flow of charges through the

dielectric material (leakage current) or dissipation of energy by polarization loss. It is worth noting

that the leakage current for an ideal capacitor is zero. The imaginary part of AC conductivity occurs

to compensate for the charges which are polarized inside the dielectric material. In fact, the current

due to imaginary conductivity does not pass through the dielectric but moves in the circuit to

compensate for the charges which are stored on the surface of capacitor.

2.6. Electrical Properties of Conductive Filler/Polymer Composites (CPCs)

2.6.1. Electrical Conductivity of CPCs

High electrical conductivity, i.e., conductive network formation, at very low filler content has

made CPCs distinctive materials for industrial applications [6, 40, 57-64]. Conductive network

formation in CPCs is better comprehended with the concept of percolation threshold [15, 65, 66].

Percolation means that at least one conductive pathway forms to allow electrical current to pass

39

across the composite, and to transform the composite from insulative to conductive. Percolation

occurs at a narrow filler concentration range, where the volume resistivity of composite abruptly

decreases by several orders of magnitude. Electrical percolation at very low filler concentrations in

CPCs leads to the production of cost-effective composites.

Many statistical, geometric, thermodynamic and structure-based models have been introduced to

anticipate the percolation threshold and electrical conductivity of CPCs [65, 67]. Even though the

percolation theory is just valid at conductive filler concentration above the percolation threshold;

however, it is the most acceptable one. Statistical percolation theory [65] estimates the percolation

threshold of CPCs as:

( )

(2

(2-27)

where ρ is the volume resistivity of CPC, ρ0 is the volume resistivity of conductive filler, V is

volume content of conductive filler, and Vc and t are percolation threshold and critical exponent,

respectively. The equation is valid for the concentrations above the percolation threshold, i.e., V >

Vc. Higher t value and lower percolation threshold correspond to well-dispersed high aspect ratio

fillers [68, 69].

As the focus of this dissertation is on MWCNT as conductive filler, the general electrical

behaviors, i.e., electrical conductivity, EMI shielding and dielectric properties, of CPCs are

investigated by presenting the electrical properties of compression molded MWCNT/PS composite,

as a typical CPC. The MWCNT/PS composites with different loading levels were prepared by

diluting the masterbatch of 20.0 wt% MWCNT in PS (MB2020-00) using a Coperion ZSK co-

40

rotating intermeshing twin-screw extruder operated at barrel temperature of 200 °C and extruder

speed of 150 rpm. Further information on material preparation can be found in our studies [41, 70].

Figure 2-15 presents a typical percolation curve of CPCs (percolation curve of MWCNT/PS

composite). In general, percolation curve of CPCs can be divided into three zones: 1) the zone far

below the percolation threshold (insulative zone), (2) the zone where percolation occurs

(percolation zone) and (3) the zone far above the percolation threshold (conductive zone).

In the insulative zone, the conductive filler loading is very low with the fillers far from each

other; thus, polymer matrix controls the charge transfer. In this zone, CPCs demonstrate resistivity

above around 10+11

Ω·m, which is close to the resistivity of pristine polymer. Conductive fillers and

insulating gaps, i.e. polymer matrix, between them can be modeled as a capacitor [63,71, 72]. At

low filler concentration, the insulating gaps are very large and the chance that nomadic charges are

transferred between conductive fillers is very low. Therefore, conductivity is the result of transport

processes within the host matrix; and as the bound charges of polymer matrix belong to valence

band, the whole composite shows insulative behavior.

41

Figure 2-15: Percolation curve of compression molded MWCNT/PS composite (A typical

percolation curve of CPCs) [41].

By increasing filler concentration, the gaps between conductive fillers decrease. When the mean

particle–particle distance reaches to below 1.8 nm, the dominant electron transfer mechanisms

become tunneling and hopping mechanisms [50, 73-75]. In narrow insulating gaps between

conductive fillers, very high field strength may develop which is higher than the macroscopic

voltage by a factor M, which is the ratio of average size of conducting aggregate to the average gap

width [75, 76]. This high field strength provides free electrons in conductive filler with sufficient

energy to tunnel through or hop over the insulative gaps (Figure 2-16). Quantum tunneling refers to

the quantum mechanical phenomenon where a particle tunnels through a barrier, that

it classically unbeatable, and emerges with the same energy in a new lattice site. For quantum

tunneling, the site separation must be small enough for the tail of electron wavefunction to extend

through the barrier. However, hopping occurs when an electron receives sufficient energy to pass an

energy barrier to change its lattice site [73-77].

42

Figure 2-16: Diagram of electron-transfer mechanisms between adjacent sites separated by a

potential energy barrier [77]. (Reprinted with the Permission of Cambridge University Press)

By further adding filler loading, the fillers get closer and ultimately at a narrow concentration

range called the percolation zone, the first conductive path forms letting the current pass through the

composite. In the percolation zone, due to direct contact between conductive fillers, the nomadic

charges in conductive filler play the dominant role in conduction mechanism. Since these free

charges belong to the conduction band, the resistivity of nanocomposite reduces by several orders

of magnitude in the percolation zone.

Next, by adding more filler content, a well-developed 3-D conductive network starts to form;

however, the volume resistivity reduces only marginally. This is due to considerable current

dissipation at the contact spots between conductive fillers, i.e., the constriction resistance, which

leads to a plateau in the percolation curve [78].

43

The electrical conductivity and percolation threshold of MWCNT/polymer composites depend

on many factors, such as intrinsic conductivity, size and aspect ratio of MWCNT, intrinsic

properties of polymer matrix (molecular structure, viscosity and crystallinity), the quality of

interaction between MWCNT and polymer matrix, mixing technique, etc [5]. Accordingly, it is

expected to observe a variety of percolation threshold and electrical conductivity for various types

of MWCNT/polymer composites. In literature, there are some good review papers discussing the

impacts of conductive filler and polymer matrix features and their interaction on electrical

conductivity and percolation threshold [68, 69, 79].

2.6.2. EMI Shielding of CPCs

CPCs present a sophisticated EMI shielding behavior due to their heterogeneous structure

holding phases with different electrical conductivities. Shielding by CPCs depends on many factors,

such as conductivity of filler and polymer matrix, dispersion of conductive filler, interaction

between conductive filler and polymer matrix, range of shielding frequency, content of filler,

thickness of shielding material, etc [20, 41, 80-85]. Achieving the knowledge of the effects of these

parameters on EMI shielding requires comprehensive theoretical and experimental study of

shielding behaviors of different types of CPCs.

Figure 2-17 demonstrates the EMI shielding behavior of MWCNT/PS composites as functions

of MWCNT concentration and composite thickness over the X-band frequency range (8.2 – 12.4

GHz). As shown in Figure 2-17, EMI SE increases with both MWCNT concentration and composite

thickness. It can be observed that for the composites with 3.0 mm thickness, the EMI SE increases

44

from 1.1 dB to 63 dB by incorporating 20.0 wt% MWCNT to the pristine PS. For the composites

with 20.0 wt% MWCNT, the EMI SE rises from 29 dB for 0.4 mm thickness to 63 dB for 3.0 mm

thickness. Polymer matrix, due to lack of nomadic charges, is transparent to EM wave, however

conductive fillers are able to attenuate EM wave. Higher EMI SE at greater MWCNT concentration

and composite thickness is due to greater amount of interacting conductive filler and

electric/magnetic dipoles.

Figure 2-17: EMI SE of the compression molded MWCNT/PS composite as functions of MWCNT

concentration and shielding plate thickness.

The direct relationship of EMI shielding and MWCNT concentration is related to two

mechanisms: Ohmic loss and polarization loss. As shown in Figure 2-18, individual conductive

fillers can be considered as a resistor holding nomadic charges; and the combination of two

individual conductive fillers and polymer matrix between them can be regarded as a nanocapacitor.

Hence, it can be claimed that a CPC is comprised of a great deal of resistor and capacitor structures,

which are in series or parallel to each other. Increase in MWCNT concentration and composite

45

thickness leads to a greater number of both resistor and capacitor structures resulting in higher

Ohmic loss and polarization loss, respectively. As a matter of fact, with increasing the content of

conductive filler, the amount interacting nomadic charges and electric/magnetic dipoles increase.

This attenuates EM wave much more efficiently.

Figure 2-18: Schematic of resistor and capacitor structures in a CPC.

Overall EMI shielding in CPCs is composed of three components: reflection, absorption and

multiple-reflection. As multiple-reflection cannot be measured independently, its influence is

inherent in shieldings by reflection and absorption. It was stated that in conductive monolithic

materials both reflection and absorption have a direct relationship with electrical conductivity, i.e.,

quantity of nomadic charges. Therefore, it is expected to observe an ascending trend for shieldings

by reflection and absorption as a function of filler content in CPCs. As depicted in Figure 2-19, both

reflection and absorption increase with MWCNT concentration. Shielding by reflection is attributed

to surface nomadic charges. Higher MWCNT concentration is associated with greater number of

surface nomadic charges, leading to larger impedance mismatch between two media. This means

46

that at a larger MWCNT concentration, there are a greater number of interacting surface nomadic

charges to reflect the incident wave.

Absorption mechanism in CPCs, due to their heterogeneous structure, is much more

sophisticated than that in conductive monolithic materials. Absorption in CPCs arises from Ohmic

loss and polarization loss. Therefore, understanding the influence of filler content on Ohmic loss

and polarization loss can direct us to obtain a better comprehension from absorption mechanism in

CPCs.

Imaginary permittivity represents the energy dissipated within CPCs by Ohmic loss and

polarization loss, and polarization loss (as a part of imaginary permittivity) is linked to real

permittivity. Figure 2-20 shows that both real permittivity and imaginary permittivity increase with

MWCNT concentration, confirming the positive influence of filler content on polarization loss and

Ohmic loss. Real permittivity in CPCs is due to the formation of a large number of nanocapacitors,

i.e., conductive fillers acting as electrodes and insulative polymeric layer acting as dielectric

material [9, 12, 86-89]. Increasing MWCNT concentration results in an increase in the number of

nanocapacitors leading to higher real permittivity (charge polarization). In addition, increasing

MWCNT concentration accompanies with a reduction in the thickness of insulative polymeric gaps

between MWCNTs causing higher applied field and greater electronic polarization of polymeric

layer. Hence, there is a direct relationship between MWCNT concentration and polarization loss,

which gives rise to shielding by absorption. In fact, the higher the real permittivity of a CPC, the

greater is the momentum generated by charge polarization, and thus the higher is the dissipation of

energy to come over the momentum to reorient the dipoles in each half cycle of alternating field.

47

Of interest to note, real permittivity in conductive monolithic materials is equivalent to that of

free space since the conduction current is much greater than the displacement current [33, 34].

Accordingly, contrary to CPCs, polarization loss does not play an important role in EMI shielding

of conductive monolithic materials.


compression molded MWCNT/PS composites as a function of MWCNT concentration. The

thickness of all the samples is 2.0 mm [41].

48

Imaginary permittivity of MWCNT/PS composites also contributes significantly to shielding by

absorption, where energy is dissipated by Ohmic loss and polarization loss. For Ohmic loss,

increasing MWCNT concentration leads to an increase in the number of dissipating mobile charge

carriers resulting in higher imaginary permittivity and, consequently, higher shielding by

absorption. In addition, increasing conductive filler content leads to the formation of conductive

networks in the composite. At greater network formation, the electrons have greater mean free paths

in which to move according to the direction of electric field in each half cycle and, consequently,

can dissipate more electrical energy [41, 90, 91].

Figure 2-20: Real permittivity and imaginary permittivity of MWCNT/PS composites over the

X-band frequency range [41].

Multiple-reflection occurs in shields where there are numerous interfacial areas like CPCs or

foamed samples [33, 80]. Multiple-reflection decreases the EMI shielding by blocking and

reflecting back the reflected waves from shielding material interior surface area. It was shown in

Equation 2-18 that for conductive monolithic materials, multiple-reflection can be ignored if

49

material’s thickness is greater than material’s skin depth. Skin depth is the distance inside a

conductive shied at which the wave power diminishes to of its incident value and has an

inverse relationship with conductivity, magnetic permeability and wave frequency. However, skin

depth in CPCs needs to be defined with a more complicated equation. For instance, two CPCs with

the same conductive filler content, or even the same electrical conductivity, may present very

different electrical properties or skin depth due to their dissimilar morphologies [41, 92].

Accordingly, it can be claimed that skin depth and multiple-reflection in CPCs are functions of

many parameters, such as conductivity and magnetic permeability of filler and polymer matrix,

dispersion of conductive filler within polymer matrix, aspect ratio of conductive filler, interaction of

conductive filler and polymer matrix, molecular structure of polymer matrix, alignment of

conductive filler, etc.

2.6.3. The Mechanisms behind the Broadband Dielectric Spectroscopy of CPCs

The dielectric spectroscopy in the heterogeneous structure of MWCNT/polymer (nonpolar)

composites can be explored by its equivalent-circuit model, as shown in Figure 2-21 [13, 93-96].

The parallel capacitor, CPE, represents the electronic polarization in polymer matrix that happens in

a time constant less than a half cycle of optical frequency (≈1015

Hz). Electronic polarization

extends from DC up to optical frequency; however, its effect is minor at low frequencies due to

strong interfacial polarization. The electronic polarization can contribute significantly to the charge

polarization at high frequencies, especially when the DC conductivity is low.

50

The RC circuit of RS-CNT-CS-CNT represents the polarization within MWCNTs, which plays an

important role at high frequencies. The polarization in MWCNTs occurs due to presence of lattice

defects (e.g., vacancies, dislocations and CO and CH attachments) in molecular structure of

MWCNTs [97-103]. For example, a defect in the armchair-type MWCNT, which can conduct

electricity, can cause the surrounding region to be semiconducting. Therefore, in molecular

structure of MWCNTs, there may be two regions with unlike conductivities that induce charge

polarization on molecular scale.

Figure 2-21: The equivalent-circuit model of MWCNT/polymer composites.

The resistance/capacitance (RC) circuit of CSI-RSI signifies the interfacial polarization that is

broadly observed at low frequencies in heterogeneous structures, such as CPCs [104]. The time

constant of an RC circuit is . At frequencies below 1/τ, the charges have enough time to

build up at the interface of the MWCNT and polymer; thus, the interfacial polarization contributes

significantly to the charge polarization. In other words, at low frequencies the accumulated charges

51

at the interface find sufficient time to adapt themselves to alternating voltage, contributing to real

permittivity. By increasing the frequency, the contribution of interfacial polarization to real

permittivity diminishes, due to insufficient time for electrons to accumulate at the interface in each

half cycle of alternating field (relaxation phenomenon).

The parallel resistor, RP-CNT, represents the resistance against the movement of free charges

across MWCNT network and corresponds to DC conductivity. The DC conductivity is in phase

with alternating voltage and originates from movement of free charges into interconnected network

of MWCNTs. The DC conductivity is usually measured under a low-frequency AC voltage, where

the effects of frequency-dependent dielectric dispersion are insignificant [56].

2.7. Effects of Conductive Filler Type (MWCNT versus CuNW) on Electrical Properties of

CPCs

Fillers are usually added to polymer matrix for many purposes, such as reducing final material

cost and/or improving electrical, thermal and mechanical properties. Many parameters play role in

filler selection, such as desired properties of composite, physical properties of filler, filler price,

compatibility between filler and polymer matrix, availability, recyclability, and so on [105].

The most desirable characteristic in CPCs is high electrical conductivity at very low filler

content. The CPCs with highly conductive fillers can surpass the conventional materials for

advanced applications like new generation of microelectronics. Therefore, intrinsic conductivity of

conductive filler is one of the most important factors to be considered in filler selection for

electrical applications.

52

As described previously, conductive network formation in CPCs is better understood based on

the concept of percolation threshold. Percolation occurs at a concentration where conductive filler

particles contact each other and begin to form a continuous network throughout the matrix. As

conductive filler is usually much more expensive than polymer matrix, the conductive network

formation at lower filler content is highly desirable for the manufacturers. The fillers with higher

aspect ratio (length over diameter) have more probability to contact each other; therefore,

presenting lower percolation threshold [62, 69, 106]. Moreover, in some CPC applications, high

thermal conductivity is required [107-109]. Examples include PCBs, which require dissipating the

generated heat during operation. Accordingly, the fillers incorporated in CPCs for advanced

applications are needed to present high electrical and thermal properties along with large aspect

ratio.

To meet the demanding requirements for advanced electrical applications, many nanofillers can

be nominated as conductive filler. However, the focus of the dissertation is on MWCNT and

CuNW. MWCNT was selected due to its high aspect ratio, unique electronic structure,

extraordinary electrical, thermal and mechanical properties and growing industrial usage. However,

the limited conductivity of MWCNT prompted us to study CuNW, too, which have higher intrinsic

conductivity but lower aspect ratio than MWCNTs.

53

2.7.1. Carbon Nanotubes

2.7.1.1. Structure and Electrical Properties

The discovery of carbon nanotubes (CNTs) can be traced back to the origin of fullerene chemistry.

Fullerenes (C60) are geometric cage-like structures of carbon atoms made of pentagonal and hexagonal

items [68, 110, 111]. This discovery led to synthesis of CNT by Iijima in 1991 [112, 113]. Nanotubes

are slender elongated fullerene where the walls are hexagonal carbon and often capped at each end.

There are two general types of carbon nanotubes: multi-walled carbon nanotube (MWCNT) and

single-walled carbon nanotubes (SWCNT). MWCNT consists of multiple rolled layers of graphite

coaxially arranged around a central hollow core with van dar Waals forces between adjacent layers,

while SWCNT is made of a single graphene cylinder [68]. Figure 2-22 depicts TEM images of

different kinds of CNTs.

Figure 2-22: TEM images of different CNTs : (a) SWCNT, (b) MWCNT with different layers of 5,

2 and 7 [112, 114].

The atomic structure of CNTs is determined in terms of chirality, which is defined by chiral vector

and chiral angle. In general, three different chiralities can be defined for CNTs: armchair, zigzag and

54

chiral (Figure 2-23). The tube chirality is defined by the chiral vector, which is explained by the

following equation:

(2-28)

where the integers (n, m) are the number of steps along the unit vector and of the hexagonal

lattice. The chiral angle determines the amount of twist in CNT [68, 115]. Using this (n, m) naming

systems, three types of orientation of carbon atoms around the nanotube circumference are itemized. If

, the nanotubes are called “armchair”. If , the CNTs are called “zigzag”. Otherwise, they

are called “chiral”. The chirality of CNTs has considerable implications on the transport properties,

specifically the electronic properties. It has been revealed that nanotubes can be either metallic or

semi-conducting, depending on tube chirality [116]. Each MWCNT contains a multi-layer of

graphene, and each layer can have different chiralities, thus the prediction of MWCNT electrical

properties is more sophisticated than that of SWCNTs.

Figure 2-23: Schematic diagram showing how a hexagonal sheet of graphene is rolled to form a

CNT with different chiralities; (a) Armchair; (B) Zigzag; (C) Chiral [68, 115].

The theoretical and experimental results have demonstrated that CNTs have extremely high

elastic modulus, greater than 1 TPa (near elastic modulus of diamond) and strength of 10-100 times

55

greater than steel but with a lower density [68]. CNTs are also fascinating materials in terms of

electrical and thermal properties. CNTs are stable up to 700°C in air, and 2800°C in vacuum; their

thermal conductivity is about two times greater than diamond while their electrical conductivity is

as high as metallic materials [117].

The electrical properties of CNTs, which is the focus of this dissertation, are closely linked to the

nature of the bonds between the carbon atoms. As a CNT can be considered as a rolled-up graphene

sheet, the bonding mechanism in a CNT is similar to that of graphite. When carbon atoms combine

to form graphite, sp2 hybridization takes place. In this process, one s-orbital and two p-orbitals

combine to form three hybrid sp2-orbitals at 120° to each other within a plane depicted in Figure 2-

24. The in-plane bond is denoted as bond. This strong covalent bond ends in the high stiffness and

strength of CNTs. The remaining p-orbital is perpendicular to the plane of the bonds and interacts

with p-orbital in the adjacent layer to form a bond. The delocalized bonds are much weaker than

bonds and are distributed over the CNT circumference. These delocalized bonds account for

high electrical conductivity of CNTs [118].

However, the presence of crystallographic defects affects the electrical properties of CNTs.

These defects include vacancies, dislocations and CO and CH attachments, etc. For convention, a

nanotube is called defect free if it is of only hexagonal [118]. The presence of structural defects in

CNTs can be viewed as a challenge as well as an opportunity for electrical applications. CNTs with

perfect molecular structure show eminent electrical conductivity and EMI shielding; whereas

manipulating the structural defects of CNTs can be useful for charge storage applications.

56

Figure 2-24: Basic hexagonal bonding structure for a graphite sheet; carbon nuclei shown as filled

circles, out-of-plane bonds represented as delocalized (dotted line), and bonds connect the

nuclei in-plane [119].

2.7.1.2. Carbon Nanotube Synthesis

Primary synthesis methods for carbon nanotubes include arc-discharge [113, 120], laser ablation

[121], gas-phase catalytic growth from carbon monoxide [122] and chemical vapor deposition

(CVD) from hydrocarbons [123]. For applications of carbon nanotubes in polymer composites,

large quantities of carbon nanotube are required. Thus only the two latter techniques, due to their

continuous mechanism, have the potential to find industrial applications.

MWCNTs employed in this dissertation, both pristine and masterbatch, are commercial products

made by CVD technique, according to the suppliers. Thus, only the mechanism behind CVD

57

technique is briefly detailed here. In this technique, a substrate is prepared with a layer of metal

catalyst particle. The substrate is heated to approximately 700 C. Then, the mixture of two gases,

i.e., a process gas (such as nitrogen) and a carbon-containing gas (such as ethylene) is flown into the

reactor. Afterwards, thermal catalytic decomposition of hydrocarbon occurs at the surface of

catalyst, where it forms CNTs. As the carbon source is provided with flowing gas, this process

draws a promising future for mass production [123, 124].

2.7.1.3. Carbon Nanotube Market

Among the abundant types of newly synthesized nanomaterials, CNTs are perhaps among the

most dynamic ones. Academia, small businesses as well as large companies, have pursued to

exploit numerous commercial applications of CNTs. Therefore, mass production of CNTs have

realized industrial feasibility and new CNT producers are now enable to produce CNTs in large

scales, depending on the specific grade, at more cost-effective prices. Figure 2-25 shows the global

market for CNT grades based on commitment production (2011-2016). The global market for

different types of CNTs was $192 and $239 million in 2011 and 2012, respectively, and is projected

to grow within the next five years at a compound annual growth rate (CAGR) of 22.4%, reaching

$527 million by 2016 [125]. This large increase can be explained in terms of technical momentum

and enormous business potential.

58

Figure 2-25: Global market for CNT grades based on committed production, (2011-2016),

($ Million) [125].

2.7.2. Copper Nanowire (CuNW)

CuNWs, due to their higher electrical conductivity relative to carbon-based materials, are

receiving great attention to be used in CPCs [19, 39]. However, there are challenges as well as

opportunities in employing CuNWs in CPCs as substitutions for carbon-based materials:

(1) Beyond the percolation threshold, the filler conductivity plays the dominant role in

defining the electrical conductivity of CPCs [42, 66]. Therefore, above the percolation

threshold, CuNW/polymer composites can present higher electrical conductivity than

CNT/polymer composites. However, oxide layer formation on the surface of CuNWs

restricts electrical conductivity and should be avoided.

(2) CuNWs are still made in batch process with low yield. This issue can overshadow the

superiority of CuNWs to CNTs in terms of industrial applications.

(3) CuNWs possess larger amount of nomadic charges than CNTs, thus demonstrate higher

EMI shielding than CNTs. However, the oxide layer formation on the surface of CuNWs

should be evaded since it prohibits the conductive network formation and reduces EMI

shielding.

59

(4) Low imaginary permittivity in CPCs is plausible by avoiding conductive network

formation. On the other hand, larger amount of nomadic charge carriers in highly

conductive fillers lead to higher real permittivity in CPCs. Having known these two

concepts, CuNWs can be innovatively introduced as novel conductive fillers for charge

storage applications. As a matter of fact, unavoidable oxide layer on the surface of

CuNWs combined with high conductivity of fresh core of CuNWs can lead to low

imaginary permittivity and high real permittivity, respectively.

The above-mentioned concepts and issues provide huge stimulation to investigate the dielectric

properties of CuNW/polymer composites for charge storage applications.

2.8. MWCNT Alignment, Induced by Injection Molding, and Electrical Properties of CPCs

The key aspect of conductive filler alignment and its influence on electrical properties is very

often disregarded during the design process of CPCs. Treating CPCs as isotropic, results in

conservative design and underutilization of CPCs at best, or can lead to insecure design at worst.

Furthermore, most of investigations on the electrical properties of CPCs have been devoted to

compression molded composites, which have randomly dispersed conductive filler; this has led to

the results that are not applicable to injection molded composites where the conductive filler is

aligned. Hence, a portion of this PhD thesis has been dedicated to investigating the influence of

MWCNT alignment on the electrical properties of MWCNT/polymer composites.

60

2.8.1. Flow Conditions in Injection molding and its Effect on Filler Alignment

In order to anticipate the pattern of conductive filler alignment in an injection molded composite,

it is a must to obtain a general understanding from the melt flow behavior in injection molding

process. During injection molding process, polymer melt undergoes a complex flow condition in the

part cavity. In fact, the combination of three major types of flow influences filler alignment,

namely: (a) in-plane shear flow, (b) in-plane tensile or compressive flow and (c) out-of-plane

fountain flow [126].

In-plane shear flow, which is the most common type of flow, occurs due to pressure gradient

along the length of a uniform cross-section. For the simplified Newtonian polymer melts, there is a

parabolic distribution for velocity, leading to maximum shear rate at the wall and no shear rate at

the center (Figure 2-26). Nevertheless, in real life polymer melts are non-Newtonian and non-

isothermal. Non-Newtonian feature of polymer melts alters the parabolic velocity distribution to a

flatter distribution. In addition, freezing occurring on the mold walls leads to temperature gradient

through thickness direction. In the cooler region near the wall, the melt viscosity rises and melt

velocity decreases. This causes a shift in maximum shear rate to a location further away from the

wall. The high shear rate at the location of peak leads to maximum filler alignment close to the wall,

but not at the wall. The low shear rate close to the center does not impact the filler alignment.

Additionally, in the center of cavity the filler reorientation could process easier due to longer

relaxation time for polymer melt.

61

Figure 2-26: Comparison between isothermal and non-isothermal velocity and shear rate

distributions for a non-Newtonian melt in thickness direction [126].

The in-plane compressive and tensile flows occur when there is a change in the shape of flow

channel (Figures 2-27 (a) and (b)). For the convergent channel, the melt undergoes a stretching

action (tensile flow) and fillers within the melt are aligned in the direction of flow. For the divergent

channel, the melt experiences compression (compressive flow) and fillers are aligned perpendicular

to the flow direction. The third type of flow is fountain flow that takes place at the melt front and

arises from thickness velocity gradient and conservation of mass (Figure 2-27(c)). The velocity

gradient conducts the melt at the front to splay outward and deposit on the wall as a thin frozen

layer. As the melt moves toward the wall in the fountain flow, the fillers undergo stretching and

rotation.

In addition to the mentioned mechanisms, the pattern of conductive filler alignment also depends

on rheological properties of melt, characteristics of filler, geometry of cavity and processing

conditions of injection molding process.

62

Figure 2-27: Influence of (a) convergent channel and (b) divergent channel on filler alignment in a

small element of polymer melt. (c) Schematic of fountain flow at the melt front [126].

2.8.2. A Brief Review on Electrical Conductivity of Injection Molded CPCs

In recent years, several studies have been performed on the electrical conductivity of injection

molded CPCs [66, 127-130]. They all reported a loss in conductivity of injection molded CPCs

relative to compression molded CPCs around the percolation threshold. Hong et al. [130]

investigated the electrical conductivity of injection molded carbon black/polystyrene composites

and claimed that conductive filler experienced a shear-induced migration from the walls to the

center. They revealed that injection molded carbon black/polystyrene composites showed a loss in

conductivity by several orders of magnitude when mean particle concentration was at or slightly

above the percolation threshold. They related this observation to conductive filler depletion on the

surface. They also claimed that removing the surface layer in micrometer scale by excimer laser led

to restoration of conductivity, confirming migration of conductive fillers.

63

In another study, Villmow et al. [127] employed a two-level, four-factor factorial design to

investigate the influence of melt temperature, injection velocity, injection pressure and mold

temperature on the electrical conductivity of MWCNT/PC composites. Their results revealed that

the melt temperature followed by the injection velocity had the greatest impact on MWCNT

alignment and electrical conductivity, while the influences of mold temperature and injection

pressure were insignificant. In other words, the composites produced at lower melt temperature and

higher injection velocity experienced higher shear rate, and thus presented greater MWCNT

alignment. They asserted that greater MWCNT alignment was associated with inferior conductive

network formation and lower electrical conductivity.

They believed that the loss in the electrical conductivity of injection molded composites relative

to compression molded composites was mostly due to highly aligned skin layer, which acted as

insulating layer due to absence of contacts between MWCNTs. They also did not observe any fiber

depletion on the composite surface. However, microscopy images showed that at composite depth

of micrometer scale, the conductive network was entirely formed. Higher conductivity at locations

close to the center was ascribed to lower shear rate and also longer relaxation time for polymer

chains to reorient.

Although the electrical conductivity of injection molded CPCs has been investigated by some

researchers; however, there is still a large vacant area to investigate the influence of conductive

filler alignment, induced by injection molding process, on other electrical properties, i.e., EMI

shielding and real and imaginary permittivities. This poses the alignment of conductive filler as an

opportunity to employ or a challenge to be avoided for electrical applications.

64

2.9. Project Motivation and Objectives

The ability to manipulate the conductive network formation within CPCs allows them to be used

in wide range of applications, such as charge storage, antistatic dissipation, ESD protection and

EMI shielding. Accordingly, the main objective of this dissertation is to create unique morphologies

of CPCs to control the conductive network formation to achieve desired electrical properties. This

was performed through manipulating mixing methods and processing conditions using various

nanofillers, and then relating the developed morphologies to the final electrical properties. Having a

comprehensive understanding of conductive network formation enables the manufacturers to

employ cost-effective raw materials and appropriate processing conditions to achieve desired

electrical properties.

It is believed that enhanced conductive network formation improves electrical conductivity and

EMI shielding; whereas, decayed conductive network formation reduces leakage current (imaginary

permittivity), which is desirable for charge storage applications [17, 104]. Accordingly, this PhD

thesis is dedicated to introducing innovative techniques to improve or deteriorate conductive

network formation to obtain desired electrical properties. In other words, conductive network

formation is considered as the key point to design innovative morphologies to achieve desired

electrical properties. Hence, the following techniques were employed to manipulate the conductive

network formation:


Changing the type of conductive filler (Copper Nanowire (CuNW) versus MWCNT)

65

Figure 2-28 shows the schematics of expected morphologies created by the above-mentioned

techniques. As depicted in Figure 2-28, playing with the employed techniques can influence the

electrical properties by improving or deteriorating conductive network formation. Figure 2-28(a)

demonstrates random distribution of MWCNTs in polymer matrix. This schematic shows a partial

conductive network formation of MWCNTs, but not a well-established one. This morphology

represents the compression molded MWCNT/polymer composites, and is used as the reference to

compare with the newly developed morphologies.

Figure 2-28: Schematics showing (a) randomly distributed MWCNT/polymer composites, (b)

aligned MWCNT/polymer composites, and (c) CuNW/polymer composites.

Figure 2-28(b) shows a schematic of aligned composites. It is believed that alignment reduces

the chance of conductive fillers contacting each other leading to decayed conductive network

formation. It has been observed that the MWCNT alignment reduces electrical conductivity [127,

128]; however, to the best of our knowledge, no study has been performed to investigate the effects

of MWCNT alignment on EMI shielding and dielectric properties. Furthermore, among the various

techniques employed for mass production of CPCs, injection molding is of great industrial

significance. The unavoidable flow-induced alignment of MWCNTs in injection molding process

66

was the stimulation to investigate effects of MWCNT alignment on the electrical properties of

MWCNT/polymer composites.

The key aspect of conductive filler alignment and its influence on electrical properties is very

often disregarded during the design process of CPCs. Treating CPCs as isotropic results in

conservative design and underutilization of CPCs at best, or can lead to insecure design at worst.

Having known these concepts, the main objective of a portion of this dissertation is to verify the

effect of MWCNT alignment on electrical properties of MWCNT/polymer composites to discover

the challenges to avoid or opportunities to employ.

In order to employ CPCs for charge storage applications, highly conductive fillers are greatly

acknowledged. Accordingly, the limited electrical conductivity of MWCNTs prompted us to

investigate the dielectric properties of CuNW/polymer composites, due to superior electrical

conductivity of CuNWs relative to MWCNTs. Highly conductive CuNWs are potentially able to

provide enhanced charge polarization. However, unavoidable oxide layer formation on the surface

of CuNWs sounds as a barrier to spoil the electrical conductivity of CuNWs.

Nonetheless, oxide layer formation can be innovatively considered as a benefit to decay

conductive network formation to reduce imaginary permittivity. As shown in Figure 2-28(c), the

oxide layer around CuNWs have the potential to avoid the direct contacts between CuNWs leading

to inferior conductive network formation (lower energy loss). On the other hand, the fresh core of

CuNWs can provide the composite with considerable free charges for interfacial polarization. This

hypothesis prompted us to compare the dielectric properties of CPCs holding MWCNTs and

CuNWs.

67

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78

Chapter 3

Materials, Processing and Characterization

3.1. Methodology

The main objective of this dissertation is to determine how unique morphologies of CPCs can be

created to control conductive network formation. This has been performed through manipulating

processing parameters and molding conditions using various nanofillers, and then relating the

obtained morphologies to the final electrical properties, i.e., electrical conductivity, EMI shielding

and dielectric properties. Figure 3-1 presents a flowchart showing the experimental strategy

employed in this dissertation to explore novel techniques to regulate conductive network formation.

In the phase I, the effects of MWCNT loading on the electrical properties of MWCNT/polymer

composites and the mechanisms behind are investigated. This phase gives a comprehensive

understanding about the relationships between conductive network formation and electrical

properties. Phase II covers the effects of MWCNT alignment induced by injection molding process

on electrical properties in the X-band (8.2 – 12.4 GHz), and introduces MWCNT alignment as a

challenge to be avoided for electrical conductivity and EMI shielding or as an opportunity to be

employed to improve dielectric properties. Phase III investigates the effects of MWCNT content on

the broadband dielectric properties of MWCNT/polymer composites, i.e., 10-1

– 10+6

Hz. Phase IV

presents CuNW as a promising filler, to be incorporated into CPCs, with superior dielectric

properties to MWCNT.

79

Figure 3-1: Experimental Strategy.

3.2. Materials

Masterbatch: Two kinds of masterbatch were used in this project: a masterbatch of 15.0 wt%

MWCNT in PC (MB6015-00) and a masterbatch of 20.0 wt% MWCNT in PS (MB2020-00). Both

masterbatches were obtained in the form of cylindrical pellets from Hyperion Catalysis

International, Cambridge, MA, USA. The length and diameter of pellets were 2.50 ± 0.25 mm and

3.50 ± 0.25 mm, respectively. According to the supplier, the MWCNTs were vapor grown and

80

typically had an outer diameter of 10-15 nm wrapped around a hollow core with a diameter of 5 nm.

The length distribution ranged between 1 and 10 µm, while the density was approximately 1.75

g/cm3.

Polycarbonate (PC): Being a good electrical insulator and having heat-resistant and flame-

retardant properties, PC is employed in various applications engaged with electrical hardwares. The

pristine PC used was LexanTM

141, kindly provided by Sabic Innovative Plastics, with melt flow

rate of 10.5g/10 min (at 300 C/1.2 kgf). According to the supplier, the density and melt

temperature are 1.19 g/cm3 and 295-315 C, respectively. The volume resistivity is 10

17 cm

according to ASTM D257 and the real permittivities at 50 Hz and 1 MHz are 3.17 and 2.96,

respectively, according to ASTM D150.

Polystyrene (PS): The neat PS employed in this dissertation was Styron® 610, which is a heat-

resistant insulating thermoplastic. Styron® 610 was kindly supplied by Americas Styrenics LLC. Its

melt flow rate and density are 10.0g/10 min (at 200 C/5.0 kgf) and 1.06 g/cm3, respectively. The

volume resistivity is 1016

cm.

Poly(vinylidene Fluoride) (PVDF): PVDF is a specialty plastic material in the fluoropolymer

family, which has many applications in electronics industry, due to its low electrical conductivity,

resistance to heat, and piezoelectric properties. The PVDF Kynar® 1000HD was purchased from

Arkema Inc. The density and melt flow rate are 1.78 g/cm3 and 1.1g/10 min (at 230 C/5.0 kgf),

respectively. The volume resistivity is 2014

cm according to ASTM D257. The real

permittivities are 10.5 and 7.0 at 100 Hz and 1 MHz according to IEC 60250, respectively.

81

MWCNT: The MWCNTs (NanocylTM

NC7000) were obtained from Nanocyl S.A. (Sambreville,

Belgium). According to the manufacturer, the MWCNTs were produced by catalytic carbon vapor

deposition (CCVD) process. Table 3-1 details the physical properties of NC7000.

Table 3-1: Physical properties of MWCNT (NC7000) [1].

Property Unit Value

Average Diameter Nanometer 9.5

Average Length Micron 1.5

Electrical Conductivity S/cm 104-10

5

Specific Gravity g/cm3 1.3-2.0

Carbon Purity % 90

Surface Area m2/g 250-300

Copper Nanowire (CuNW): CuNWs synthesized and employed in this dissertation had an average

diameter of 30 nm and average length of 1.5 µm (L/D ~50). The synthesis of nanowires is an

advanced technique whose science is understood by a limited number of research groups in the

world, including Polymer Processing Group (PPG) at University of Calgary. Figure 3-2 shows

schematic of synthesis of metal nanowires by template-directed synthesis [2, 3]. In order to

synthesize the CuNW; firstly, the aluminum plates are annealed in air at 500 °C for 24 hr. The

porous aluminum oxide (PAO) templates were prepared by anodization of Al templates in dilute

solution of sulfuric acid. Afterwards, the electrodeposition is carried out by dipping the PAO

templates in an electrolyte solution between two metal plates and applying an alternating voltage for

a period of time, i.e. 10 min. Finally, nanowires are liberated by dissolving alumina in 1 M NAOH

82

solution. The metal nanowires can be functionalized to disperse better in CPCs. More information

on the nanowires synthesis is detailed elsewhere [2, 3].

Figure 3-2: Consecutive steps of nanowires synthesis [2, 3].

3.3. Sample Preparation, Processing and Molding

3.3.1. Phase I

In this phase, 15.0 wt% MWCNT/PC masterbatch and pristine PC were dried under vacuum at

120 oC for 4 hr. A Haake rheomix series 600 batch mixer was utilized to dilute the masterbatch to

make composites with different loading levels. Pristine PC was first mixed for 5 min at 300 ˚C and

50 rpm, and then the masterbatch was inserted to the melt and mixed for additional 10 min. A

Carver (Carver Inc. Wabash, IN) compression molder was used to make rectangular samples 42×25

mm with four different thicknesses of 0.25, 0.60, 1.50 and 1.85 mm to obtain electrical conductivity

and EMI shielding data. The compression molding process was carried out at 280 oC for 5 min

AC

Electrodeposition

Synthesis of

Template

Liberation

of

nanowires

Polymer

Blending

Polymer

Nanocomposite

Al Plate

annealed in

air 550 C

Surface

functionalization

Cu, Fe, Ni or Ag

Remove

bulk

depositionReuse Al

83

under pressure of 34.4 MPa. The data obtained from phase I provide significant information

regarding the mechanisms behind electrical conductivity and EMI shielding of CPCs as functions of

composite thickness and filler loading.

3.3.2. Phase II

3.3.2.1. Materials Preparation

MWCNT/PS masterbatch and pristine PS were dried at 50 °C for at least 4 hr under vacuum. The

composites with different concentrations of MWCNT were prepared using a 25 mm Coperion ZSK

co-rotating intermeshing twin-screw extruder operated at extruder speed of 150 rpm and residence

time of 2 min (Figure 3-3). The twin-screw extruder included 10 thermal zones starting from the

hopper and ending at the die. The temperature profile of the extruder was set as follows considering

the processing conditions recommended by the PS supplier:

Zone 1 (Hopper): 190 C; Zone 2: 194 C; Zone 3: 204 C; Zone 4: 189 C; Zone 5: 179 C; Zone

6: 182 C; Zone 7: 181 C; Zone 8: 180 C; Zone 9: 180 C; Zone 10 (Die): 200 C

Considering the density of neat PS and MWCNT are 1.06 and 1.75 g/cm3, respectively; the

concentrations of prepared nanocomposites in terms of weight percent and volume percent are

presented in Table 3-2.

Table 3-2: The concentrations of the prepared MWCNT/PS nanocomposites in terms of weight

percent and volume percent.

MWCNT Concentration (wt%) 0.1 0.30 0.50 1.0 2.00 3.50 5.00 10.0 20.0

MWCNT Concentration (vol%) 0.06 0.18 0.30 0.60 1.22 2.15 3.09 6.30 13.2

84

Figure 3-3: An image of Coperion ZSK co-rotating intermeshing twin-screw extruder employed for

diluting the MWCNT/PS masterbatch.

3.3.2.2. Experimental Design and Composite Molding

In order to explore the effects of molding conditions on the electrical properties of the injection

molded MWCNT/PS composites, a series of injection molding experiments, denoted as EXP, were

carried out on a 5.00 wt% MWCNT/PS composites using a two-level, four-factor factorial design to

study the impact of four processing parameters, i.e., mold temperature (C1), melt temperature (C2),

injection/holding pressure (C3) and injection velocity (C4) on the volume resistivity of the molded

composites. The set points were selected with the maximum possible interval, considering the

limitations of the employed injection molding machine and also the recommended processing

conditions of pure PS. Constant holding and cooling times of 8 and 10 seconds were applied for all

the experiments, respectively. Further details on the employed experimental design can be found

85

elsewhere [4]. Tables 3-3 and 3-4 show the experimental design and the set points of the processing

parameters, respectively.

Table 3-3: Experimental design showing the two-level, four factor factorial design. The factors are

mold temperature (C1), melt temperature (C2), injection/holding pressure (C3) and injection velocity

(C4).

EXP # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Fac

tors

C1 - - - - - - - - + + + + + + + +

C2 - - - - + + + + + + + + - - - -

C3 - - + + - - + + - - + + + + - -

C4 - + + - - + + - - + + - - + + -


experiments. The processing parameters are mold temperature (C1), melt temperature (C2),

injection/holding pressure (C3) and injection velocity (C4).

Figure 3-4 shows a schematic of the mold employed in the injection molding process with the

dimensions provided in Table 3-5. The cavity was fed by an edge gate and its thickness was 2.0

mm. A detailed description of the designed mold and injection molding machine can be found

elsewhere [5].

Processing Parameters

C1 (°C) C2 (°C) C3 (bar) C4 (mm.sec-1

)

+ 60 240 100 240

- 25 215 60 24

86

Figure 3-4: A schematic view of the designed mold.

Table 3-5: Dimensions of the designed mold.

Figure 3-5 shows the resistivity of the injection molded MWCNT/PS composites in thickness

direction at different processing conditions. The results showed a decrease of up to ten orders of

magnitude in volume resistivity by adding 5.00 wt% MWCNT, compared with pure PS.

Interestingly, depending on the processing conditions, differences in the volume resistivity up to six

orders of magnitude was observed in the thickness direction of the injection molded

nanocomposites. As depicted in Figure 3-5, the highest resistivity of the composites was obtained

for the first three and last three experiments, where C2 (melt temperature) was minimal. In addition,

the lowest amount of volume resistivity can be seen in EXPs 5, 8, 9 and 12, where C2 (melt

temperature) had the highest values, and C4 (injection velocity) had the lowest values. A lower melt

temperature and higher injection velocity impose greater shear stress on the polymer matrix melt

leading to greater MWCNT alignment. As there is a reverse relationship between MWCNT

alignment and conductive network formation, the composites showed higher volume resistivity at

lower melt temperature and higher injection velocity and vice versa [4].

Parameter a b c, d e f

Value 22.86 10.16 1 2 10

87

Figure 3-5: Volume resistivities of the injection molded MWCNT/PS composites with 5.00 wt%

MWCNT loading at different molding conditions in the thickness direction [4].

To analyze the data of the resistivity, statistical software (MinitabTM

, ver. 14) was used to find

the importance of each factor. The effects of the main factors on the volume resistivity of the

molded nanocomposites are plotted in Figure 3-6. As can be seen in Figure 3-6, C2 (melt

temperature) and C4 (injection velocity) showed the greatest impact on the volume resistivity of the

samples, while the impacts of C1 (mold temperature) and C3 (injection/holding) pressure were

insignificant. Therefore, it can be concluded that the melt temperature had the greatest impact on

volume resistivity of the molded samples followed by the injection velocity, while the impacts of

mold temperature and injection/holding pressure were insignificant. Further information on the

main factor effects and interaction effects can be obtained elsewhere [4].

88

Figure 3-6: Minitab main effect plot of the volume resistivity mean of the injection molded samples

[4].

To investigate the influence of MWCNT alignment on electrical properties at different MWCNT

concentrations, we used the results obtained from experimental design of 5.00 wt% MWCNT to

select three processing conditions with the maximum possible variation in MWCNT alignment, i.e.,

volume resistivity. In other words, knowing the tremendous influence of melt temperature and

injection velocity on MWCNT alignment and volume resistivity of MWCNT/PS nanocomposites,

three different injection molding experiments, i.e., EXP #11, 12 and 14 were employed to make

samples with various MWCNT alignments at different MWCNT concentrations. The samples

fabricated using EXPs #11, 12 and 14 were used to investigate the effects of MWCNT alignment on

the electrical properties of MWCNT/PS composites at different MWCNT concentrations (chapters

5 and 6). EXPs #11, 12 and 14 correspond to EXPs # 2, 3 and 1 in chapters 5 and 6, respectively.

To have a better understanding of the effects of MWCNT alignment on the electrical properties,

the electrical properties of the injection molded samples were compared with those of the

compression molded samples. A Carver compression molder (Carver Inc., Wabash, IN) was used to

89

make the samples of randomly distributed MWCNTs, with the same dimensions as the injection

molded samples. The compression molding process was performed at 210 °C for 10 min under 38

MPa pressure.

3.3.3. Phase III

In this phase, pristine polystyrene (Styron® 610) and MWCNTs (Nanocyl

TM NC7000) were dried

at 50 °C for 4 hr under vacuum. Nanocomposites with different concentrations of MWCNTs were

manufactured through solution mixing technique. In the solution mixing method, nanocomposites

with various MWCNT contents were made by mixing different volumes of 100 mg/ml PS/N,N-

dimethylformamide (DMF) solution and 0.66 mg/ml MWCNT/DMF suspension. Each mixture was

stirred for 15 min and then ultrasonicated for 30 min in a sonication bath. The two mixtures were

then combined and stirred for an extra 10 min. Afterwards, the suspension was dripped into a large

amount of methanol, where the volume ratio of methanol to DMF was approximately three to one.

Upon contact of the suspension with the methanol, the PS chains coagulated instantly, because of

their insolubility in methanol. The coagulated chains captured the MWCNTs and prohibited them

from reagglomeration. The final mixture was filtered and dried in a fume hood for 16 hr and then

transferred to a vacuum oven for 12 hr at 50 °C to remove the remaining solvents.

The composites obtained from the solution mixing technique were then molded using a Carver

compression molder (Carver Inc., Wabash, IN) at 210 °C for 10 min under a pressure of 38 MPa.

The compression molded samples had a thickness of 1.0 mm, width of 25.0 mm and length of 42.0

mm. Then, the broadband dielectric properties of molded samples were measured.

90

3.3.4. Phase IV

The PVDF Kynar® 1000HD and MWCNTs (Nanocyl

TM NC7000) were dried at 50 °C for 4 hr

under vacuum. The MWCNT/PVDF and CuNW/PVDF nanocomposites were produced by solution

mixing technique. PVDF was dissolved into DMF at 80 ºC under continuous stirring to obtain a

solution with concentration of 0.1 g/ml. Meanwhile, MWCNTs and CuNWs were also dispersed

into DMF under sonication at room temperature for 30 min. The concentrations of MWCNT and

CuNW suspensions were 0.00033 and 0.00500 g/ml, respectively. Cooling down the PVDF/DMF

solution to room temperature, the MWCNT/DMF and CuNW/DMF suspensions were mixed with

PVDF/DMF solution separately using magnetic stirring for 5 min. Subsequently, the suspensions

were dripped into methanol (non-solvent to PVDF), where the volume ratio of DMF to methanol

was 1:3. Upon contact of the suspension with the methanol, the PVDF chains retracted and

precipitated instantly, due to their insolubility in methanol. The retracted chains entrapped the fillers

and prevented them from reagglomeration.

The mixtures were then filtered and placed in an evaporation dish for 24 hr in a fume hood.

Next, the MWCNT/PVDF nanocomposites were dried at 80ºC for 24 h in a vacuum oven; whereas,

the CuNW/PVDF nanocomposites were dried for 96 hr at room temperature under vacuum. Finally,

the MWCNT/PVDF and CuNW/PVDF nanocomposites with the concentrations between 0.4 and

1.5 vol% were produced by the compression molding of the prepared materials at 200 ºC for 10 min

under pressure of 35 MPa.

91

3.4. Electrical Properties Measurement Setups

3.4.1. Surface/Volume Resistivity Measurement

Usually, the setups utilized to measure the conductivity of materials displays the conductance in

terms of surface/volume resistivity. Volume resistivity is reciprocal of electrical conductivity and

defined as the electrical resistance through a cube of a material. When expressed in ohmcm, it

would be the electrical resistance through a one-centimeter cube of a material. Volume resistivity is

considered as an important factor while dealing with the bulk of materials, such as EMI shielding

and charge storage.

Surface resistivity is reciprocal of surface conductivity and defined as the electrical resistance of

the surface of a material. When expressed in ohm per square, it is equivalent to resistance across a

square section of a material. Since the surface length is fixed, the measurement is independent of

the physical dimensions (i.e., thickness and diameter) of the sample. Surface resistivity is an

important term when coping with the static electricity of materials, such as ESD protection and

antistatic dissipation.

In this PhD thesis, the resistivity measurements were performed using two different setups. For a

volume resistivity of more than 10+4

ohm·cm, a Keithley 6517A electrometer connected to a

Keithley 8009 test fixture was used. For the samples with a volume resistivity of less than 10+4

ohm·cm, the measurements were conducted according to the ASTM 257-75 standards, using a

Loresta GP resistivity meter (MCP-T610 model, Mitsubishi Chemical Co., Japan) connected with a

four-pin probe. The applied voltage for all the resistivity measurements was 10 V.

92

In the 8009 Test Fixture, as shown in Figure 3-7, volume resistivity is measured by applying a

voltage potential across opposite sides of an insulator sample and measuring the resultant current

through the sample.

Figure 3-7: The equivalent circuit for 8009 Test Fixture used to measure volume resistivity [6].

For the configuration shown in Figure 3-7, the volume resistivity can be calculated as following:

(3-1)

v: volume resistivity

R: measured resistance in ohms (

)

A: area of the sample

t: average thickness of the sample

Surface resistivity of insulative samples is measured by applying a voltage potential across the

surface of the sample and measuring the resultant current (Figure 3-8). The same model of test

fixture as volume resistivity but unlike configuration was used to measure the surface resistivity

93

(Figure 3-8). For the configuration shown in Figure 3-8, the surface resistivity can be calculated as

following:

(3-2)

: surface resistivity (per square)

R: measured resistance in ohms (

)

P: the effective perimeter of the guarded electrode

g: distance between the guarded electrode and the ring electrode

Figure 3-8: The equivalent circuit for 8009 Test Fixture used to measure surface resistivity [6].

For the samples with a low surface/volume resistivity, it is very significant to reduce or eliminate

the contact resistance to avoid any confounding effect: a voltage drop forms due to an interfacial

phenomenon at a point (between the current electrode and the sample surface), where the specific

current flows in. Accordingly, a four-point probe configuration was used to eliminate the effect of

contact resistance. Figure 3-9 shows a schematic of electrode construction and 4-terminal

configuration for the four-point probe. In the four-terminal method, a known current is passed

94

through the two outer probes and output voltage (V) is measured across the inner probes using a

voltmeter. In Figure 3-9, r1, r2 and Rx represent the contact resistance, resistance of cable and

resistance of sample, respectively. It is necessary to keep the impedance of voltmeter high not to let

electrical current flow into the terminal measuring the voltage.

Figure 3-9: (a) Electrode construction, (b) equivalent circuit for 4-point probe technique [7].

95

3.4.2. EMI Shielding Setup

EMI shielding properties measurements in the X-band (8.2 – 12.4 GHz) frequency range were

carried out in a WR-90 rectangular waveguide using an Agilent programmable network analyzer

(PNA) (Model E8364B). Figure 3-10 depicts a schematic diagram of network analyzer used to

measure the EMI shielding properties. A network analyzer consists of a signal source, a receiver

and a display. The source dispatches a signal at a single frequency to the material under test (MUT).

The receiver is adjusted to that frequency to detect the reflected and transmitted waves from MUT.

The magnitude and phase data will be measured for each signal. The source then switches to the

next frequency and the measurement is repeated. Finally, the reflection and transmission

measurement responses as a function of frequency will be displayed.

Scatter parameters, also called S-parameters, are used to calculate shielding parameters in a

two-port EMI shielding setup. The S-parameters describe the performance of a two-port EMI

shielding setup completely [8, 9]. The S-parameters are defined as:

| S11 |: Reflected voltage magnitude divided by the incident voltage magnitude in port 1

| S12 |: Transmitted voltage magnitude from port 2 to port 1 divided by incident voltage magnitude

in port 2

| S21 |: Transmitted voltage magnitude from port 1 to port 2 divided by incident voltage magnitude

in port 1

| S22 |: Reflected voltage magnitude divided by the incident voltage magnitude in port 2

If MUT is homogeneous, S11 should be equal to S22, and S21 also should be equivalent to S12.

Since power of each signal is proportional to square of field strength, | S11 |2

is equivalent to

96

reflected power divided by incident power in port 1 or | S12 |2

is equivalent to transmitted power

from port 1 to port 2 divided by incident power in port 1. The parameters a1 (a2) are the incident

field strengths and b1 (b2) are the transmitted plus reflected field strengths. As the reflector detector

for port 1 detects the sum of reflected wave from port 1 and transmitted wave from port 2 to port 1;

hence, the S-parameters can be obtained solving following matrices:

(3-3)

(3-4)

The reflectance and transmittance are defined as follow:

|

| | |

| | (3-5)

|

| | |

| | (3-6)

where R and T are reflectance and transmittance, respectively, and PI, PR and PT are incident,

reflected and transmitted powers, respectively.

Thus,

(

) ( ( | |

)) (3-7)

(

) (

| |

| |

) (3-8)

(3-9)

where SER and SEA are shieldings by reflection and absorption, respectively, and SEOA is overall

shielding effectiveness. It is worth mentioning that no device has been developed to measure

shielding by multiple-reflection separately; thus, shielding by multiple-reflection is inherent in

shieldings by reflection and absorption.

97

Figure 3-10: (a) Schematic of network analyzer diagram, (b) S-parameters diagram in a network

analyzer [8, 9].

98

3.4.3. Dielectric Spectroscopy Setup

In this dissertation, the broadband dielectric spectroscopy of CPCs was carried out with an

impedance / gain-phase analyzer (Solartron SI 1260) in the frequency range of 10-1

– 10+6

Hz. The

sample holder used for dielectric spectroscopy was a 12962A sample holder with electrode diameter

of 10 mm. Prior to the measurements, the electrodes were painted on the samples with a silver paste

to reduce the effect contact resistance with sample holder electrodes. The impedance analyzer

generated a voltage over a wide frequency band and applied it to the sample through the sample

holder, and then measured in-phase and out-of phase currents. The obtained voltage and current

data were used to calculate impedance and dielectric properties.

Figure 3-11 shows a schematic of the sample holder employed for dielectric spectroscopy. The

sample holder make use of a guard ring on the fixed electrode in order to decrease the influence of

stray field lines at the edge of the sample which would otherwise result in measurement errors. The

guard ring ensures that the electric field lines are parallel throughout the part of the sample, which

improves the impedance measurement [10].

Figure 3-11: Electrode arrangement of 12962A sample holder [10]

99

The impedance of nanocomposites was calculated using the following equations:

(3-10)

(3-11)

(3-12)

where Z is impedance, is AC voltage and IR and IC are resistive and capacitive

currents, respectively. Substituting IR and IC from Equations 2-23 and 2-24 and reorganizing the

final equations give:

( ) (3-13)

( ) (3-14)

(3-15)

where, : real permittivity, : Imaginary permittivity, ε0: the real permittivity of free space and S

and d: the area and thickness of the sample, respectively.

3.5. References

[1] NanocylTM

NC7000 series – Product Datasheet – Thin Multi-walled Carbon Nanotubes.

Available from: http://www.nanocyl.com: Nanocyl S.A.; 2009.

[2] Gelves GA, Al-Saleh MH, Sundararaj U. Highly electrically conductive and high

performanceEMI shielding nanowire/polymer nanocomposites by miscible mixing and

precipitation. Journal of Materials Chemistry. 2011;21(3):829-36.

http://www.nanocyl.com/de/content/download/417/2536/file/DM-Qual-05-TDS%20NC7000-V05.pdf

100

[3] Gelves GA. Synthesis of copper and silver nanowires in porous aluminum oxide templates

and preparation of polymer nanocomposites. Edmonton, AB, Canada, University of Alberta,

PhD Thesis, 2007.




[5] Mahmoodi M, Arjmand M, Sundararaj U, Park S. Effect of gate and runner design on

electrical properties of multi-walled carbon nanotube/polystyrene nanocomposites. Extended

abstracts, SPE-ANTEC Tech. Boston, 2011; p. 525-30.

[6] Instruction manual for model 8009 resistivity test fixture. Keithley Instruments, Inc.; 2003.

[7] Instruction manual for low resistivity meter (Lorest-GP). Mitsubishi Chemical Co.; 2004.

[8] Basics of measuring the dielectric properties of materials. Application note; Agilent

Technolgies, 2006, p. 1-31.

[9] Agilent network analyzer basics. Agilent Technologies, 2004, p. 1-94.

[10] Instruction guide for Solartron sample holder. Available from:

http://www.solartronanalytical.com: AMETEK, Inc. [cited August 2013].

http://www.solartronanalytical.com/

*Carbon. 2011;49(11):3430-3440.

101

Chapter 4

Electrical and Electromagnetic Interference Shielding Properties of Flow-

Induced Oriented Carbon Nanotubes in Polycarbonate*

4.1. Presentation of the Article

This article can be divided into two general sections as followings:

Investigating the electrical properties of MWCNT/PC composites as functions of MWCNT

loading and composite thickness, i.e., electrical conductivity and EMI shielding

Effect of MWCNT alignment on electrical conductivity of MWCNT/PC composites

In the first section, it was observed that there was an ascending trend for electrical conductivity

and EMI shielding as a function of MWCNT content. This was related to increased amount of

interacting mobile charges and also enhanced conductive network formation. Furthermore, the

mechanisms behind the electrical behaviors of CPCs are comprehensively discussed. In the second

section, the influence of MWCNT alignment, induced by an injection molding machine, on

electrical conductivity of MWCNT/PC composites is detailed. The results revealed that MWCNT

alignment had an adverse influence on electrical conductivity, which was related to inferior

conductive network formation at greater MWCNT alignments. The information presented in this

article is an appropriate starting point exploring the realm of electrical properties of CPCs.

102

Electrical and Electromagnetic Interference Shielding Properties of Flow-

Induced Oriented Carbon Nanotubes in Polycarbonate

Mohammad Arjmand1, Mehdi Mahmoodi

2, Genaro A. Gelves

1, Simon Park

2, Uttandaraman

Sundararaj1

1Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Canada 2Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary,

Canada

4.2. Abstract

The electrical and electromagnetic interference shielding effectiveness (EMI SE) properties of

multi-walled carbon nanotubes/polycarbonate (MWCNT/PC) composites are investigated. The

composites were prepared by diluting masterbatch (15 wt% MWCNT) using a Haake mixer and

then injection molding into a dog-bone mold. Various MWCNT alignments were created by

changing operating conditions. Electrical resistivity measurements were carried out at three

different areas at both parallel and perpendicular to the flow direction. The results showed higher

resistivity and percolation threshold at higher alignments in both parallel and perpendicular to the

flow directions. By applying Ohm’s law it was seen that after percolation, the field emission

mechanisms are more important at higher orientations. Higher MWCNT alignments were observed

in areas with higher resistivities, and this was verified using SEM, TEM and Raman spectroscopy

techniques. Additionally, EMI SE measurements were done on compression-molded samples at

different concentrations and thicknesses. The results showed that both EMI SE by reflection and

absorption increased with increase in MWCNT loading and shielding material thickness.

103

4.3. Introduction

Owing to their unique properties such as excellent electrical and mechanical properties, low

density and high aspect ratio, carbon nanotubes (CNTs) have outstanding potential to be used as

nanofiller for polymer composites [1-3]. In the last decade, applications of CNT have been mostly

dedicated to polymer/CNT composites due to their versatility, easy processability, potential to

reduce production cost and flexibility in final material design.

Outstanding electrical properties of CNTs have led to fast growth in research and development

of conductive polymer composites (CPCs). Conductivity at very low concentrations has made CPCs

ideal materials for industrial applications. Conductive network formation in CPCs is better

understood based on the concept of percolation threshold [4]. Percolation means that at least one

pathway forms to allow the electrical current to pass through the sample which alters the material

from insulative to conductive. Percolation occurs at a particular filler concentration where the

electrical conductivity of the composite abruptly increases by several orders of magnitude.

Electrical percolation at very low filler concentration in CNT-polymer composites leads to

production of cost-effective composites.

Electrostatic discharge (ESD) dissipation and electromagnetic interference (EMI) shielding are

the major applications for CPCs [5]. The surface resistivity or volume resistivity of filled polymer

defines its application. For ESD dissipation, typically a surface resistivity of 106-10

9 Ω/□ is required

while for EMI shielding applications, a surface resistivity of lower than 10 Ω/□ and EMI SE of

around 30 dB is needed [6]. If a part has conductivity in the ESD dissipation range, it can be

utilized to bleed off charge to avert harmful arcing discharges. ESD applications comprise chip and

104

circuit board carries for shipping of electronic equipments [7]. Many electronic devices innately

emit electromagnetic signals. Since these signals can interfere with the operation of other electronic

devices, related agencies have applied regulations for electromagnetic compatibility of electronic

housings. Electromagnetic compatibility (EMC) means that a device does not affect itself or other

devices by emitted emissions. Therefore, EMC standards must be met or exceeded for saleable

electronics products [8]. An EMI SE of 30 dB, corresponding to 99.9% of incident radiation, is

regarded as an adequate level of shielding for many applications [6,9].

Among the materials used as EMI shielding barriers, metal-coated polymers own the largest

share of shielding material for electronic enclosures in the market; however, there are serious

drawbacks such as recyclability, delamination and hidden cost in coating that can make CPCs more

promising materials than metal-coated polymers for the future. The EMI shielding mechanisms in

CPCs are more sophisticated than in metal-coated polymers. Understanding these mechanisms is

critical to design these materials appropriately to avoid overshielding which results in higher

product cost and to avoid undershielding which may cause failure in the final material application

[10]. Reflection, absorption and multiple-reflection are three dominant mechanisms of EMI

shielding in CPCs [11]. To reflect electromagnetic waves, shielding materials should have mobile

charge carriers on the surface to interact with the incoming electromagnetic waves [12-14]. Metals

are by far the most used materials for shielding due to the presence of free electrons that can reflect

and absorb incident waves. The absorption loss is a function of σ·μ whereas reflection loss is a

function of σ/μ where σ and μ are conductivity and magnetic permeability, respectively [7]. The

third mechanism of shielding is multiple-reflection, which usually occurs when there are numerous

surface areas or interfacial areas in conductive material like filler-added or foamed material.

105

Generally speaking, parameters such as aspect ratio, conductivity, orientation, dispersion and

concentration of conductive filler influence percolation threshold, conductivity and EMI SE of

CPCs [15]. Processing method is another significant factor that can influence the above-mentioned

parameters. Accordingly, having a good comprehension of processing methods gives direction to

researchers to control the final properties appropriately. Usually, homogeneous dispersion cannot be

attained because of high van der Waals interactions between CNTs, which leads to tangled

intertwined agglomerates. To exploit CNT properties, including electrical properties, efficiently,

these fillers should be dispersed in polymer well. Among the known methods to disperse CNT, melt

mixing is the most popular due to its compatibility with current industrial methods and because it is

environmentally benign. It has been reported that composites filled with higher aspect ratio fibers

have higher EMI SE and conductivity [16,17] and lower percolation threshold than those with lower

aspect ratio fibers; therefore, the blending conditions should be optimized to have the best

dispersion and lowest aspect ratio loss to get the best electrical properties.

CNT alignment can affect the electrical properties of CPCs greatly. Alignment of one-

dimensional CNTs leads to strong anisotropy in mechanical, electrical and even optical properties

of composites [18-25]. Behnam et al [26] simulated the dispersion of high aspect ratio conductive

filler and alleged that minimum resistivity occurs for partially aligned nanotubes. Abbasi et al [19]

studied the influence of nanotube alignment on electrical properties of CNT-based polycarbonate

nanocomposites using micro-injection molding and compared the results with compression-molded

samples. They reported that the high degree of alignment achieved by micro-injection molding led

to higher percolation threshold than that seen in compression-molded samples. However, Jou et al

[18,20] reported that they achieved higher EMI SE and conductivity in LCP composites with

106

longitudinal fiber orientation than the ones with random fiber orientation. In addition, Du et al [23]

also found that in SWNT/PMMA composite the highest conductivity occurs for slightly aligned

rather than isotropic systems.

The focus of this paper is the effect of multi-walled carbon nanotube (MWCNT) alignment on

electrical properties of MWCNT/polycarbonate (PC) system using dog-bone samples made via

injection molding. Flow-induced alignment of MWCNTs was achieved by applying intensive

drag/shear force during the molding process. The degrees of alignment were investigated using

SEM, TEM and Raman spectroscopy. The data were compared with the alignment data for

compression-molded rectangular samples, which give random distribution of MWCNT. Besides,

EMI SE of rectangular compression-molded samples was measured and corresponding shielding

mechanisms were analyzed.

4.4. Experimental

4.4.1. Composite Preparation and Molding

In this study, 15 wt% MWCNT/PC masterbatch was purchased from Hyperion Catalysis

International, Cambridge, MA, USA. The pristine polycarbonate used was Lexan 141, kindly

provided by Sabic Innovative Plastics, with melt flow index of 10.5 g/min and density of 1.19

g/cm3. Prior to mixing, all the materials were dried under vacuum at 120

oC for 4 hours.

A Haake rheomix series 600 batch mixer was used to dilute the PC/MWCNT masterbatch to

make samples with 0.1, 0.3, 0.5, 1.0, 1.5, 2.0, 3.5, 5.0, 7.5 and 10 wt% MWCNT. Granular

107

polycarbonate was first mixed for 5 minutes at 300 ˚C and 50 rpm, and then masterbatch was added

to the melt and mixed for additional 10 minutes. In all cases, the amount of material added filled

78% of the mixer volume at the mixer temperature. To prepare the material for use in the injection

molding system, the mixed compound was ground using a Retsch Brinkmann grinder with a 3 mm

sieve while liquid nitrogen was poured into the grinding system to avoid overheating and

morphology alteration.

An injection molding machine (Boy 12A) was used to inject the material into a two-cavity mold

according to the ASTM D638 test method. As demonstrated in Figure 4-1(a), the dog-bone

specimens were 63.5 mm in total length with a gage section of 9.53 mm, 3.18 mm and 4 mm in

length, width and thickness, respectively. The screw diameter was 18 mm with a length/diameter

(L/D) ratio of 20. The mold base was made out of steel, and the mold insert was fabricated from

Aluminum 7075. An electrical heating system was used to control the mold temperature. Injection

molding was performed with a holding pressure of 60 bar, mold temperature of 80 oC and barrel

temperature of 300 oC. Figure 4-1(b) depicts the experimental setup of the injection molding

system. A Carver (Carver Inc. Wabash, IN) compression molder was used to make rectangular

samples 42×25 mm with four different thicknesses of 0.25, 0.60, 1.50 and 1.85 mm to get EMI SE

data. The compression molding process was carried out for 5 min at 5000 psi.

108

(a) (b)

Figure 4-1: (a) Schematic of the dog-bone sample. The three different areas studied in the

specimens are indicated, (b) Experimental setup.

4.4.2. Electrical and EMI Shielding Measurements

The electrical resistivity measurements were done on both rectangular and dog-bone samples. All

the sample surfaces were cleaned with ethanol prior to measurements. For dog-bone samples, the

measurements were done at three different areas, as demonstrated in Figure 4-1(a), in directions

both parallel and perpendicular to the flow. To measure the volume resistivity of the molded

samples, two different resistivity measurement machines were used. For the samples with volume

resistivity less than 104 Ω·cm, volume resistivity measurements were performed according to

ASTM 257-75 standards employing a Loresta GP resistivity meter (MCP-T610 model, Mitsubishi

Chemical Co., Japan). We used a four-pin probe so that the effect of contact resistance does not

confound the measurement. In this method, a constant current is passed through the two outer

probes and output voltage (V) is measured across the inner probes using a voltmeter. For volume

109

resistivity larger than 104 Ω·cm, a Keithley 6517A electrometer connected to Keithley 8009 test

fixture (Keithley instruments, USA) was used and resistivity was measured at an applied voltage of

10 V.

The EMI shielding measurements were carried out over the X-band (8.2 – 12.4 GHz). The

sample under test was sandwiched between two X-band waveguide sections, which were connected

to separate ports of an Agilent Vector Network Analyzer (model 8719 ES). The Vector Network

Analyzer (VNA) sends a signal down the waveguide incident to the sandwiched sample and then

the reflected and transmitted signals are measured by the VNA. EMI SE is expressed in dB and

defined by the following equation [9,11]:

(

) (

) ( ) (4-1)

where Pin is the incident energy field, Pout is the transmitted energy field and E and H are the root

mean square (rms) of electric and magnetic field strength of the electromagnetic wave, respectively.

Equation 4-1 can also be used to calculate the contributions of reflection and absorption to total

EMI SE considering relevant incident and transmitted energy fields.

4.4.3. Morphological Characterization

Scanning and transmission electron microscopy (SEM and TEM) were used to investigate the

morphology of molded nanocomposites. A high resolution Philips XL30 was used to obtain SEM

images. All the samples were cryo-fractured prior to SEM tests. TEM tests were processed using a

Hitachi H-7650. The samples were ultra-microtomed using diamond knife at room temperature

110

before TEM observation. For dog-bone samples, morphological characterizations were done for the

samples in directions both parallel and perpendicular to the flow.

4.4.4. Raman Spectroscopy

Raman spectroscopy method was used to further investigate the degree of alignment in different

areas, namely area 1, 2 and 3 and to compare it with compression-molded samples. In order to do

this, a Renishaw spectrometer equipped with an in Via Raman microscope was employed.

Excitation was provided by NIR laser (785 nm) in regular mode. Measurements were performed in

directions both parallel and perpendicular to the flow. The MWCNT alignment was determined

comparing the Raman spectra obtained from parallel and perpendicular directions.

4.5. Results and Discussion

4.5.1 Electrical Conductivity of MWCNT/PC Composites

Statistical percolation theory [2,4] predicts the dependence of volume resistivity on filler

concentration using a scaling law of the form

( ) (4-2)

where ρ is the composite volume resistivity, ρ0 is the volume resistivity of conductive filler and Vc

and t are percolation threshold and critical exponent, respectively. Higher t values and lower

percolation thresholds correspond to well-dispersed high aspect ratio fillers [4].

111

Figure 4-2 presents the percolation curve for compression-molded samples. Using percolation

theory, the percolation threshold and critical exponent of the compression-molded samples were

found to be 2.63 and 0.28 vol%, respectively. Compared to other studies on MWCNT/PC [19, 27-

30], our results show lower percolation threshold, which indicates better dispersion of MWCNT in

polymer matrix and less reduction in MWCNT aspect ratio during mixing.

Figure 4-2: Percolation curve for rectangular (compression-molded) samples of MWCNT/PC

composite.

Understanding the conduction mechanisms will allow us to determine applications for CPCs at

various concentrations. Figure 4-2 can be divided into three regions: 1) the region before

percolation at low concentrations, (2) the region where percolation occurs and (3) the region after

percolation. In the region before percolation, the MWCNTs are far from each other and the

conductance is limited by the polymer matrix which has resistivity on the order of 1015

-1017 Ω·cm.

The MWCNTs and the insulating gap, i.e. polymers, between them can be modeled as a capacitor

[31]. When the concentration of MWCNTs is very low, the insulating gaps between the capacitor

112

plates, i.e. MWCNTs, are very large and the chance that electrons are transferred from one plate to

another is very low. When the mean gap width between MWCNTs is larger than 10 nm,

conductivity is the result of transport processes within the polymer host matrix [6]. By applying an

electric field, the insulative material starts to redistribute its charges (protons and electrons)

partially; this is called polarization. The higher the polarization, the higher are the permittivity and

the electrical conductivity [31]. In this case, polarized charges are bounded and cannot be easily

dislocated. According to Band Theory [32,33], only some electrons can get adequate energy to go

from the valence band to the conduction band. The gap between the valence band and the

conduction band is the forbidden zone. The higher the concentration of MWCNTs in polymers, the

lower is the gap width and the higher is the chance that electrons will pass the barrier.

By increasing MWCNT concentration, the gaps between the conductor materials (MWCNTs)

decrease. When the mean particle-particle distance goes below 10 nm, the dominant electron

transfer mechanism is internal field emission [34]. Internal field emission is a general term for

describing a number of processes in which the electrons have low probability of passing forbidden

zones [31-37]. In narrow insulating gaps between conductive fillers, very high field strength may

develop which is higher than the macroscopic voltage by a factor M that is the ratio of average size

of conducting aggregate to the average gap width [38,39]. This high field strength provides free

electrons sufficient energy to cross the insulative gap.

By increasing filler loading further, the filler particles get closer and eventually at percolation

threshold, the first network forms which lets the current pass through. In the second region, where

percolation occurs, the free electrons in conductive filler will play the role of charge carriers more

113

dominantly due to direct contact between MWCNTs. Since these free electrons belong to the

conductive band [32], the resistivity of nanocomposite reduces by several orders of magnitude at

percolation threshold. After percolation, increasing the conductive filler content alters the volume

resistivity only marginally. In the third region, the region after percolation, two effects control the

conductivity: (1) the constriction resistance of contact spots and (2) tunneling resistance between

separated particles [40]. A Considerable amount of current dissipates at the contact spots between

the conductive fillers. After percolation, as the filler concentration increases, the clusters initiate

connections with each other to form a 3-D network which leads to increase in conductivity.

However, the constriction resistance restricts conductivity increase due to large number of contact

spots. Consequently, as demonstrated in Figure 4-2, constant resistivity at high concentrations was

achieved.

Figures 4-3(a-c) depict the percolation curve of compression-molded and injection-molded

samples. The percolation curve for compression-molded samples is presented in these figures to

better show the effect of alignment. For injection-molded samples, the percolation curve is

demonstrated for three different areas. As demonstrated in Figure 4-1(a), area 1 is the area near the

gate while areas 2 and 3 are the neck and runner parts, respectively. All the measurements for

injection-molded samples were carried out in directions both parallel and perpendicular to the flow.

In this article, parallel and perpendicular to the flow resistivities are denoted as and ,

respectively. As the size of four-pin probe used for characterization of conductive materials is larger

than the length of sample in the perpendicular to the flow direction, we were not able to measure

volume resistivity at high MWCNT concentrations. However, measuring volume resistivity at lower

concentrations, i.e. high resistivity, in the direction perpendicular to the flow was done employing

114

the Keithley instrument. As confirmed in the following section by characterization methods, the

order of the degree of alignment is as following:

Area 3 > Area 2 > Area 1> Compression-molded samples

Greater alignment occurs due to higher levels of applied shear rate on the nanocomposite melt.

As can be seen in Figure 4-3, alignment of MWCNTs led to higher resistivity than compression-

molded samples (random distribution). Alignment of MWCNTs decreased the likelihood of

MWCNTs being adjacent or connected with each other. is higher than random distribution even

at high concentrations. Since alignment diminishes the likelihood of MWCNTs connection,

tunneling mechanism becomes significant after percolation in aligned samples. This means that in

aligned samples there may be lots of conductive pathways, which are near each other but not

connected.

115

Figure 4-3: Percolation curve for rectangular (compression-molded) samples and injection-molded

samples (parallel and perpendicular to the flow direction) at (a) area 1, (b) area 2 and (c) area 3.

116

To investigate the above hypothesis, we applied the method introduced by Chakanov et al [38].

We applied very high voltage, 500 V, for very short time on aligned samples with different

concentrations and then measured resistivity at 10 V. Interestingly, it was observed that percolation

curve for aligned samples tended to the percolation curve for random distribution of nanofillers.

This thought to be a result of the dielectric breakdown of aligned injection-molded samples at high

electric field. Dielectric breakdown is irreversible damage that occurs due to high electric field and

is in the form of carbonization of polymer leading to formation of conductive pathways [31,38].

Compression-molded samples were also investigated for this effect and the changes were much

lower. We believe that changes in percolation curve when applying high voltage is due to high

electric field applied in small gaps between clusters that leads to dielectric breakdown making the

insulating gaps conductive. As explained before, the real voltage applied in the gaps is much larger

than the macroscopic voltage.

Figures 4-3(a-c) show that the electrical resistivity perpendicular to the flow is even higher than

electrical resistivity parallel to the flow. This anisotropy can be clarified using the concept that the

inherent resistance of a MWCNT is much lower than MWCNT-MWCNT contact resistance. Since

the current will need to cross less MWCNT-MWCNT contacts in the parallel direction compared to

the perpendicular direction, the resistivity and percolation threshold in the direction perpendicular

to the flow are higher.

In these injection-molded aligned samples, at high concentrations, resistivity decreases

marginally with increase in MWCNT volume fraction due to tunneling-conduction mechanism

transformation. For further investigation of the effect of alignment on the conduction mechanism,

the current-voltage characteristics were investigated for the composites at different concentrations

117

of MWCNT in thickness direction (see Figure 4-4). Ohmic behavior is expected if the graphitic type

of conductivity exists in the composite [38,41,42]. According to Figure 4-4, the composite with

random distribution of MWCNT shows Ohmic behavior at around 1.5 wt% (R2 ≈ 1 for linear

regression), while in the injection-molded sample (area 3), Ohmic behavior is dominant at around

3.5 wt% (R2 ≈ 1 for linear regression).

Figure 4-4: Current-voltage characteristics of a) compression-molded sample, b) injection-molded

sample (area 3) in thickness direction. 1The measured current of composites holding 0.5 wt% of

MWCNT in Fig. 3(a) and 1.5 wt% of MWCNT in Fig. 3(b) have been multiplied by 50 to enable its

visualization in the plot.

118

As previously explained, after percolation, tunneling mechanism is more significant in injection-

molded samples than compression-molded ones. Non-Ohmic behavior is due to increase in

probability of electron transfer through the insulative barrier with increase in electric field.

According to Figure 4-4, non-Ohmic behavior can be observed in aligned injection-molded sample

(area 3) at higher concentrations than compression-molded samples, which verifies that at high

concentrations, field emission mechanism is more dominant in aligned injection-molded samples

than compression-molded ones.

Table 4-1 shows percolation thresholds, critical exponents and correlation factors calculated

using percolation theory (see Equation 4-2) for the compression-molded samples and different areas

of dog-bone samples, corresponding to various alignments. According to Table 4-1, compression-

molded samples present higher critical exponent and lower percolation threshold than injection-

molded aligned samples owing to the higher probability of the connection between MWCNTs. By

increasing the alignment in injection-molded samples, the percolation threshold increases due to

reduced likelihood of connection. Critical exponent (t) is representative of conductivity increase

after percolation with increasing the filler content. The higher is the aspect ratio of filler, the larger

is the value of critical exponent [4]. Generally, high aspect ratio filler promotes the probability that

clusters will connect with each other to develop a 3-D network, which results in larger critical

exponents. Analogously, as evidenced in Table 4-1, by increasing the alignment, the critical

exponent decreases relating to a reduction in probability of connection of clusters after percolation.

119

Table 4-1: Percolation thresholds, critical exponents and correlation factors for compression-

molded samples and injection-molded samples at different areas, corresponding to different

alignments.

Log (ρ0 (Ω·cm)) Vc t R2

Compression-

molded -1.81 0.0028 2.64 0.984

Injection-molded samples

Area 1 -0.6842 0.0064 2.52 0.9913

Area 2 -0.434 0.0083 2.38 0.9845

Area 3 +0.3035 0.0095 2.10 0.9945

4.5.2. Morphological Analysis

Figure 4-5(a) shows the SEM micrograph of the compression-molded sample of PC with 1.5

wt% MWCNT whereas Figures 4-5(b-c) show SEM images of aligned injection-molded sample

(area 3) in directions parallel and perpendicular to the flow, respectively. It is seen in Figure 4-5(a)

that MWCNTs are entangled to each other; however individual MWCNTs can be easily

distinguished. Analogous intertwined structures of MWCNTs have been reported in literature

[27,43,44]. The diameter seen in Figure 4-5(a) is larger than the diameter reported by Hyperion, 15-

50 nm, indicating that a polymer layer has been adsorbed on the MWCNT surface confirming good

adhesion between polymer and conductive filler. The bright dots observed throughout the PC matrix

are ascribed to the ends of the broken MWCNTs owing to their high conductivity.

Due to orientation of MWCNTs as a result of shear force, the microtomed sections in the flow

direction should exhibit more tube segments than sections cut perpendicular to the flow, which

120

should show more MWCNTs cross sections (bright spots). Possible appearances of cut surfaces in

flow-induced aligned samples were illustrated by Pötschke et al [27]. As can be seen in Figures 4-

5(b-c), for the sections parallel to flow, a lower number of bright spots, corresponding to MWCNTs

cross sections, can be observed than for sections perpendicular to the flow direction. These two

images confirm the partial alignment of MWCNTs in injection-molded samples.

Figure 4-5: SEM images of PC+1.5 wt% MWCNT. (a) compression-molded sample; (b) aligned

injection-molded sample (area 3), parallel to the flow direction; (c) aligned injection-molded sample

(area 3), perpendicular to the flow direction.

121

Figures 4-6(a-b) demonstrate the TEM micrographs of aligned injection-molded sample (area 3)

in directions parallel and perpendicular to the flow. As evidenced in Figure 4-6, the cut parallel to

the flow direction mostly shows MWCNT segments whereas the cut perpendicular to the flow

direction displays dark spots, corresponding to MWCNT cross sections. The MWCNTs are

uniformly dispersed as individual tubes in the whole polymer matrix without significant

agglomeration, which confirms our theory about low percolation threshold. It is worthwhile to

mention that applying high shear force also aids in MWCNTs deagglomeration. Due to the curved

structure of MWCNTs, some sections may be cut by the diamond knife or embedded in the polymer

matrix; therefore, the lengths visible in the TEM sections do not represent the whole length of

MWCNTs.

122

Figure 4-6: TEM micrograph of aligned injection-molded sample (area 3): a) Parallel to the flow

direction, b) Perpendicular to the flow direction.


Raman spectroscopy was employed to verify MWCNT alignment at different sample areas. This

method counts on inelastic scattering of infrared light by molecules upon coming back to their

primary energy level after excitation [19]. Figure 4-7 shows Raman spectra of compression-molded

123

sample and area 3 in the dog-bone sample corresponding to the lowest and highest degree of

alignment, respectively. Three bands can be observed in Raman spectra of PC/MWCNT, namely D,

G and G' bands. The D band is the most sensitive band to MWCNT alignment and corresponds to

sp2 hybridized graphitic structure. The G band relates to in-plane vibration of graphitic wall and is

less sensitive to MWCNT orientation than D band, and G' band is not sensitive to MWCNT

alignment [45]. The and parallel/perpendicular to the flow direction were utilized to

determine the degree of alignment. Table 4-2 summarizes the results obtained from Raman

spectroscopy of the compression-molded sample and various areas of the injection-molded sample.

As evidenced in Table 4-2, the intensity ratios for the compression-molded sample is near 1, which

shows no preferential alignment in the compression-molded sample. The intensity ratios and then

the alignment have the following order:

Area 3 > Area 2 > Area 1> compression-molded samples.

Figure 4-7: Raman spectra of PC/5 wt% MWCNT nanocomposites.

124

Table 4-2: Raman intensity ratios parallel/perpendicular to the flow direction of compression-

molded and injection-molded samples of PC/MWCNT.

Raman spectroscopy ratio parallel/perpendicular

Compression molding 1.042 1.026

Area 1 1.391 1.267

Area 2 1.559 1.378

Area 3 1.649 1.445

This result is in complete agreement with electrical conductivity data. According to Tables 4-

1and 4-2, the electrical resistivity increases with increase in alignment. Increasing alignment

decreases the chance of MWCNTs to contact with each other; therefore, volume resistivity and

percolation threshold increase while critical exponent decreases. For instance, area 3 with D band

intensity ratio of 1.649 has the highest alignment and percolation threshold of 0.95 vol%, while

compression-molded sample with D band intensity ratio of 1.042 shows a percolation threshold

around 0.28 vol%.

4.5.4. Electromagnetic Interference Shielding Measurements and Mechanism

Electromagnetic interference shielding effectiveness (EMI SE) is the ability of a material to

attenuate an incident electromagnetic wave and can be calculated using Equation 4-1. EMI SE

consists of three different mechanisms; namely reflection, absorption and multiple-reflection. When

an electromagnetic wave crosses a medium with different intrinsic impedance from the space in

which electromagnetic wave is propagating, a portion of electromagnetic wave is reflected from the

shielding material exterior surface. To reflect an electromagnetic wave, the shielding material

125

should have mobile charge carriers on the surface to interact with the incoming wave. It should be

considered that the first reflection from shielding material interior surface is a part of reflection

mechanism, too. The portion of electromagnetic wave that penetrates through the material can be

attenuated through absorption mechanism. The absorption loss is more important for magnetic

fields than electric fields since the electric field is mostly reflected at the first interface [12].

Generally, the penetrating wave leads to formation of electric/magnetic dipoles in the material.

Electric/magnetic dipoles can attenuate the electromagnetic field but their effect is less than the

effect of mobile charge carriers in the shielding material. Multiple-reflection is the third mechanism

which has negative effect on EMI SE [7,10,12]. This mechanism requires large surface or interfacial

area in the shield. Multiple-reflection represents internal reflections within the shielding material.

Several equations have been developed to quantify the contributions of reflection and absorption

to EMI SE of monolithic materials [8-10]. The shieldings by reflection and absorption are given by

the following equations:

( ) (4-3)

( ) (4-4)

where R and A are shielding by reflection and absorption, respectively; C1 and C2 are constants; f is

frequency; µ is magnetic permeability; σ is electrical conductivity; and t is thickness of shielding

material. Strictly speaking, these equations are not complete for filler-added materials since they do

not account for filler inherent specifications and volume fractions. In addition, the effect of

multiple-reflection is disregarded in these equations. Additionally, after the percolation threshold,

adding more filler increases EMI SE while the percolation curve reaches a plateau. According to

126

Equations 4-3 and 4-4, both absorption and reflection increase with increase in conductivity;

absorption has a direct relation with (fµ) while reflection decreases with increase in (fµ).

Figure 4-8 depicts EMI SE of compression-molded samples as a function of MWCNT

concentration and shielding plate thickness. Figure 4-8 shows the average values over the X-band

frequency range. As shown in this figure, EMI SE increases with both MWCNT concentration and

plate thickness. The increase in EMI SE by increase in MWCNT content is due to formation of

more networks of conductive filler and larger source of free electrons in the material that can

interact with incoming electromagnetic wave. Increase in MWCNT concentration leads to growth in

both conductivity and EMI SE; accordingly, it has been concluded that increase in EMI SE is due to

increase in conductivity. However, it is worthwhile to note that conductivity needs connectivity

while EMI SE does not [5,7]. According to Figure 4-8, EMI SE increases with increase in sample

thickness, which is due to higher amount of conductive filler that interact with the incoming

electromagnetic wave.

127

Figure 4-8: EMI SE of MWCNT/PC compression-molded samples as a function of MWCNT

concentration and shielding plate thickness.

To investigate the effect of thickness on EMI SE more precisely, the contributions of absorption

and reflection to EMI SE as a function of MWCNT concentration and material thickness were

inspected (Figure 4-9). Both reflection and absorption increase with increase in MWCNT

concentration and shielding material thickness. According to Equation 4-4, there is a direct relation

between absorption and material conductivity and shielding material thickness. Figure 4-9(a) shows

that absorption increases with both MWCNT concentration and shielding material thickness.

Actually, increasing conductive filler concentration and shielding material thickness is equivalent to

having more mobile charge carriers and more conductive filler networks that can attenuate the

penetrating wave.

As shown in Figure 4-9(b), the reflection also increases with both MWCNT content and

shielding material thickness. There is a direct relation between reflection and MWCNT

concentration because there are more mobile charge carriers on the surface at higher concentrations.

128

Figure 4-9: (a) Contribution of absorption, (b) Contribution of reflection to the overall EMI SE for

compression-molded samples as a function of shielding material thickness and MWCNT

concentration.

However, the relation between reflection and shielding material thickness is more sophisticated

and depends on factors such as conductive filler concentration and shape, shielding material skin

depth and the distance between fillers in polymer medium [10]. The measured shielding by

129

reflection is the sum of reflected wave from shielding material exterior and interior surfaces,

reflected wave from filler surface area and multiple-reflection effect. Increasing the shielding

material thickness increases the amount of filler reflecting surface area. The increase in filler

surface area in the shield can have two effects on the contribution of reflection to shielding: (1) it

can increase the reflection coefficient by increasing the reflecting surface area provided by

nanofiller and (2) it can decrease the reflection coefficient by blocking and reflecting back the

reflected waves from shielding material interior surface area and other filler surface area (multiple-

reflection effect).

Multiple-reflection effect decreases the chance of reflected waves from shielding material

interior surface and other filler surface area to reach exterior surface of the shielding material and to

join to total reflected wave. It is worthwhile to mention that the effect of multiple-reflection is

negligible if the contribution of absorption to EMI SE is more than 10 dB or the shielding material

thickness is larger than its skin depth. According to Figure 4-9(b), it can be seen that the positive

effect of thickness increase (more filler reflecting surface area) on reflection dominates its negative

effect (multiple-reflection effect); therefore, reflection increases with increase in thickness for the

range of concentrations studied.

4.6. Conclusions

Electrical resistivity measurements showed that increasing the alignment of nanotubes in

MWCNT/PC composites significantly reduces the likelihood of contact between MWCNTs.

Accordingly, higher percolation thresholds and lower critical exponents were achieved at greater

MWCNT alignments. At the same filler loading, higher electrical resistivity was observed in the

130

direction perpendicular to the flow relative to the direction parallel to the flow at all areas of the

dog-bone samples. Verifying Ohm’s law after percolation showed that the field emission

mechanism is much more dominant in injection-molded aligned samples than those with random

distribution of MWCNT. Characterization methods like SEM, TEM and Raman spectroscopy

confirmed higher orientation in areas with larger electrical resistivities.

For the samples with random distribution of MWCNT, shielding by reflection and absorption

increased with increase in MWCNT concentration and shielding material thickness. Increase in

shielding by absorption through increasing MWCNT concentration and shielding material thickness

is expected due to greater conductive filler content and higher conductivity. However, increase in

shielding effectiveness by reflection with increasing thickness indicates that the positive effect of

thickness increase (more filler reflecting surface area) on reflection is dominant over its negative

influence (multiple-reflection) for the range of concentrations studied.

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134

Chapter 5

Comparative Study of Electromagnetic Interference Shielding Properties of

Injection Molded versus Compression Molded Multi-walled Carbon

Nanotube/Polystyrene Composites*


This article is concerned with comparing the electrical properties of injection molded versus

compression molded MWCNT/PS composites over the X-band frequency range in terms of

MWCNT alignment, i.e., electrical conductivity, EMI shielding and dielectric properties.

Unavoidable flow-induced alignment of MWCNTs in injection molding process was the stimulation

to investigate effects of MWCNT alignment on the electrical properties of MWCNT/polymer

composites. To the best of our knowledge, this study is the first one in the area investigating the

effects of MWCNT alignment on EMI shielding and dielectric properties and detailing the

mechanisms behind.

The information obtained from the experimental design of 5.00 wt% MWCNT/PS composites in

chapter 3 were used to select three processing conditions, with maximum possible variation in

MWCNT alignment, to make MWCNT-aligned composites at different MWCNT concentrations.

Accordingly, EXPs #11, 12 and 14 in the experimental design correspond to EXPs # 2, 3 and 1 in

this article, respectively. The electrical properties of injection molded composites were compared

135

with those of compression molded composites, where MWCNTs were randomly distributed. The

results revealed that the injection molded composites showed poorer electrical properties than the

compression molded composites. This observation was related to inferior conductive network

formation arising from MWCNT alignment. As the electrical properties of the compression molded

samples were superior to those of the injection molded samples, it can be concluded that in injection

molding process molding conditions and mold design should be performed so as to obtain random

distribution of MWCNTs.

136

Comparative Study of Electromagnetic Interference Shielding Properties of

Injection Molded versus Compression Molded Multi-walled Carbon

Nanotube/Polystyrene Composites

Mohammad Arjmand1, Thomas Apperley

2, Michal Okoniewski

2, Uttandaraman Sundararaj

1

1Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Canada 2Department of Electrical and Computer Engineering, University of Calgary, Calgary, Canada

5.2. Abstract

This study compares electromagnetic interference (EMI) shielding properties of injection molded

versus compression molded multi-walled carbon nanotube / polystyrene (MWCNT/PS) composites,

i.e., properties such as EMI shielding effectiveness (EMI SE), electrical conductivity, real

permittivity and imaginary permittivity. The injection molded (MWCNT-aligned) samples showed

lower EMI shielding properties than compression molded (randomly distributed MWCNT) samples,

that was attributed to lower probability of MWCNTs contacting each other due to MWCNT

alignment. The compression molded samples showed higher electrical conductivity and lower

electrical percolation threshold than the injection molded samples. The compression molded

samples at MWCNT concentrations of 5.00 and 20.0 wt% showed real permittivity 2 times and

imaginary permittivity 5 times greater than the injection molded samples. The EMI SE for the

compression molded samples at MWCNT concentrations of 5.00 and 20.0 wt% was 15.0 and 30.0

dB, respectively, significantly greater than EMI SE for the injection molded samples. Lower EMI

SE for the injection molded samples was ascribed to lower electrical conductivity, real permittivity

(polarization loss) and imaginary permittivity (Ohmic loss). Comparison of the EMI shielding

137

properties of the compression molded versus injection molded samples confirmed that EMI

shielding does not require filler connectivity; however it increases with filler connectivity.

5.3. Introduction

Electromagnetic interference (EMI) occurs when undesirable signals superimpose upon a signal

of interest. These signals may originate from a device used as a transmitter or from a device that is

not supposed to transmit but has parts that transmit in a certain frequency range. EMI effects can

range from interruption of operation to degradation of electronics or electrical equipments [1].

Accordingly, EMI has become a significant technical challenge given the rapid development of

electronic devices, such as laptops, cell phones, weather radars, TV picture transmitters, and the

like. [2-7].

To reduce EMI issues, appropriate agencies such as CISPR (Comité International Spécial des

Perturbations Radioélectriques) have applied regulations for electromagnetic compatibility (EMC)

of electronic enclosures. EMC means that a device does not influence itself or other devices by its

emissions and these standards must be met or exceeded for commercial electronics. Considering

EMC regulations, an EMI shielding effectiveness (EMI SE) of at least 30 dB, which corresponds to

shielding of 99.9% of incident radiation, i.e., 0.1% is transmitted, is regarded commercially as an

adequate level of shielding for many applications [1, 7].

Recently, conductive filler/polymer composites (CPCs) have attracted a great deal of interest to

be used for EMI shielding applications due to their light weight, low cost, resistance to corrosion

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and design flexibility [8,9]. Different conductive fillers have been embedded into polymer matrices

in order to get CPCs with desired EMI shielding properties, such as EMI SE, electrical conductivity,

real permittivity and imaginary permittivity [8-14]. Among different conductive fillers used in

CPCs, carbon nanotubes (CNTs) have fascinated researchers due to their unique electronic structure

and extraordinary properties. CNTs are capable of carrying a high current density (ca. 106-10

9

A/cm2) without observable oxidative damage, which makes them versatile fillers for composites

used for electrical and EMI shielding applications [15, 16].

Structural perfection, aspect ratio, dispersion, distribution and alignment of CNTs are among the

most important parameters that have great influence on the EMI shielding properties of

CNT/polymer composites. It has been shown that for greater metallic behavior, higher aspect ratio

and better dispersion of CNTs, there is an enhancement in the EMI SE of CNT/polymer composites

[4, 5, 17]. This enhanced EMI SE may be due to higher amount of available interacting mobile

charge carriers leading to more energy dissipation. Nevertheless, the effects of alignment of CNTs

on electrical conductivity, real permittivity and imaginary permittivity and their relationship with

EMI SE is a concept that has not been well comprehended and requires further investigation.

Hitherto, to the best of our knowledge, only a few papers have been dedicated to the study of effects

of alignment on electrical conductivity of CNT/polymer composites [18-21]; moreover,

investigations discussing effects of CNT alignment on the other EMI shielding properties are even

more rare [22, 23].

The inevitable flow-induced alignment of CNTs in injection molding process was the inspiration

to investigate effects of CNT alignment on the EMI shielding properties of CNT/polymer

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composites. Most of investigations on the EMI shielding properties of CPCs have been devoted to

compression molded samples which have randomly distributed conductive filler; this has led to

results that are not applicable to injection molded samples where the conductive filler is aligned

[3,5,9]. Therefore, this study compares the EMI shielding properties of injection molded versus

compression molded multi-walled carbon nanotube / polystyrene (MWCNT/PS) composites in

terms of MWCNT alignment.

5.4. Experimental

5.4.1. Composite Preparation

A masterbatch of 20.0 wt% MWCNT in PS was obtained in the form of cylindrical pellets from

Hyperion Catalysis International, Cambridge, MA, USA. The length and diameter of pellets were

2.50 ± 0.25 mm and 3.50 ± 0.25 mm, respectively. The masterbatch was diluted with a neat PS

(Styron® 610) kindly supplied by Americas Styrenics LLC, to prepare the nanocomposite samples

of various loadings.

Prior to mixing, all the materials were dried at 50 °C for at least 4 hr under vacuum. The

composites with different concentrations of MWCNT were prepared using a 25 mm Coperion ZSK

co-rotating intermeshing twin-screw extruder operated at barrel temperature of 200 °C and extruder

speed of 150 rpm. At these conditions, the residence time was 2 min. Considering the density of

neat PS and MWCNT are 1.06 and 1.75 g/cm3, respectively; the concentrations of prepared

nanocomposites in terms of weight percent and volume percent are presented in Table 5-1.

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volume percent.

5.4.2. Experimental Design and Composite Molding

In our previous studies [23, 24], a series of injection molding experiments were carried out on a

5.00 wt% MWCNT/PS composites using a two-level, four-factor factorial design to study the

impact of four processing parameters, i.e., mold temperature (C1), melt temperature (C2),

injection/holding pressure (C3) and injection velocity (C4) on the volume resistivity of the molded

samples. The results showed that the melt temperature had the greatest impact on volume resistivity

of the molded samples followed by the injection velocity, while the impacts of mold temperature

and injection/holding pressure were insignificant. It was also shown that the volume resistivity had

a direct relationship with MWCNT alignment [21, 23]. A lower melt temperature and higher

injection velocity impose greater shear stress on the polymer matrix melt which leads to greater

MWCNT alignment [18, 19].

Accordingly, knowing the tremendous influence of melt temperature and injection velocity on

MWCNT alignment and volume resistivity of MWCNT/PS nanocomposites, three different

injection molding experiments, called EXP #1, 2 and 3, with various levels of melt temperature and

injection velocity were employed to make samples with various MWCNT alignments at different

MWCNT concentrations. Levels of processing parameters used in EXP #1, 2 and 3 are shown in

Table 5-2. The samples fabricated using EXP #1, 2 and 3 were used to investigate the effects of



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MWCNT alignment on the EMI shielding properties of MWCNT/PS composites at different

MWCNT concentrations.


experiments (EXPs). The processing parameters are mold temperature (C1), melt temperature (C2),

injection/holding pressure (C3) and injection velocity (C4).

An injection molding machine (Boy 12A) was used to inject MWCNT/PS nanocomposite melt

into a 1-cavity mold. The melt temperature and injection velocity set points were selected to be as

large as possible within the limitations of the injection molding machine and the recommended

processing conditions of neat PS. Constant holding and cooling times of 8 and 10 seconds,

respectively, were applied for all runs. The holding pressure was set to be the same as the injection

pressure for all the experiments.

Figure 5-1 shows a schematic of the mold design employed in the injection molding process and

the mold dimensions are listed in Table 5-3. The thickness of cavity was 2.0 mm. To make sure that

all the cavities were filled simultaneously, the runner and gate dimensions were balanced using

CFD software (MoldflowTM

, Ver. 5) for neat PS. A detailed description of the designed mold and

injection molding machine can be found in our previous study [23]. To have a better understanding

of the effects of MWCNT alignment on the EMI shielding properties, the EMI shielding properties

of the injection molded samples were compared with those of the compression molded samples. A

Processing Parameters

C1 (°C) C2 (°C) C3 (bar) C4 (mm.sec-1

)

EXP #1 60 215 100 240

EXP #2 60 240 100 240

EXP #3 60 240 100 24

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Carver compression molder (Carver Inc., Wabash, IN) was used to make the samples of randomly

distributed MWCNTs, with the same dimensions as the injection molded samples. The compression

molding process was performed at 210 °C for 10 min under 38 MPa pressure.

Figure 5-1: A schematic view of the designed mold.

Table 5-3: Dimensions of the designed mold.

5.4.3. EMI Shielding Properties Measurements

In order to cover a large range of electrical conductivities (10-15

-10+1

S·cm-1

), three measurement

systems were used to determine the electrical conductivity of the molded samples. For samples with

an electrical conductivity of larger than 10-2 S·cm

-1, the electrical conductivity measurements were

conducted according to the ASTM 257-75 standards using a Loresta GP resistivity meter (MCP-

T610 model, Mitsubishi Chemical Co., Japan) connected with a four-pin probe, which was used so

Parameter Value (mm)

a 22.86

b 10.16

c, d 1

e 2

f 10

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that the effect of contact resistance did not impact the measurements. The inter-pin spacing was 5.0

mm and the pin diameter was 2.0 mm. For an electrical conductivity between 10-2

and 10-5 S·cm

-1, a

Keithley 617 (Keithley instruments, USA) connected to an 804B disk & ring test fixture (Electro-

Tech systems, Inc., USA) was employed. The samples were placed between the elastomeric disk

electrode with 10.0 mm diameter and base copper plate. A conductive rubber was also used to

decrease the contact resistance between the samples and base copper plate. For electrical

conductivities less than 10-5 S·cm

-1, the measurements were performed using a Keithley 6517A

electrometer connected to a Keithley 8009 test fixture (Keithley instruments, USA). The applied

voltage for all the conductivity measurements was 10 V. The samples were rectangular with the

dimensions of 22.86 mm × 10.16 × 2.0 mm. The conductivity measurements were carried out in

directions both parallel to the flow and thickness. For each datum, the conductivity of at least three

specimens was measured.

EMI SE, real electrical permittivity and imaginary electrical permittivity were also found for the

samples used in the conductivity experiments. EMI shielding properties measurements in the X-

band (8.2 – 12.4 GHz) frequency range were carried out in a WR-90 rectangular waveguide using

an Agilent programmable network analyzer (PNA) (Model E8364B). To measure the EMI shielding

properties, the MWCNT/PS samples were placed inside the cross section of the rectangular

waveguide. The S-parameters of each sample were recorded and used to calculate EMI SE and also

real permittivity and imaginary permittivity via the Nicolson-Ross-Weir method [25, 26]. EMI SE is

expressed in dB and is the logarithm of the ratio of the incident power to the transmitted power [7,

21]. Contributions of reflection and absorption to overall EMI SE were also calculated using

relevant incident and transmitted power for each mechanism.

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5.4.4. Morphological Characterization and Raman Spectroscopy

In order to investigate the morphology of the molded nanocomposites, TEM observations were

performed using a Hitachi H-7650. Prior to the TEM observations, the samples were

ultramicrotomed using a diamond knife at room temperature.

In order to obtain detailed information about the alignment of MWCNTs, Raman spectra were

collected from the compression molded and injection molded samples. A Renishaw spectrometer

equipped with an inVia Raman microscope was employed to obtain the Raman spectra. Excitation

was provided by a near-infrared (NIR) laser beam (785 nm) in regular mode. Measurements were

performed at two normal orientations of the laser beam with respect to the flow direction in the

samples. The MWCNT alignment was determined by comparing the Raman spectra obtained from

parallel and perpendicular directions.


5.5.1. Morphological Analysis and Raman Spectroscopy

TEM micrographs of an injection molded sample (EXP #1) and a compression molded sample

of 5.00 wt% MWCNT/PS composite are shown in Figures 5-2(a) and 5-2(b), respectively. As

shown in these images, the MWCNTs are uniformly dispersed as individual tubes in the polymer

matrix without any significant agglomeration, which shows that MWCNTs were well dispersed

during mixing via twin-screw extrusion. It should be mentioned that applying a high shear force in

the injection molding process also contributed to a better dispersion of MWCNTs.

145

Figure 5-2: TEM micrographs of (a) an injection molded sample (EXP #1), and (b) a compression

molded sample. Both are 5.00 wt% MWCNT/PS composite. The white arrow in (a) indicates the

flow direction.

The aligned segments of MWCNTs can be easily seen in Figure 5-2(a), where the white arrow

shows the direction of MWCNT alignment. Due to the curved structure of MWCNTs, some

portions of MWCNTs may be embedded in the PS matrix; as a result, the observable length in

Figure 5-2(a) may not be the entire length of MWCNTs. Possible appearances of cut surfaces in

MWCNT-aligned samples have been illustrated by Pötschke et al. [27]. Figure 5-2(b) shows the

random distribution of MWCNTs in the PS matrix. No distinct direction can be observed for the

alignment of MWCNTs.

The Raman spectroscopy technique was applied to the 5.00 wt% MWCNT/PS composites.

Two significant characteristics in the Raman spectra of the MWCNT/polymer composites are the D

band (disorder band), and the G band (graphite band). The disorder-induced D band, related to sp2

hybridized graphitic structure, is a more responsive band to the MWCNT alignment than G band,

which corresponds to in-plane vibration of the graphitic wall. The DPA/DPE and GPA/GPE

146

parallel/perpendicular to the flow direction were used to determine the degree of MWCNT

alignment [28]. Table 5-4 presents the results from the Raman spectra of the compression molded

samples and injection molded samples. The compression molded samples demonstrated intensity

ratios near one, which proves a random distribution of MWCNTs; whereas, the EXP #1 of the

injection molded samples showed the highest intensity ratios, correlated to the greatest MWCNT

alignment. Greater alignment occurs due to higher levels of applied shear rate on the nanocomposite

melt. According to Table 5-4, the order of the intensity ratios, and consequently MWCNT

alignment, from the highest to the lowest were EXP #1 > EXP #2 > EXP #3 > compression molded

samples. Considering the different morphologies of the injection molded and compression molded

samples and Raman spectroscopy results, partial alignment of MWCNTs in the injection molded

samples is confirmed.

Table 5-4: Raman intensity ratios parallel/perpendicular to the flow direction of the compression

molded and injection molded samples of 5.00 wt% MWCNT/PS composites.

5.5.2. Comparison of Electrical Conductivity and EMI SE of Injection Molded versus Compression

Molded MWCNT/PS Composites

The formation of a conductive network in CPCs can be clarified with the concept of the

electrical percolation threshold [28, 29]. Electrical percolation is the concentration at which the

Raman spectroscopy ratios parallel/perpendicular

DPA/DPE GPA/GPE

Compression Molding 1.01 1.01

EXP #1 1.66 1.51

EXP #2 1.53 1.44

EXP #3 1.35 1.27

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filler particles come into contact with each other and form a continuous conductive pathway in the

composite, which allows the electrical current to pass through the sample.

Figure 5-3(a) shows the percolation curves of the injection molded (parallel to the flow) samples

and compression molded samples. As can be seen in Figure 5-3(a), the injection molded (MWCNT-

aligned) samples showed a lower electrical conductivity and higher percolation threshold than

compression molded (randomly distributed MWCNTs) samples. Considering Figure 5-3(a) and

Raman spectroscopy results, it can be stated that the greater the alignment of MWCNTs, the lower

the electrical conductivity and the higher the percolation threshold of CPCs. As a matter of fact, the

alignment of MWCNTs decreased the likelihood of MWCNTs being connected with each other,

which resulted in a lower electrical conductivity and higher percolation threshold [21, 30].

At high concentrations of MWCNT, increasing MWCNT content resulted in relatively lower

enhancement in the electrical conductivity than the enhancement in electrical conductivity at

MWCNT concentrations around percolation threshold. The constriction resistance at the MWCNT’s

contact spots restricted the increase in electrical conductivity at high MWCNT concentrations [31].

As can be seen in Figure 5-3(a), all the percolation curves reach a plateau at high MWCNT

concentrations with approximately the same electrical conductivity for all the samples. However,

the plateau is reached at different MWCNT concentrations for each sample: compression molded

samples reach a plateau at 5.00 wt%, EXP #3 at 10.0 wt%, EXP #2 at 15.0 wt% and EXP# 1 at 20.0

wt%. These results suggest that the MWCNT networks were well formed in both the injection

molded and compression molded samples at high MWCNT concentrations. It should be mentioned

that the percolation curves of the parallel to the flow and thickness directions showed almost the

148

same trend, however the parallel to the flow electrical conductivities were around one order of

magnitude higher than those in the thickness direction for most of MWCNT concentrations.

Therefore, there must be a better conductive network formation in the direction parallel to the flow

[23, 32].

Figure 5-3: (a) Electrical conductivity and (b) EMI SE for the compression molded and injection

molded samples of the MWCNT/PS composites as a function of MWCNT concentration. The data

related to the electrical conductivity of the injection molded samples were achieved in parallel to

the flow direction. The thickness of all the samples was 2.0 mm.

149

Figure 5-3(b) shows the EMI SE of the compression molded and injection molded samples as a

function of MWCNT concentration. The EMI SE results are the average values over the X-band

frequency range. The EMI SE increased with increase in MWCNT concentration for both the

compression molded and injection molded samples. The EMI SE for the compression molded

samples at 5.00 wt% was 25.4 dB while it increased to more than 63.6 dB at 20.0 wt%. This

increase was mostly due to greater amount of interacting mobile charge carriers at higher MWCNT

concentrations [2, 4]. However, it was interesting to observe that the EMI SE in the injection

molded samples was significantly lower than compression molded samples, particularly at high

MWCNT concentrations. For instance, the injection molded samples made by EXP #1 at 5.00 and

20.0 wt% MWCNT exhibited EMI SE around 15 and 30 dB, respectively, lower than compression

molded samples. Even more interesting was the fact that all the samples had the same volume

resistivity at 20.0 wt% but exhibited significantly different EMI SE. For example, although the

compression molded sample and EXP# 1 sample both had electrical conductivity around 1.0 S·cm-1

at 20.0 wt% MWCNT, the EMI SE was double for the compression molded sample versus the EXP

#1 sample. This discrepancy between the compression molded and injection molded samples

suggests that the compression molded samples had more extensive connected MWCNT network

than the injection molded samples.

Figures 5-4(a) and 5-4(b) show the EMI SE of the compression molded and injection molded

(EXP #1) samples, respectively, at different MWCNT concentrations as a function of

electromagnetic wave frequency. The MWCNT concentrations shown in Figure 5-4 cover low,

medium and high MWCNT loadings. EXPs #2 and #3 in the injection molding process

demonstrated the same trend as EXP #1.

150

The EMI SE for the compression molded samples showed a slight ascending trend with increases

in frequency. For instance, the compression molded samples at 2.00 wt% of MWCNT showed an

EMI SE of around 4.5 dB at 8.2 GHz, which increased to 7.2 dB at 12.4 GHz. The differences

between the EMI SEs at low and high frequencies increased with increases in MWCNT

concentration. The compression molded samples at 20.0 wt% of MWCNT showed an EMI SE of

57.4 dB at 8.2 GHz, which increased to 66.4 dB at 12.4 GHz. For the injection molding process, the

composites showed EMI SE performances that were almost independent of the frequency.

Considering 30 dB as an adequate level of shielding for commercial applications, it can be claimed

that compression molded and injection molded samples at 10.0 and 20.0 wt% of MWCNT,

respectively, satisfy the requirement for commercial EMI shielding applications over the whole X-

band frequency range.

151

Figure 5-4: EMI SE, as a function of electromagnetic wave frequency, of (a) the compression

molded samples and (b) injection molded (EXP #1) samples. The thickness of all the samples was

2.0 mm.

In view of Figure 5-3(b) and Raman spectroscopy results, it can be claimed that the CPCs with

greater MWCNT alignment showed lower EMI SE. Besides, it can be interpreted that greater

MWCNT connectivity in the compression molded samples caused higher EMI SE in the

compression molded samples than injection molded samples. These results are in agreement with

152

researchers who believe that EMI shielding does not require filler connectivity; however, it

increases with filler connectivity [2, 4, 33, 34].

5.5.3. Effects of MWCNT Alignment on Shielding Mechanisms in MWCNT/PS Composites

To investigate effects of MWCMT alignment on EMI shielding more precisely, the contributions

of the reflection and absorption to the overall EMI SE were examined as a function of MWCNT

concentration and alignment (Figures 5-5(a) and 5-5(b)). The difference in the connectivity of the

MWCNTs in the compression molded and injection molded samples is the key to interpret the

reflection and absorption mechanisms.

To shield by reflection, the material must have mobile charge carriers (electrons or holes) to

interact with incoming electromagnetic wave [4]. As shown in Figure 5-5(a), the shielding by

reflection increased with increase in MWCNT concentration, which can be related to higher amount

mobile charge carriers at greater MWCNT concentrations. The shielding by reflection was 2.7 dB at

2.00 wt% of MWCNT, which increased to 7.8 dB at 20.0 wt% of MWCNT. As there is a direct

relationship between electrical conductivity and shielding by reflection in conductive monolithic

materials [6, 35], a higher shielding by reflection was expected in the compression molded CPCs

than injection molded ones. However, as shown in Figure 5-5(a), it is surprising to observe that the

shieldings by reflection of the compression molded and injection molded samples were almost the

same at different MWCNT concentrations. The similar shieldings by reflection in the compression

molded and injection molded samples may be explained by comparable area of the MWCNT

153

surface projection normal to the incoming electromagnetic wave whether the MWCNTs were

aligned or not.

Figure 5-5(b) shows that the shielding by absorption increased with increase in MWCNT

concentration and decrease in MWCNT alignment. Increase in absorption by increasing MWCNT

concentration is a well-established concept, which has been ascribed to higher amount of mobile

charge carriers at higher MWCNT concentrations [2, 4, 5]. According to Figure 5-5(b), unlike the

shielding by reflection, the shielding by absorption was highly sensitive to MWCNT alignment. The

samples made by EXP #1, which had the greatest MWCNT alignment, showed the lowest

absorption; whereas, the compression molded samples demonstrated the highest absorption. These

results suggest that shielding by absorption is related to MWCNT connectivity. Accordingly,

electrical parameters influencing shielding by absorption and related to filler connectivity must be

investigated.

Higher absorption at greater MWCNT concentrations can also be related to higher imaginary

permittivity (Ohmic loss) and higher real permittivity (polarization loss) of the MWCNT/PS

composites [17]. Figures 5-6(a) and 5-6(b) show the real permittivity and imaginary permittivity,

respectively, of the compression molded and injection molded samples as a function of MWCNT

concentration. The absolute values of the permittivities of the compression molded samples shown

in Figure 5-6 are of the same order of magnitude as those reported in previous studies that were also

performed in the X-band [36-39].

154


compression molded and injection molded samples of the MWCNT/PS composites as a function of

MWCNT concentration. The thickness of all the samples was 2.0 mm.

Real permittivity in MWCNT/polymer composites originates from a large number of

nanocapacitors, i.e., MWCNTs acting as electrodes and insulative polymeric layer acting as

dielectric material, and also presence of structural defects (polarization centers) in MWCNTs [40-

43]. Increasing MWCNT concentration led to an increase in both the number of nanocapacitors and

155

polarization centers, leading to higher real permittivity (charge polarization). Additionally,

increasing MWCNT concentration led to a decrease in the thickness of insulative polymeric gaps

between MWCNTs leading to greater electronic polarization of polymeric layer [44]. Therefore,

increasing MWCNT concentration led to greater polarization loss giving rise to shielding by

absorption. Imaginary permittivity of MWCNT/PS composites resulting from Ohmic loss also

contributed significantly to shielding by absorption, where energy is dissipated by movement of

mobile charge carriers along the MWCNTs. Increasing MWCNT concentration resulted in an

increase in number of dissipating mobile charge carriers leading to higher imaginary permittivity

and, consequently, higher shielding by absorption.

As can be observed in Figure 5-6(a), the real permittivity in the compression molded samples

was greater than injection molded samples. The large difference between the real permittivities of

the compression molded and injection molded samples suggests that the polarization of PS matrix

contributed significantly to the real permittivity in the X-band. In narrow insulative gaps between

conductive fillers, very high field strength may build up, which is higher than the macroscopic field

strength by a factor of M (i.e., M is the ratio of the average size of the conducting MWCNT

aggregates to the average gap width) [10, 45, 46]. This high field strength contributes significantly

to the electronic polarization of the polymer matrix. Since the chance of MWCNTs contacting each

other in the compression molded samples was greater, the insulative gaps of the polymer were

thinner, leading to a higher electric field and greater electronic polarization of the PS matrix.

Therefore, the compression molded samples showed greater real permittivity than injection molded

samples. Higher polarization of the PS matrix played an important role in greater polarization loss

and increased shielding by absorption in the compression molded samples.

156

Figure 5-6: (a) Real permittivity and (b) imaginary permittivity for the compression molded and

injection molded samples of the MWCNT/PS composites as a function of MWCNT concentration.

Figure 5-6(b) shows that the imaginary permittivity of the injection molded samples was lower

than that of the compression molded samples and the amount of this difference increased

tremendously with increase in MWCNT concentration. For instance, at 5.00 wt%, the imaginary

permittivities of the compression molded and injection molded (EXP #1) samples were 36 and 5,

respectively, while they increased to 502 and 94, respectively, at 20.0 wt%. The higher imaginary

157

permittivity of the compression molded samples may be related to the greater network formation,

i.e., there was greater MWCNT connectivity in these samples. Therefore, the electrons had a greater

mean free path in which to move according to the direction of electric field in each half cycle and,

consequently, could dissipate more electrical energy [47]. Greater electrons’ mean free path at

lower MWCNT alignments can be related to lower thickness of insulative gaps between MWCNTs,

i.e., greater MWCNT network formation, leading to larger conduction current via mechanisms of

conduction, hopping and tunneling. The greater electrical energy loss by free electrons in the

compression molded samples, due to greater electrons’ mean free path, contributed to higher

shielding by absorption in these samples.

5.6. Conclusions

Comparing the EMI shielding properties of the injection molded samples, where the conductive

filler is aligned, versus compression molded samples, which have randomly distributed conductive

filler, of MWCNT/PS composites showed that MWCNT alignment had an adverse effect on EMI

shielding properties. Inferior EMI shielding properties, i.e., properties such as EMI SE, electrical

conductivity and real and imaginary permittivities of the injection molded samples relative to the

compression molded samples were related to MWCNT alignment which led to poorer MWCNT

network formation.

The injection molded samples showed lower electrical conductivity and higher percolation

threshold than compression molded samples due to MWCNT alignment. The lower real permittivity

for the injection molded samples was ascribed to lower electric field in insulative gaps between

158

MWCNTs, due to lower chance of MWCNT connectivity, resulting in lower electronic polarization

of polymeric layer. The lower imaginary permittivity of the injection molded samples was also

attributed to inferior MWCNT network formation, where the smaller mean free paths of the

conduction electrons led to decreased energy dissipation. Lower EMI SE for the injection molded

sample than the compression molded samples was related to lower electrical conductivity, real

permittivity (polarization loss) and imaginary permittivity (Ohmic loss) leading to lower

electromagnetic wave energy dissipation. Comparison of the EMI shielding properties of

composites with different states of conductive network formation verified that EMI shielding does

not require filler connectivity; however it significantly increases with filler connectivity.

Since the electrical conductivity, EMI SE, real permittivity and imaginary permittivity of the

compression molded samples were greater than those of the injection molded samples, it can be

concluded that designing a mold for injection molding that achieves a random MWCNT distribution

is crucial in order to attain high EMI shielding properties.

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Chapter 6

An Innovative Method to Reduce the Energy Loss of Conductive Filler/Polymer

Composites for Charge Storage Applications*


This article introduces conductive filler alignment, induced by injection molding process, as an

innovative technique to improve the dielectric properties of MWCNT/PS composites for charge

storage applications. The information obtained from the experimental design of 5.00 wt%

MWCNT/PS composites in chapter 3 were used to select three processing conditions, with

maximum possible variation in MWCNT alignment, to make MWCNT-aligned composites at

different MWCNT concentrations. Accordingly, EXPs #11, 12 and 14 in the experimental design

correspond to EXPs # 2, 3 and 1 in this article, respectively. In order to prove the positive impact of

MWCNT alignment on dielectric properties, the dielectric properties of the injection molded

composites, where MWCNTs were aligned, were compared with those of the compression molded

composites, where MWCNTs were randomly distributed. The results demonstrated that MWCNT

alignment reduced the dissipation factor through deteriorating the conductive network formation. It

is notable to mention that the findings regarding the positive influence of MWCNT alignment,

induced by injection molding machine as a mass production setup, on the dielectric properties of

MWCNT/PS composites is of great industrial significance.

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An Innovative Method to Reduce the Energy Loss of Conductive Filler/Polymer

Composites for Charge Storage Applications

Mohammad Arjmanda, Mehdi Mahmoodi

b, Simon Park

b, Uttandaraman Sundararaj

a

a Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Canada

b Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Canada

6.2. Abstract

In this study, we present conductive filler alignment as a novel approach to reduce the

dissipation factor of conductive filler/polymer composites and to widen the typically narrow

concentration window near the percolation threshold, which is used to tune the dielectric properties,

i.e., real permittivity and imaginary permittivity. The effects of multi-walled carbon nanotube

(MWCNT) alignment on the dielectric properties for MWCNT/polystyrene composites in the X-

band (8.2 to 12.4 GHz) were investigated by comparing the dielectric properties of injection molded

samples, where MWCNTs were aligned, versus compression molded samples, where MWCNTs

were randomly distributed. Raman spectroscopy technique was employed to verify partial

alignment of MWCNTs in the injection molded samples. The compression molded samples showed

an insulator-conductor transition window at 0.50 - 2.00 wt% of MWCNT, whereas the injection

molded samples showed a significantly wider transition window at 3.50 - 10.00 wt% of MWCNT.

Broader insulator-conductor transition window reduces challenges and risks in manipulating

conductive filler/polymer composites around the percolation threshold to regulate the dielectric

properties. Moreover, it was observed that MWCNT alignment improved the dielectric properties

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by reducing the dissipation factor. For instance, at MWCNT concentrations of 0.50 and 2.00 wt%,

the compression molded samples showed dissipation factors of 0.06 and 0.59, respectively, while

the injection molded samples presented the dissipation factors considerably lower and equal to 0.01

and 0.18, respectively. This study shows that injection molding process, as an industrial technique,

can be employed to improve significantly the dielectric properties of conductive filler/polymer

composites for charge storage applications.

6.3. Introduction

Consumers are demanding lighter weight and smaller electronic devices in today’s marketplace;

therefore, printed circuit board (PCB) space is becoming a scarce resource. Accordingly, industry is

now moving toward replacing large surface mounted capacitors with miniature capacitors

embedded into PCBs [1,2]. The material requirements for embedded capacitors include high real

permittivity, low leakage current (imaginary permittivity) and process compatibility with PCBs.

Recently, conductive filler/polymer composites (CPCs) have been proposed as candidates for

embedded capacitors, due to their high real permittivity, low cost, light weight and process

compatibility with PCBs [3-5]. According to the percolation theory, a high real permittivity with a

low leakage current in CPCs can only be achieved at filler loadings very close to the percolation

threshold [6]. This poses a challenge to use CPCs as charge storage materials, because of the

typically narrow insulator-conductor transition window around the percolation threshold. Two

strategies are usually used to avoid the direct contact between conductive fillers and thereby

obstruct the insulator-conductor transition: (1) covering the surface of conductive fillers with an

insulative layer [3,7]; and, (2) introducing secondary particles as insulating barriers between

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conductive fillers [8,9]. Both of these methods require additional processing steps to obtain the final

composite and may also adversely affect the real permittivity.

Herein we present conductive filler alignment as a novel approach to reduce imaginary

permittivity and to hinder the sharp insulator-conductor transition in CPCs. In this study, a multi-

walled carbon nanotube/polystyrene (MWCNT/PS) composite, as a typical CPC, was employed to

investigate the effects of conductive filler alignment on dielectric properties, i.e., real permittivity

and imaginary permittivity. MWCNTs were chosen as the conductive fillers, due to their unique

electronic structure and growing industrial usage. The alignment of MWCNTs was induced by

applying a high shear/drag force using an injection molding machine. The results showed that the

MWCNT alignment led to a tremendous decrease in the dissipation factor of the molded samples

arising from lower probability of the MWCNTs neighboring or contacting each other. The

alignment of the MWCNTs also impeded the sharp increase in the imaginary permittivity near the

percolation threshold. This feature of the MWCNT-aligned samples broadens the narrow filler

concentration window near the percolation threshold in CPCs, which is used to adjust the dielectric

properties.

6.4. Material and Methods

6.4.1. Materials

A masterbatch of 20.0 wt% MWCNT in PS was obtained from Hyperion Catalysis International,

Cambridge, MA, USA. According to the supplier, the MWCNTs were vapor grown and typically

had an outer diameter of 10-15 nm wrapped around a hollow core with a diameter of 5 nm. The

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lengths ranged between 1 and 10 µm, while their density was approximately 1.75 g/cm3. The

masterbatch was diluted with a pure PS (Styron® 610), with a density of 1.06 g/cm

3, kindly

provided by Americas Styrenics LLC, in order to prepare nanocomposite samples with different

MWCNT concentrations. Prior to mixing, all the materials were dried at 50 °C for at least 4 hr

under vacuum. The composites with different concentrations of MWCNT were prepared employing

a 25 mm Coperion ZSK co-rotating intermeshing twin-screw extruder operated at a barrel

temperature, extruder speed and residence time of 200 °C, 150 rpm and 2 min, respectively.

Considering the densities of neat PS and MWCNTs, the concentrations of prepared nanocomposites

in terms of weight percent and volume percent are presented in Table 6-1.


volume percent.

6.4.2. Composite Molding

Our previous investigations showed that there is a direct relationship between MWCNT

alignment and volume resistivity [10,11]. This relationship and also the inverse relationship

between volume resistivity and imaginary permittivity were the inspirations for the investigation of

the effects of MWCNT alignment on the dielectric properties. Our previous studies showed that the

melt temperature followed by the injection velocity had the greatest impact on the MWCNT

alignment of the injection molded MWCNT/PS nanocomposites [12]. On the other hand, the mold

temperature and injection/holding pressure did not significantly affect the MWCNT alignment.



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Given the remarkable effects of the melt temperature and injection velocity on the MWCNT

alignment in the injection molded MWCNT/PS nanocomposites, the injection molding process was

carried out at the lowest possible melt temperature, i.e., 215 °C and the highest possible injection

velocity, i.e., 240 mm.sec-1

to obtain the MWCNT/PS nanocomposites with the greatest MWCNT

alignment. The mold temperature and injection/holding pressure employed were 60 °C and 100 bar,

respectively. The injection molded samples were used to investigate the effect of MWCNT

alignment on the dielectric properties.

An injection molding machine (Boy 12A) was used to inject the MWCNT/PS nanocomposite

melt into a rectangular cavity. The cavity was fed with an edge gate and had dimensions of 22.86 ×

10.16 × 2.0 mm. A detailed description of the designed mold and injection molding machine can be

found in our previous studies [11,12]. To achieve a more comprehensive picture of the effects of

MWCNT alignment on the dielectric properties, the dielectric properties of the aligned injection

molded samples were compared with those of the compression molded samples, where MWCNTs

were randomly distributed. A Carver compression molder (Carver Inc., Wabash, IN) was employed

to fabricate the compression molded samples with the same dimensions as the injection molded

samples. The compression molding process was carried out at 210 °C for 10 min under 38 MPa

pressure.


In order to investigate the morphology of the compression and injection molded samples,

transmission electron microscopy (TEM) was employed. The TEM analysis of the nanocomposites

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was carried out on ultramicrotomed sample sections using a Tecnai TF20 G2 FEG-TEM (FEI,

Hillsboro, Oregon, USA) at a 200 kV acceleration voltage with the standard single-tilt holder. The

samples were ultramicrotomed to sections of ~ 70 nm at room temperature using a Leica EM UC6.

The images were captured by a Gatan UltraScan 4000 CCD (Gatan, Pleasanton, California, USA) at

2048x2048 pixels.

6.4.4. Determination of Carbon Nanotube Length Distribution

The investigations of carbon nanotube length distribution using a TEM procedure was developed

by Krause et al. [13].The evaluation of nanotube length distribution was conducted for the as-

extruded, compression molded and injection molded composites containing 2.00 and 10.0 wt% of

MWCNT to examine the effects of both the processing and the MWCNT concentration (viscosity)

on length distribution.

In order to assess the nanotube length distribution in the composites, chloroform was used to

dissolve the PS matrix at room temperature for 4 hr without any additional treatment, until only

MWCNTs remained. All dispersions were treated with a low energy ultrasonic equipment for 3

min, and then one drop of dispersion was placed on a copper grid and dried at air. A transmission

electron microscope was used to take images of the collected MWCNTs. Measurement of the length

of the MWCNTs was carried out for 500 individual MWCNTs using the ImageJ software. In order

to measure the length of very long nanotubes, several images were stiched together.

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Raman spectroscopy was employed to verify the alignment of MWCNTs in the injection molded

samples. A Renishaw spectrometer equipped with an inVia Raman microscope was used to obtain

the Raman spectra from the molded samples. The samples were excited by a near-infrared (NIR)

laser beam in regular mode. The Raman intensity measurements were performed at two normal

orientations of the laser beam with respect to the flow direction, i.e., parallel and perpendicular, to

obtain information about the MWCNT alignment.

6.4.6. Electrical and Dielectric Properties Measurements

The in-flow volume resistivity measurements were performed using two different setups. For the

samples with a volume resistivity of less than 104 Ω·cm, the measurements were conducted

according to the ASTM 257-75 standards, using a Loresta GP resistivity meter (MCP-T610 model,

Mitsubishi Chemical Co., Japan) connected with a four-pin probe. For a volume resistivity of more

than 104 Ω·cm, the measurements were performed using a Hiresta-UP resistivity meter (MCP-

HT450 model, Mitsubishi Chemical Co., Japan) connected with a piece of URS probe.

The thickness volume resistivity measurements were conducted employing two different

systems. For the samples with a volume resistivity of less than 104 Ω·cm, the volume resistivity

measurements were conducted using a Keithley 2400 sourcemeter, while for a volume resistivity

more than 104 Ω·cm, a Keithley 6517A electrometer was used. Both types of Keithleys were

connected to a Keithley 8009 test fixture (Keithley Instruments, USA). The applied voltage for all

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the resistivity measurements was 10 V. For each datum, the resistivity of at least three specimens

was measured.

To evaluate the potential of CPCs as charge storage materials for high-frequency range

applications, it is essential to characterize the high-frequency dielectric properties of CPCs.

Accordingly, the dielectric properties in the X-band (8.2 to 12.4 GHz) frequency range were

investigated in this study. The dielectric properties in the X-band are important for many military

and commercial applications, e.g., Doppler, weather radars and TV picture transmitters [14]. The

complex permittivity measurements in the X-band were carried out in a WR-90 rectangular

waveguide using an Agilent programmable network analyzer (Model E8364B). The S-parameters of

each sample were recorded one at a time and used to calculate the complex permittivity with the

Nicolson-Ross-Weir method [15,16]. For each datum, the S-parameters of at least three specimens

were measured. It should be mentioned that in the dielectric spectroscopy, the electromagnetic wave

interacted with the samples in the thickness direction; therefore, all the dielectric properties reported

in this article belong to the thickness direction.


6.5.1. Morphological Analysis and Raman Spectroscopy

TEM micrographs of an injection molded sample and a compression molded sample of 5.00 wt%

MWCNT/PS composite are shown in Figures 6-1(a) and 6-1(b), respectively. In these images,

individual MWCNTs are clearly observable without any significant agglomeration, indicating that

the MWCNTs were disentangled and dispersed well during mixing via twin-screw extrusion.

172

The aligned segments of MWCNTs can be easily seen in Figure 6-1(a), where the white arrow

shows the direction of MWCNT alignment. Due to the curved structure of MWCNTs, the

MWCNTs were not ideally aligned in the flow direction; however, Figure 6-1(a) confirms partial

alignment of MWCNTs in the injection molded samples. Figure 6-1(b) shows that MWCNTs were

randomly distributed in the compression molded samples, and no distinct direction can be observed

for the alignment of MWCNTs.

Figure 6-1: TEM micrographs of (a) an injection molded sample, and (b) a compression molded

sample. Both are 5.00 wt% MWCNT/PS composite. The white arrow in (a) indicates the flow

direction.

In order to obtain more detailed information about the alignment of MWCNTs, a Raman

spectroscopy technique was employed. The Raman spectra of MWCNT/polymer composites

provide two important features: the D band (disorder band) and G band (graphite band). The D

band, correlating to disorder in the sp2 hybridized graphitic structure, is more responsive to the

alignment of MWCNTs than the G band, which corresponds to the in-plane vibration of the

graphitic wall [17] Higher intensity ratios of and (parallel/perpendicular to the flow

direction) correspond to higher MWCNT alignment. The injection molded samples showed

173

and ratios equal to 1.66 and 1.51, respectively, whereas the compression molded samples

exhibited and of 1.01 and 1.01, respectively. From the Raman spectroscopy results, it

can be claimed that the MWCNTs were randomly distributed in the compression molded samples,

while they were partially aligned in the injection molded samples.

6.5.2. The Effects of Processing and Molding on MWCNT Length Distribution

Figure 6-2 presents the length distribution of MWCNTs for the as-extruded, injection molded

and compression molded MWCNT/PS composites with 2.00 wt% MWCNT loading. The MWCNT

length distribution for the as-extruded composites ranged from less than 100 nm to 2400 nm.

Considering the length distribution of MWCNTs in the masterbatch, i.e. 1-10 µm, it is obvious that

twin-screw extrusion significantly shortened the length of MWCNTs by applying a high shear rate.

Investigating the MWCNT length distribution of the composites showed that the as-extruded,

compression molded and injection molded composites presented average MWCNT lengths of 417,

411 and 363 nm, respectively. All the composites showed standard deviations equal to 230 nm.

These results show that the compression molding process did not affect the MWCNT length while

the injection molding process led to a 12% reduction in the MWCNT length. This reduction can be

attributed to the shear rate applied in the injection molding process.

To investigate the effect of MWCNT concentration, which correlates to melt viscosity, on the

MWCNT length distribution, MWCNT length distributions of 2.00 and 10.0 wt% MWCNT/PS

composites were compared with each other. It was observed that 10.0 wt% MWCNT/PS composites

174

showed a very similar length distribution to that of 2.00 wt% MWCNT/PS composites, indicating

that MWCNT concentration did not impact the MWCNT length distribution.

Figure 6-2: Effects of molding on length distribution of MWCNTs in 2.00 wt% MWCNT/PS

composites.

6.5.3. The Effects of MWCNT Alignment and Length on the Dielectric Properties

In addition to a high dielectric permittivity, CPCs used as capacitors must show a low leakage

current. In general, the leakage current of a CPC has an inverse relationship with its volume

resistivity; therefore, investigating the effect of the MWCNT alignment on the volume resistivity

will aid us in comprehending the effect of the MWCNT alignment on the leakage current. Figure 6-

3 depicts the volume resistivity of the compression molded and injection molded samples in the

flow and thickness directions as a function of MWCNT concentration. Despite the MWCNT

alignment, the volume resistivity of the injection molded samples showed very similar trends in

175

both the in-flow and thickness directions. This fact can be related to comparable MWCNT network

formation in both directions, arising from the curved structure of the MWCNTs. For both injection

molded and compression molded samples, the volume resistivity showed a steep decline at a

particular concentration (percolation threshold) and a decaying trend at higher MWCNT

concentrations which can be ascribed to the formation of additional conductive networks in the

composites.

As shown in Figure 6-3, the volume resistivity and percolation threshold in the injection molded

samples were higher than those in the compression molded samples. The percolation threshold in

the compression molded samples obtained from the percolation theory was 0.70 wt%; however, it

was interesting to observe that the percolation threshold in the injection molded samples was about

six times greater than the percolation threshold in the compression molded samples. The higher

volume resistivity and percolation threshold in the injection molded samples can be attributed to the

lower probability of MWCNTs neighboring or contacting each other due to MWCNT alignment

[10,18]. Lower aspect ratio of the MWCNTs in the injection molded samples can also be considered

as another reason for higher volume resistivity of the injection molded samples. Other studies

showed that decrease in MWCNT aspect ratio can lead to lower conductivity and higher percolation

threshold, due to significant decrease in chance of MWCNTs contacting each other [19,20].

Another important characteristic depicted in Figure 6-3 is that the steep decline in the volume

resistivity of the injection molded samples around the percolation threshold was muted in

comparison to that of the compression molded samples. The logarithm of the volume resistivity for

the compression molded samples at 0.50, 1.00 and 2.00 wt% of MWCNT are 13.3, 8.7 and 5.5,

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respectively, showing an insulator-conductor transition at the concentration window of 0.50 - 2.00

wt%. The logarithm of the volume resistivity for the injection molded samples at the MWCNT

concentrations of 3.50, 5.00 and 10.00 wt% are 13.0, 10.2 and 3.6, respectively, roughly indicating

an insulator-conductor transition at the concentration window of 3.50 - 10.0 wt%. The broader

concentration window of the insulator-conductor transition in the injection molded samples can be

attributed to MWCNT alignment and a lower MWCNT aspect ratio in the injection molded

samples. This provides a significant advantage for aligned samples for use as capacitors.

Figure 6-3: Volume resistivity for the compression molded and injection molded samples of the

MWCNT/PS composites as a function of MWCNT concentration.

As mentioned previously, a high real permittivity with a low leakage current in CPCs can only

be achieved at filler loadings very close to the percolation threshold. The increased real permittivity

observed in CPCs near the percolation threshold results from the formation of a large number of

nanocapacitors, i.e., conducting clusters isolated by thin layers of polymer [14]. These

nanocapacitors enable CPCs to store large amount of charges. The insulator-conductor transition

177

that occurs in CPCs at the percolation threshold leads to a drastic variation in the volume resistivity

and imaginary permittivity; thereby it prohibits using CPCs as charge storage materials above the

percolation threshold. Accordingly, there is a very narrow concentration window near the

percolation threshold for high aspect ratio fillers, such as MWCNTs, to adjust the dielectric

properties. In contrast, for samples with significant MWCNT alignment, there is a moderate

descending trend of the volume resistivity around the percolation threshold; thus it can be claimed

that the MWCNT alignment can provide a wider concentration window around the percolation

threshold to regulate the dielectric properties.

Figures 6-4(a) and 6-4(b) show the imaginary and real permittivities, respectively, of the

compression molded and injection molded samples as a function of MWCNT concentration in the

frequency range of the X-band. The absolute values of the complex permittivities of the

compression molded samples, shown in Figure 6-4, are of the same order of magnitude as those

reported previously in the X-band [21, 22]. As can be observed in Figure 6-4(a), the imaginary

permittivity increased with increase in the MWCNT concentration for both types of samples. In

general, the imaginary permittivity of CPCs can result from the polarization loss, e.g., distortional

and interfacial, and/or Ohmic loss. Increase in the MWCNT concentration is equivalent to an

increase in the amount of mobile charge carriers (Ohmic loss) and the number of nanocapacitors

(polarization loss), both of which can account for an enhancement in the imaginary permittivity.

Figure 6-4(a), however, shows that the imaginary permittivities of the injection molded samples

were significantly lower than those of the compression molded samples. The imaginary

permittivities for the compression molded samples at the MWCNT concentrations of 0.50, 1.00 and

178

2.00 wt% (compression molding transition window) were 0.21, 1.16 and 6.14, respectively;

whereas, the imaginary permittivities for the injection molded samples at these concentrations were

significantly lower and equal to 0.02, 0.12 and 0.35, respectively. Lower imaginary permittivity of

the injection molded samples relative to the compression molded samples can be related to inferior

network formation arising from MWCNT alignment and lower MWCNT aspect ratio.

The differences between the imaginary permittivities of the compression molded and injection

molded samples were even greater at higher MWCNT concentrations. The compression molded

samples at MWCNT concentrations of 3.50, 5.00 and 10.00 wt% (the injection molding transition

window) showed the imaginary permittivities equal to 17.52, 36.24 and 189.85, respectively, while

the injection molded samples showed the imaginary permittivities equal to 1.48, 5.01 and 42.63,

respectively. By increasing the MWCNT concentration, the imaginary permittivities of the

compression molded samples grew more than those of the injection molded samples; therefore, it

can be claimed that the movement scales of the electrons in each half cycle of the alternating field

in the compression molded samples, because of the greater network formation, must have grown

considerably more than those of the injection molded samples. This is what led to a very large

difference between the imaginary permittivities for the two types of samples at high MWCNT

concentrations. Moreover, the higher applied field between the conductive fillers in the compression

molded samples provided more chances for the electrons to pass through the polymer layer in the

form of conduction current. This fact originated from higher probability of the conductive fillers

neighboring each other and thus lower thickness of the insulative gaps. This resulted in more energy

loss for the compression molded samples.

179

Figure 6-4: (a) Imaginary permittivity and (b) real permittivity, as a function of MWCNT

concentration, for the compression molded and injection molded samples of the MWCNT/PS

composites in the X-band.

Figure 6-4(b) shows that the real permittivity increased with increases in the MWCNT

concentration. The enhancement of the real permittivity with an increased MWCNT concentration

is well-established, and is attributed to an increase in number of nanocapacitors and a decrease in

180

the thickness of insulative polymer gaps (nanodielectrics), both of which contributed to greater

charge polarization. Moreover, it is believed that the real permittivity of MWCNT/polymer

composites is influenced by the polarization within the MWCNTs, and this also contributes to the

greater real permittivity at higher MWCNT concentrations [2,14].

As presented in Figure 6-4(b), it was surprising to observe that the MWCNT alignment had an

adverse influence on the real permittivity. At MWCNT concentrations of 0.50, 1.00 and 2.00 wt%

(the compression molding transition window), the compression molded samples showed the real

permittivities equal to 3.58 and 5.06 and 10.37, respectively, while the real permittivities of the

injection molded samples were 3.21, 3.70 and 5.24, respectively. At the MWCNT concentrations of

3.50, 5.00 and 10.00 wt% (the injection molding transition window), the compression molded

samples showed the real permittivities equal to 15.20, 21.25 and 41.30, respectively; whereas the

injection molded samples exhibited the real permittivities equal to 8.22, 12.29, and 15.52,

respectively. The difference between the real permittivities of the compression molded and injection

molded samples can be ascribed to the greater probability that MWCNTs are in close proximity to

each other in the compression molded samples. In the narrow insulative gaps between the

conductive fillers, there may be a buildup of very high field strength, which is higher than the

macroscopic field strength by a factor of M (i.e., the ratio of the average size of the conducting

MWCNT aggregates to the average gaps width) [23, 24]. This high field strength significantly

contributed to the electronic polarization of the PS matrix. In the compression molded samples, the

insulative gaps of the polymer were thinner leading to a higher applied field and greater electronic

polarization of the PS matrix. Therefore, the compression molded samples showed greater real

permittivity than the injection molded samples.

181

Chin et al. [25] measured the dielectric properties of MWCNTs in three distinct arrangements

with respect to incident electromagnetic wave, namely parallel, perpendicular and random

distributions. Their results showed that dielectric properties were very high when the

electromagnetic wave oscillated along the axis of the nanotubes and dropped significantly when it

oscillated normal to the axis of MWCNTs. Random distribution of MWCNTs showed an

intermediate value due to the combination of vertical and horizontal arrangements of MWCNTs

from the electromagnetic wave. Higher dielectric properties in the longitudinal direction were

related to field induced intra-band transition.

The data presented in this article are in a very good agreement with the data reported by Chin et

al. As verified by the TEM images, the MWCNTs in the injection molded samples showed mostly

perpendicular arrangements with respect to the incident electromagnetic wave. However, the

compression molded samples, due to the random distribution of MWCNTs, showed a combination

of vertical and horizontal arrangements of MWCNTs. Therefore, the inferior dielectric properties of

the injection molded samples, relative to the compression molded samples, can also be justified

considering different MWCNT arrangements.

MWCNT alignment reduced both the real permittivity and imaginary permittivity; therefore, it is

necessary to evaluate the overall impact of MWCNT alignment on the dielectric properties. Hence,

the dissipation factors (imaginary permittivity/real permittivity) of the compression molded and

injection molded samples at different MWCNT concentrations were compared with each other. As

can be observed in Figure 6-5, the MWCNT alignment decreased the dissipation factors at all the

MWCNT concentrations, demonstrating its positive effect on the dielectric properties. For instance,

182

at the MWCNT concentrations of 0.50, 1.00 and 2.00 wt%, the dissipation factors of the

compression molded samples were 0.06, 0.23 and 0.59, respectively, while the injection molded

samples presented the dissipation factors significantly lower and equal to 0.01, 0.03 and 0.07,

respectively. These results prove that the positive effect of the MWCNT alignment on reducing the

dissipative energy dominated its adverse effect on decreasing the capacitive energy.

Figure 6-5: Dissipation factors for the compression molded and injection molded samples of the

MWCNT/PS composites as a function of MWCNT concentration in the X-band.

6.6. Conclusions

In conclusion, it was shown MWCNT alignment, induced by an injection molding machine, in

the MWCNT/PS composites positively influenced the dielectric properties. MWCNT alignment

widened the typically narrow concentration window near the percolation threshold, which is used to

tune the dielectric properties, thereby reducing challenges and risks in manipulating CPCs as charge

storage materials. It was also shown that the MWCNT alignment reduced both the real permittivity

183

and imaginary permittivity; nonetheless, the positive effect of the MWCNT alignment on reducing

the imaginary permittivity overshadowed its negative effect of reducing the real permittivity. The

positive impact of MWCNT alignment on the dielectric properties presented in this article is

industrially significant because injection molding is one of the most common fabrication methods

for polymer nanocomposites and it can be used to control and tune dielectric properties.

6.7. References

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Kim JB, Yi JW, and Nam JE. Dielectric polymer matrix composite films of CNT coated

with anatase TiO(2). Thin Solid Films 2011; 519: 5050-5.

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Lei YJ, Zhao R, Zhan YQ, Meng FB, Zhong JC, Yang XL, and Liu XB. Generation of

multiwalled carbon nanotubes from iron-phthalocyanine polymer and their novel dielectric

properties. Chem Phys Lett 2010; 496: 139-42.

[5]

Xu JW, Wong M, and Wong CP. Super high dielectric constant carbon black-filled polymer

composites as integral capacitor dielectrics. in Proc. of ECTC. Las Vegas, USA, 2004, pp.

536-41.

[6]

Dang ZM, Yao SH, Yuan JK, and Bai JB. Tailored Dielectric Properties based on

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Nanocomposites. J Phys Chem C 2010; 114: 13204-9.

[7]

Czerw R, Guo ZX, Ajayan PM, Sun YP, and Carroll DL. Organization of polymers onto

carbon nanotubes: A route to nanoscale assembly. Nano Lett 2001; 1: 423-7.

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Yao SH, Yuan JK, Dang ZM, and Bai JB. High dielectric performance of three-component

nanocomposites induced by a synergetic effect. Mater Lett 2010; 64: 2682-4.

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Shen Y, Lin YH, Li M, and Nan CW. High dielectric performance of polymer composite

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Mahmoodi M, Arjmand M, Sundararaj U, and Park S. The electrical conductivity and


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[13] Krause B, Villmow T, Boldt R, Mende M, Petzold G, Potschke P. Influence of dry grinding

in a ball mill on the length of multiwalled carbon nanotubes and their dispersion and

percolation behavior in melt mixed polycarbonate composites. Compos Sci Tech 2011; 71:

1145-53.

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Jiang MJ, Dang ZM, Bozlar M, Miomandre F, and Bai JB. Broad-frequency dielectric

behaviors in multiwalled carbon nanotube/rubber nanocomposites. J Appl Phys 2009; 106:

084902-6.

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Nicolson AM and Ross GF. Measurement of intrinsic properties of materials by time-

domain techniques. IEEE Trans Instrum Meas 1970; IM19: 377-82.

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Weir WB. Automatic measurement of complex dielectric-constant and permeability at

microwave-frequencies. Proc IEEE 1974; 62: 33-6.

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Abbasi S, Carreau PJ, and Derdouri A. Flow induced orientation of multiwalled carbon


properties. Polymer 2010; 51: 922-35.

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Behnam A, Guo J, and Ural A. Effects of nanotube alignment and measurement direction on

percolation resistivity in single-walled carbon nanotube films. J Appl Phys 2007; 102:

044313-7.

[19] Li J, Ma PC, Chow WS, To CK, Tang BZ, Kim J-K. Correlations between percolation

threshold, dispersion state, and aspect ratio of carbon nanotubes. Adv Funct Mater 2007; 17:

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[20] Kim D, Yun Y, Bak H, Cho S, Jin H-J. Aspect ratio control of acid modified multiwalled

carbon nanotubes. Current Appl Phys 2010; 10: 1046-52.

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Watts PCP, Ponnampalam DR, Hsu WK, Barnes A, and Chambers B. The complex

permittivity of multi-walled carbon nanotube-polystyrene composite films in X-band. Chem

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[22]

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and complex permittivity and permeability of Fe encapsulated within carbon nanotubes. Adv

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*Submitted to Polymer Engineering and Science

186

Chapter 7

Broadband Dielectric Properties of Multi-walled Carbon Nanotube/Polystyrene

Composites*


This paper is oriented to study the dielectric properties of MWCNT/polymer composites over the

broadband frequency range, i.e., 10-1

– 106 Hz. The dielectric properties inspected in this article

include real permittivity, imaginary permittivity and AC conductivity, which are analyzed in both

insulative and conductive regions over the whole frequency range. The broadband dielectric

properties presented in this article are of great significance from two aspects:

(1) This article can be used as an introductory section to understand the mechanisms behind

the broadband dielectric properties of CPCs. In other words, this article provides the

readers with general information about the dielectric spectroscopy of CPCs and helps the

researchers to design new morphologies for desired dielectric properties. For instance, the

innovative technique presented in chapter 8 to obtain enhanced broadband dielectric

properties was designed according to the information obtained in this article.

(2) As EMI shielding properties are linked to dielectric properties, obtaining the broadband

dielectric properties can provide the researchers with a notable insight to predict the

broadband EMI shielding properties of CPCs.

187

Broadband Dielectric Properties of Multi-walled Carbon Nanotube/Polystyrene

Composites

Mohammad Arjmand, Uttandaraman Sundararaj

Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Canada

7.2. Abstract

This study investigates the dielectric properties of multi-walled carbon nanotube

(MWCNT)/polystyrene composites over the broadband frequency range, i.e., 10-1 – 10

6 Hz. The

results showed that the real permittivity and imaginary permittivity increased remarkably with

increased MWCNT concentration. For instance, at 100 Hz, the real permittivity and imaginary

permittivity of the pristine PS was 2.71 and 0.01, respectively, which increased to 5.22×104 and

3.28×107 at 3.50 wt%, respectively. The increase of the real permittivity was related to the

formation of a large number of nanocapacitor structures, i.e., MWCNTs as nanoelectrodes and

polymer matrix as dielectric material, i.e., interfacial polarization. The increase in the imaginary

permittivity with MWCNT loading was attributed greater number of dissipating charges,

enhanced conductive network formation and boosted polarization loss arising from interfacial

polarization. It was also observed that the real and imaginary permittivities were frequency-

independent in the insulative region, whereas they decreased drastically with frequency in the

conductive region. The descending trend of real permittivity with frequency in the conductive

region was related to charge polarization relaxation; whereas, the reduction of imaginary

permittivity with frequency was attributed to lower Ohmic loss and polarization loss.

188

7.3. Introduction

Driven by the ever-growing demand for versatile microelectronics with increased

functionality, high performance and cost-effectiveness, the new and distinctive solution of

system-in-package (SiP) has been proposed to meet these requirements [1]. SiP is an assembly of

several types of chips, such as logic, memory and passive, in a package that performs as a unique

system [2-4].

In a typical SiP, discrete passives outnumber the active integrated circuits by several times

and occupy more than 70% of the area of printed circuit boards (PCBs) [3]. Among the passive

components, capacitors dominate in terms of numbers and occupied surface areas; therefore,

capacitors have become the major challenge in the development and miniaturization of SiPs.

Embedded capacitors have, thus, been introduced as a breakthrough in the size reduction and

performance enhancement of SiPs. Embedded capacitors have some other advantages over

currently used surface-mounted capacitors, such as decreased number of discrete capacitors,

decreased number of solder joints, and improved design options [4].

Polymers filled with ferroelectric particles have drawn great interest as embedded capacitors

due to inherent advantages, including process compatibility with PCBs, mechanical flexibility,

high adhesion strength and ability to be molded [5-9]. However, the current ferroelectric-

polymer composites fall significantly short of the growing requirements for advanced

applications. In order to achieve a satisfactory real permittivity, a large amount of ferroelectric

filler is required, which results in the reduction of adhesion strength and mechanical properties

[10, 11]. This poses challenges, as well as opportunities, for the development of novel embedded

capacitors. Accordingly, conductive filler/polymer composites (CPCs) have been proposed as

189

alternatives to address the drawbacks of ferroelectric/polymer composites [12]. High real

permittivity in CPCs is related to the formation of a large number of nanocapacitors, i.e.,

conductive nanofiller as nanoelectrode and polymer matrix as nanodielectric [13].

Different conductive fillers, such as carbon black, gold, silver and nickel nanoparticles, and

more recently carbon nanotubes (CNTs), have been used to fabricate CPCs for charge storage

applications [14-18]. Among the various conductive fillers, CNTs have been envisioned as

revolutionary conductive fillers for charge storage applications, due to their large surface area

and excellent electrical, thermal and mechanical properties. These fascinating properties are

great stimulation to inspect the dielectric properties of MWCNT/polymer composites for charge

storage applications. Furthermore, obtaining the broadband dielectric properties can provide the

researchers with a notable insight to predict broadband EMI shielding properties of CPCs [19].

Accordingly, this study is devoted to investigating the broadband dielectric properties of

MWCNT/polystyrene (PS) composites and detailing the mechanisms behind. Moreover, the

results presented in this article shed light onto the relationships between conductive network

formation, DC conductivity, AC conductivity and expected dielectric properties.

7.4. Experimental

7.4.1. Materials and Composite Preparation

Polystyrene (Styron® 610) with a density of 1.06 g/cm

3 and a melt flow index of 10.0 g/10

min (200 °C/5 kg) was kindly provided by Americas Styrenics LLC. The MWCNTs (NanocylTM

NC7000) were obtained from Nanocyl S.A. (Sambreville, Belgium). According to the

190

manufacturer, the MWCNTs were produced with the catalytic carbon vapor deposition (CCVD)

process and had an average diameter of 9.5 nm, a length of 1.5 μm and a surface area of 250-300

m2/g. Before processing, all the materials were dried at 50 °C for 4 hr under vacuum.

Nanocomposites with different concentrations of MWCNTs, i.e., 0.02, 0.10, 0.20, 0.30, 0.50,

1.00, 2.00 and 3.50 wt%, were produced through a solution mixing technique. In this technique,

nanocomposites with various MWCNT loadings were produced by mixing different volumes of

100 mg/ml PS/N,N-dimethylformamide (DMF) solution and 0.66 mg/ml MWCNT/DMF

suspension. Each mixture was stirred for 15 min and then ultrasonicated for 30 min in a

sonication bath (VWR, Model 150HT, 480 W, 50 Hz). The two mixtures were then combined

and stirred for an additional 10 min. Next, the suspension was dripped into a large amount of

methanol (MeOH), where the volume ratio of MeOH to DMF was approximately three to one.

Upon contact of the suspension with the MeOH, the PS chains retracted and precipitated

instantly, due to their insolubility in MeOH. The retracted chains entrapped the MWCNTs and

prevented them from reagglomeration. The final mixture was filtered and dried in a fume hood

for 16 hr and then transferred to a vacuum oven for 12 hr at 50 °C to remove the remaining

solvents.

The composites resulting from the solution mixing technique were then molded using a

Carver compression molder (Carver Inc., Wabash, IN) at 210 °C for 10 min under a pressure of

38 MPa. The compression molded samples had a thickness of 1.0 mm, width of 25.0 mm and

length of 42.0 mm.

191

7.4.2. Electrical and Dielectric Properties Measurements

Direct current (DC) conductivity measurements of the molded samples were conducted

employing two different setups. For the nanocomposites with conductivities lower than

10-2 Sm

-1, a Keithley 6517A electrometer connected to a Keithley 8009 test fixture (Keithley

Instruments, USA) was used. The measurements were performed at a frequency of 0.1 Hz. For

the samples with electrical conductivities more than 10-2 Sm

-1, the measurements were

conducted according to the ASTM 257-75 standards using a Loresta GP resistivity meter (MCP-

T610 model, Mitsubishi Chemical Co., Japan) connected to an ESP four-pin probe. The four-pin

probe eliminated the effect of contact resistance. The applied voltage was 10 V for all the DC

conductivity measurements. The dielectric properties of the nanocomposites were measured with

an impedance / gain-phase analyzer (Solartron SI 1260) in the frequency range of 10-1

– 10+6

Hz.

Prior to the measurements, the electrodes were painted on the samples with a silver paste.

7.4.3. Morphological Characterization

Light microscopy (LM) and transmission electron microscopy (TEM) techniques were

employed to investigate the dispersion and distribution of MWCNTs. LM in transmission mode

was carried out on thin sections of MWCNT/PS composites (1.00 wt%) with 5.0 µm thickness.

The samples were cut with a Reichert-Jung Ultramicrotome (Ultracut B model). The microtomed

layers were mounted on a glass slide and then cover slipped using a ProLong® Gold. A weight

was placed on the cover slip to assure that the thin sections were flat. The micrographs were

captured using 10x objective magnification on a Leica DMRXA2 microscope equipped with a

camera AndorTM

iXon 885. The entire cross-sectional area was imaged.

192

The TEM analysis of the nanocomposites was carried out on ultramicrotomed sample sections

using a Tecnai TF20 G2 FEG-TEM (FEI, Hillsboro, Oregon, USA) at a 200 kV acceleration

voltage with the standard single-tilt holder. The images were captured on a Gatan UltraScan

4000 CCD (Gatan, Pleasanton, California, USA) at 2048x2048 pixels. The samples were

ultramicrotomed to sections of ~ 70 nm at room temperature using a Leica EM UC6.



In order to exploit the dielectric properties of MWCNT/polymer composites efficiently,

MWCNTs must get well dispersed and distributed in polymer matrix. In fact, well dispersion and

distribution contribute to efficient occurrence of charge polarization all across the composite.

Accordingly, morphological analyses of the made composites were performed to achieve an idea

about the states of MWCNT dispersion and distribution in PS matrix. Distribution is more of a

microscopic scale and is homogeneous dispersal of individual MWCNTs or their agglomerates in

the nanocomposite; dispersion is of nanoscopic scale and is disentanglements of MWCNT

agglomerates [20-22].

The process of MWCNT dispersion and distribution into polymer matrix comprises two steps:

1) wetting and infiltration of polymer melt into primary agglomerates and 2) dispersion and

distribution of MWCNTs by rupture and erosion mechanisms [20]. In the rupture mechanism,

large agglomerates are broken into smaller ones; whereas, the erosion mechanism includes

erosion of individual MWCNTs or bundles from the surface of large agglomerate. To obtain

good dispersion and distribution, all the mechanisms must take place efficiently at less than a

193

critical time, since prolonging the mixing process may lead to MWCNT breakage. Further details

on the mechanisms of MWCNT dispersion and distribution in polymer matrix can be found

elsewhere [20-23].

LM micrograph, shown in Figure 7-1, depicts a good view from the distribution state of

MWCNTs in PS matrix. Figure 7-1 demonstrates that large MWCNT agglomerates were

relatively well ruptured, eroded and distributed in the solution-mixed sample, thereby leading to

a good state of MWCNT distribution. Although some large MWCNT agglomerates are

observable, however the overall state of MWCNT distribution is satisfactory.

Figure 7-1: LM micrograph of MWCNT/PS composites with 1.00 wt% loading.

In order to obtain a good opinion from the dispersion state of MWCNTs, the TEM

micrographs of the made composites were taken. Figure 7-2(a) shows low-magnification TEM

image of MWCNT/PS composites; whereas, Figures 7-2(b) and (c) depict high-magnification

TEM images of MWCNT/PS composites in the polymer-rich and agglomerated areas,

respectively.

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Figure 7-2: TEM micrographs of the solution-mixed samples at (a) low magnification, (b) high

magnification (polymer-rich area) and (c) high magnification (agglomerated area).

As shown in Figure 7-2(a), no large agglomerate is observable in the solution-mixed sample.

The black arrows point to the MWCNT agglomerates. Figure 7-2(b) presents the dispersion of

MWCNTs in polymer-rich areas. It is obvious that the concentration of MWCNTs in the

polymer-rich area is considerable. This can be attributed to enhanced erosion of MWCNTs from

the surface of large or small agglomerates in the solution-mixed samples. Figure 7-2(c)

demonstrates the dispersion of the MWCNTs in the agglomerated areas. It can be seen that the

polymer melt infiltrated into agglomerates and disentangled them partially. However, the

agglomerated areas required much more time and energy to get thoroughly disentangled. In view

195

of the LM and TEM images, it can be inferred that MWCNT were relatively well dispersed and

distributed in the polymer matrix; therefore, they were prone to present notable dielectric

properties for MWCNT/polymer composites.

7.5.2. DC Conductivity

The new generation of microelectronics demands polymer-based capacitors with high real

permittivity and low imaginary permittivity. According to the percolation theory, a high real

permittivity with a low leakage current in CPCs can only be realized at filler loadings very close

to the percolation threshold [9, 13]. The insulator-conductor transition that occurs at the

percolation threshold precludes CPCs from being used as charge storage materials beyond the

percolation threshold. Therefore, determination of the percolation thresholds of CPCs is the first

step in their development for charge storage applications.

Figure 7-3 depicts the percolation curve (DC conductivity) of the solution-mixed samples.

The percolation curve of the MWCNT/PS composites can be divided into three distinct regions

in terms of electrical conductivity, i.e., the insulative region, the percolation region, and the

conductive region. In the insulative region, the MWCNTs loadings were very low with the

MWCNTs far from each other; thus, the PS matrix controlled the charge transfer. In this region,

the solution-mixed samples demonstrated conductivities ranging from 10-13

to 10-11

Sm-1

, which

were close to the conductivity of pure PS.

With increases in the MWCNT concentration, at a critical MWCNT concentration, i.e., called

the percolation threshold, the first conductive path formed, resulting in the insulator-conductor

196

transition. Employing the percolation theory [24, 25] led to the percolation threshold equal to

0.06 for the solution-mixed MWCNT/PS composites. This threshold is comparable to the lowest

percolation thresholds reported for MWCNT/PS composites in the literature, confirming good

dispersion and distribution of MWCNTs throughout the polymer matrix [26, 27]. In the

conductive region (MWCNT loadings far above the percolation threshold), the conductivity rose

with increased MWCNT concentration until a plateau was reached. The existence of the plateau

in the percolation curve of CPCs signified the formation of a three-dimensional conductive

network.

Figure 7-3: The percolation curve (DC conductivity) of the solution-mixed samples of the

MWCNT/PS composites.

7.5.3. AC Conductivity

In general, leakage current of a material in an alternating field originates from its electrical

conductivity. Accordingly, it is important to have a profound understanding of the electrical

conductivity in an AC field. Generally, AC conductivity is defined as following [28]:

197

( ) (7-1)

where AC AC conductivity, ɛ´ real permittivity, ɛʺ imaginary permittivity, angular frequency

and ɛ0 permittivity of free space. For CPCs, AC conductivity is expressed as follows [28-31]:

( ) (7-2)

where σDC is DC conductivity and A and s are parameters dependent on temperature, and

concentration and type of fillers. It is well known that σAC is the sum of all dissipative effects,

including Ohmic conduction (σDC) created by free charges as well as frequency-dependent

dielectric dispersion (A(ω)s). Of interest to note, DC conductivity, which originates from

resistive current, is usually independent of frequency and is industrially measured under a low-

frequency AC voltage, where the influence of capacitive currents is negligible.

To comprehensively investigate the dielectric behaviors, including AC conductivity, of the

MWCNT/PS composites over the broadband frequency range, it is necessary to study the

dielectric properties in both the insulative and conductive regions. Considering 0.06 as the

percolation threshold of the solution-mixed samples, the MWCNT loadings chosen for dielectric

spectroscopy were 0.02, 0.10, 0.50 and 3.50 wt%, which covered the whole insulative and

conductive regions for the made composites.

Figure 7-4 demonstrates the AC conductivity of the solution-mixed MWCNT/PS composites

over the broadband frequency range. It was observed that at low MWCNT concentrations

(insulative region), the AC conductivity had a strong ascending trend with frequency. Figure 7-4

shows that the AC conductivity of the composite holding 0.02 wt% MWCNT at 106 Hz was

around 10-5

S·m-1

, which was seven orders of magnitude greater than its DC conductivity. As a

198

matter of fact, at low filler loadings due to large insulative gaps between conductive fillers, the

DC conductivity (low-frequency AC conductivity) was very low. However, with frequency

increase, the role of capacitive currents highlighted, since high-frequency voltage facilitated

frequent development of capacitive currents in a time frame. This led to ascending trend of AC

conductivity as a function of frequency in the insulative region.

Figure 7-4: AC conductivity of the solution-mixed MWCNT/PS composites.

By increasing the MWCNT concentration, the effect of the DC conductivity increased and the

magnitude of the DC conductivity approached to that of AC conductivity at high frequencies. In

other words, due to well-established conductive network formation at high filler loadings, the

free electrons had the conquering role in generating the conductivity over the whole frequency

range. It can be observed that for MWCNT concentrations of 0.10, 0.50 and 3.50 wt%, which

were in the conductive region, the DC and AC conductivities were close to each other and

independent of frequency.

199

7.5.4. Charge Polarization Mechanisms in MWCNT/Polymer Composites

In general, charge polarization in MWCNT/polymer (nonpolar) composites originates from

three sources, namely 1) interfacial polarization, 2) MWCNT polarization, and 3) electronic

polarization of polymer. Interfacial (Maxwell–Wagner–Sillars) polarization is usually observed

in heterogeneous systems with phases with different conductivities, such as MWCNT/polymer

composites [32-34]. At the internal phase boundaries of polymer and MWCNTs, nomadic charge

carriers can be entrapped and give rise to charge polarization. As interfacial polarization takes

place at large scale (mesoscopic scale), it has usually been observed at low frequencies, due to its

large relaxation time with respect to electric field frequency at high frequencies

MWCNT polarization also contributes to the real permittivity of MWCNT/polymer

composites, particularly at high frequencies where interfacial polarization is weak. It is believed

that the crystallographic defects in MWCNT structures may act as polarized centers [14, 35]. For

instance, a defect in the armchair-type CNT, which can conduct electricity, can cause the

surrounding region to be semiconducting. Therefore, in the molecular structure of MWCNTs,

there may be two regions with different conductivities that induce charge polarization on the

molecular scale.

The electronic polarization of polymer matrix is the third side of the charge polarization

triangle in MWCNT/polymer composites. In the narrow insulative gaps between MWCNTs,

there may be a buildup of very high field strength, which is higher than the macroscopic field

strength by a factor of M (i.e., M is the ratio of the average size of the conducting MWCNT

aggregates to the average gap width) [36, 37]. This high field strength contributes considerably to

200

the electronic polarization of polymer matrix and, thus, real permittivity at high frequencies

(optical frequency) [19].

The electric dipole has a magnitude equals to strength of each charge times the separation

between charges. Considering the scale at which charges are polarized at different polarization

mechanisms, the degree of contribution of polarization mechanisms to real permittivity has the

following order: interfacial, atomic and electronic. It should be mentioned that with frequency

increase, the slow polarization mechanisms give up in turn, leaving the faster ones to contribute

real permittivity.

7.5.5. The Broadband Behavior of Real Permittivity

Figure 7-5 presents the real permittivity of the solution-mixed composites with different

MWCNT loading levels over the broadband frequency range. As shown in Figure 7-5, the real

permittivity increased tremendously with increased MWCNT concentration. For instance, at 100

Hz, the real permittivity of the pristine PS was 2.71, which increased to 6.00 and 5.22×104

at

0.02 and 3.50 wt%, respectively. The three distinct regions mentioned for the DC conductivity

percolation curve, namely the insulative, percolation and conductive regions, can be employed to

explain the evolution process of real permittivity with MWCNT concentration.

By adding a small amount of MWCNTs to the PS matrix (insulative region), some

nanocapacitor structures, i.e., MWCNTs separated by thin layers of polymer, were formed; and,

the real permittivity increased slightly relative to the pristine PS. In addition, the charge

polarization in the semiconductive MWCNTs also contributed to higher real permittivity at

201

greater MWCNT loadings. When MWCNT loading approached the percolation threshold

(percolation region), an abrupt growth in the real permittivity was observed. This increase can be

attributed to the formation of a large number of nanocapacitors, allowing the composite to store

the charge, i.e., interfacial polarization. As a matter of fact, as the percolation threshold was

approached, there was an increase in the number of nanoelectrodes (MWCNTs) and a decrease

in the thickness of nanodielectrics (PS layers between MWCNTs), both of which contributed to

the real permittivity. Beyond the percolation threshold (conductive region), despite the formation

of conductive paths, the real permittivity carried on growing with increased MWCNT

concentrations, since a great deal of MWCNTs were still wrapped with the PS matrix.

Figure 7-5: Real permittivity, as a function of frequency, of the solution-mixed samples at

different MWCNT concentrations.

In view of Figure 7-5 and the percolation threshold of the solution-mixed samples, it can be

claimed that the real permittivity was almost independent of frequency in the insulative region,

whereas it varied with frequency in the conductive region. For instance, the real permittivity of

202

the solution-mixed samples at 0.02 wt% (insulative region) was frequency-independent;

however, at 3.50 wt% (conductive region), the real permittivity demonstrated a decaying trend in

the low frequency range (10-1

– 3×100 Hz), then was constant up to 2×10

4 Hz, and finally

showed another decaying trend above 2×104 Hz.

In order to predict the dielectric behaviors of CPCs as a function of frequency, it is imperative

to understand the charge polarization mechanisms over the whole frequency range. In CPCs, the

dependency of real permittivity on frequency relies on the presence of nanocapacitor structures.

At low MWCNT concentrations (insulative region), due to the lack of a large amount of

nanocapacitor structures, the real permittivity was constant over the whole frequency range;

whereas, the abundance of nanocapacitor structures close to or above the percolation threshold

(conductive region) led to the frequency-dependent real permittivity (Figure 7-5).

The very high real permittivity of the MWCNT/PS composites close to or above the

percolation threshold in the low frequency range originated from low-frequency dispersion

(LFD) mechanism (Figure 7-5) [38, 39]. LFD has similar mechanism as interfacial polarization,

but occurs at lower frequencies. In LFD mechanism, due to sufficiently low frequencies,

nomadic charge carriers with low drift velocity also found sufficient time to move towards

internal interfaces and pile up. This led to very large real permittivities. It was observed that LFD

declined sharply with frequency, which can be related to the LFD relaxation phenomenon.

In the intermediate frequency range, the real permittivity resulted from interfacial

polarization. In the interfacial polarization mechanism, only charge carriers with high drift

velocity got enough time to pile up at the interfaces in each half cycle of alternating electric field.

These charge carriers were able to keep pace with alternating field over a wide frequency band.

203

This led to a constant real permittivity in the intermediate frequency range, until interfacial

relaxation happened. It was interesting to observe that with increases in MWCNT concentration,

the interfacial relaxation occurred at lower frequencies. This can be related to reduced relaxation

time of MWCNT/PS composites with higher MWCNT loadings, which arose from reduced

thicknesses of nanodielectrics and enhanced capacity of nanocapacitors. In the high frequency

range, the real permittivity showed a descending trend with frequency due to interfacial

relaxation. With the decay of the interfacial polarization in the high frequency range, the roles of

the MWCNT polarization and PS polarization found more importance.

7.5.6. The Broadband Behavior of Imaginary Permittivity

Imaginary permittivity is representative of energy dissipation within a dielectric and is

considered as a critical factor whether a material is appropriate for charge storage or not. CPCs

functioning as charge storage materials are needed to show a low imaginary permittivity (leakage

current). Imaginary permittivity is composed of two components; namely Ohmic loss and

polarization loss. Ohmic loss arises from DC conduction and represents the dissipation of

electrical energy by mobile charge carriers moving throughout the dielectric material.

Polarization loss originates from the friction accompanying the orientation of electric dipoles in

each half cycle of an AC field. Therefore, it can be said that the polarization loss, as a portion of

imaginary permittivity, has a direct relationship with real permittivity. In other words, the higher

the real permittivity of a dielectric, the greater is the momentum generated by charge

polarization, and thus the higher is the dissipation of energy to come over the momentum to

reorient the dipoles in each half cycle of alternating field.

204

As shown in Figure 7-6, the imaginary permittivity was very low at MWCNT concentrations

far below the percolation threshold; however, it increased tremendously as the MWCNT

concentration approached the percolation threshold. For instance, it was observed that at 100 Hz,

the imaginary permittivity of 0.02 wt% MWCNT/PS composite was 0.01, which increased to

3.28×107 at 3.50 wt% loading. Several factors constitute the direct relationship between

imaginary permittivity and MWCNT concentration. Firstly, increase in MWCNT content

accompanies with increase in the amount of dissipating nomadic charges and formation of

conductive networks in the composites. In fact, at enhanced conductive network formation, the

electrons had greater mean free paths in which to move according to the direction of the electric

field in each half cycle and, consequently could dissipate more electrical energy [19]. Moreover,

large amount of energy can be dissipated by free charges at the contact spots between MWCNTs.

The boosted polarization loss originating from interfacial polarization at filler loadings close to

or above the percolation threshold is another important factor contributing to imaginary

permittivity.

It was also observed that the imaginary permittivity was independent of frequency in the

insulative region; however, it was highly sensitive to frequency in the conductive region. As

depicted in Figure 7-6, the imaginary permittivity of conductive samples showed several orders

of magnitude reduction by sweeping the whole frequency range. The descending trend of

imaginary permittivity with frequency in the conductive region can be attributed to the reduced

available times for free electrons to sweep the network in each half cycle of alternating field, i.e.,

lower Ohmic loss. In addition, with frequency increase, the interfacial polarization relaxation

occurs, which is associated with lower polarization loss due to incomplete dipole reorientation.

205

Figure 7-6: Imaginary permittivity, as a function of frequency, of the solution-mixed samples at

different MWCNT concentrations.

7.6. Conclusions

Characterization techniques, such as LM and TEM showed that MWCNTs were well

dispersed and distributed all across the composites, contributing to better exploitation of

MWCNT electrical properties for charge storage applications. Comparing the DC and AC

conductivities results showed that the AC conductivity was highly sensitive to frequency in

insulative region, whereas it was almost constant with frequency in the conductive region. The

DC and AC conductivities in the conductive region at high frequencies were close to each other.

The dielectric spectroscopy showed that the real and imaginary permittivities increased

tremendously as the MWCNT concentration approached the percolation threshold. The increase

in the real permittivity was related to the formation of a large number of nanocapacitors

(MWCNTs as nanoelectrodes and PS as nanodielectrics). The increase in the imaginary

206

permittivity was attributed to greater number of dissipating charges, enhanced conductive

network formation and boosted polarization loss arising from interfacial polarization.

It was also found that the real and imaginary permittivities were almost constant with

frequency in the insulative region, while they descended drastically with frequency in the

conductive region. The descending trend of real permittivity with frequency was related to

charge polarization relaxation. The reduction of imaginary permittivity with frequency in the

conductive region was attributed to the reduced available times for free electrons to sweep the

network (lower Ohmic loss) and also lower polarization loss due to interfacial polarization

relaxation.

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*Submitted to Polymer

210

Chapter 8

Novel Composites of Copper Nanowire/PVDF with Superior Dielectric

Properties*


This article introduces CuNW as a competent substitution for MWCNT to be employed in

CPCs for charge storage applications. The CPCs used for charge storage applications are

required to present high real permittivity and low imaginary permittivity. In order to obtain high

real permittivity, highly conductive fillers are greatly acknowledged. The limited electrical

conductivity of MWCNTs prompted us to investigate the dielectric properties of CuNW/polymer

composites, due to superior electrical conductivity of CuNWs to MWCNTs. However,

unavoidable oxide layer formation on the surface of CuNWs sounds as a barrier to exploit the

electrical conductivity of CuNWs. Nonetheless, in this study the oxide layer formation was

innovatively employed as a benefit to decay the conductive network formation to reduce the

imaginary permittivity. As a matter of fact, high conductivity of fresh core of CuNWs combined

with the presence of oxide layer on their surfaces led to novel composites with superior dielectric

properties.

211

Novel Composites of Copper Nanowire/PVDF with Superior Dielectric

Properties

Aline Bruna da Silva1, Mohammad Arjmand

2, Uttandaraman Sundararaj

2,

Rosario E. S. Bretas1

1Department of Materials Engineering, Universidade Federal de São Carlos, São Carlos, Brazil

2Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Canada

8.2. Abstract

Novel copper nanowire (CuNW)/poly(vinylidene fluoride) (PVDF) nanocomposites with high

dielectric permittivity and low dielectric loss were prepared by coagulation technique followed

by melt compression. Their dielectric properties over the broadband frequency range, i.e. 101 –

106 Hz, were compared with multi-walled carbon nanotubes (MWCNT)/PVDF nanocomposites

prepared by the same technique. It was observed that the CuNW/PVDF nanocomposites showed

higher dielectric permittivity, lower dielectric loss and thus significantly lower dissipation factor

than of the MWCNT/PVDF nanocomposites. For instance, at filler concentrations of 0.8 and

1.5v% and at a frequency of 20 Hz, the MWCNT/PVDF nanocomposites presented dissipation

factors of 2.4103 and 1.310

4; whereas the CuNW/PVDF nanocomposites showed the

dissipation factors significantly lower and equal to 2.0 and 3.9, respectively. This behavior was

ascribed to a higher conductivity of the fresh core of CuNWs relative to MWCNTs, which

provided the composites with greater amount of mobile charge carriers participating in the

interfacial polarization (higher dielectric permittivity). Moreover, the presence of oxide layer on

the CuNW surfaces decayed the conductive network formation leading to a low dielectric loss.

212

8.3. Introduction

Polymer nanocomposites with high dielectric permittivity have found great attention to store

electrical energy and have a high potential for a broad range of applications, such as

communications devices, actuators, artificial muscles, charge-storage capacitors systems, etc [1-

3]. Easy processability of the polymer matrix combined with high dielectric permittivity of the

filler draws a promising future for these nanocomposites. Nonetheless, the low dielectric

permittivity of the polymer matrix still constitutes a challenge to obtain a versatile polymer

composite with a high dielectric permittivity (high-k polymer composite).

The most traditional method to increase this permittivity is, thus, to disperse a high-k

insulating ceramic powder into the polymer matrix to form a composite [4]. However, to meet

the demanding requirements for new generation of electronics a large amount of ceramic is

usually required, resulting in loss of flexibility and mechanical strength. Another strategy is to

produce percolative composites using conductive or semi-conductive fillers. As the volume

fraction of the conductive fillers increases to the vicinity of the percolation threshold, these

composites can present an abrupt increase in dielectric permittivity [1, 5, 6], while retaining the

polymer matrix flexibility. When the concentration of the conductive filler is close to the

percolation threshold, a large amount of conductive fillers approximates to each other but still

remains insulated by thin layers of dielectric material, forming a great deal of nanocapacitors

(conductive nanofiller as nanoelectrode and polymer matrix as nanodielectric) [1, 6-8].

The effective dielectric permittivity of the conductive filler/polymer composite (CPC) can be

several orders of magnitude higher than of the insulating polymer matrix. Furthermore, lower

percolation threshold of CPCs relative to traditional composites leads to lower costs and easier

213

processability [7]. The high dielectric permittivity in CPCs is not a direct consequence of the

intrinsically high-k fillers, but is due to huge increase in interfacial polarization, i.e., an effective

increase of electrode surface area due to contiguity of conductive filler near the percolation

threshold [6, 8-10]. However, high dissipation factors above the percolation threshold arising

from conductive network formation preclude the use of CPCs with high filler loadings for charge

storage applications [5, 7].

Many studies have focused on developing CPCs with low dissipation factors; some strategies

are available to prevent the direct contact between the conductive particles, such as coating the

surface of the conductive filler with a thin insulating layer [11, 12], using surface-oxidized metal

particles [13], incorporating a secondary ferroelectric filler as barrier layer [14, 15] or aligning

the conductive filler [16]. All these techniques require further processing or they have an adverse

effect on the dielectric permittivity of the made composites.

In this study, we present a novel copper nanowire/poly(vinylidene fluoride) (CuNW/PVDF)

nanocomposite with higher dielectric permittivity and lower dissipation factor than the multi-

walled carbon nanotube (MWCNT)/PVDF nanocomposite obtained by similar technique. PVDF

was chosen as the matrix because it is a semi-crystalline polymer that has extensive applications

due to its thermal stability, chemical resistance, pyro and piezoelectric properties, high

permittivity and relatively low dissipation [1, 5, 17]. MWCNT/polymer nanocomposites were

chosen for comparison due to their superior electrical and dielectric properties, originating from

the extraordinary electrical properties together with giant surface area of MWCNTs.

CuNWs are susceptible to oxidation due to a very large surface area, which has made them

inappropriate for many electrical applications. The goal of this work was to use this weakness as

214

a benefit, producing novel CuNW/PVDF nanocomposites in which the oxide layer on the surface

of the CuNWs plays the role of an insulating barrier. In other words, the oxide layer as insulating

barrier is prone to avoid direct contact between the fillers above the percolation threshold

reducing the dissipation factor. The resultant high dielectric permittivity and low dissipation

factor of these innovative nanocomposites make them particularly attractive for technological

applications as storage energy materials.

8.4. Experimental

8.4.1. Materials

The PVDF Kynar® 1000HD was purchased from Arkema Inc. The density and melt flow rate

are 1.78 g/cm3 and 1.1g/10 min (at 230 C/5.0 kgf), respectively. The dielectric permittivities are

10.5 and 7.0 at 100 Hz and 1 MHz according to IEC 60250, respectively. The MWCNTs

(NanocylTM

NC7000) were obtained from Nanocyl S.A. (Sambreville, Belgium). According to

the manufacturer, the MWCNTs were produced with the catalytic carbon vapor deposition

(CCVD) process and had an average diameter of 9.5 nm, a length of 1.5 μm and a surface area of

250-300 m2/g. The synthesis of CuNWs was an in-house technology, in which CuNWs were

synthesized through AC electrodeposition of Cu in porous aluminum oxide (PAO) templates.

Afterwards, CuNWs were liberated from Al electrodes, collected in 150 ml methanol and bath

sonicated for 30 min. Next, the nanowires were collected by filtration in nylon membranes (0.45

mm pore size) and dried for 2 hr under vacuum. The synthesized nanowires had averages

diameter and length of 30 nm and 1.5 µm, respectively. Details of the synthesis and liberation are

215

described in a previous work [18, 19]. Figure 8-1 shows micrographs of MWCNT (as-received)

and synthesized CuNW.

Figure 8-1: TEM micrographs of (a) as-received MWCNT (NC7000), (b) synthesized CuNW.

8.4.2. Mixture Preparation

The PVDF Kynar® 1000HD and MWCNTs (Nanocyl

TM NC7000) were dried at 50 °C for 4 hr

under vacuum. The MWCNT/PVDF and CuNW/PVDF nanocomposites were produced by

solution mixing technique. PVDF was dissolved into DMF at 80 ºC under continuous stirring to

obtain a solution with concentration of 0.1 g/ml. Meanwhile, MWCNTs and CuNWs were also

dispersed into DMF under sonication at room temperature for 30 min. The concentrations of

MWCNT and CuNW suspensions were 0.00033 and 0.00500 g/ml, respectively. Cooling down

the PVDF/DMF solution to room temperature, the MWCNT/DMF and CuNW/DMF suspensions

were mixed with PVDF/DMF solution separately using magnetic stirring for 5 min.

Subsequently, the suspensions were dripped into methanol (non-solvent to PVDF), where the

volume ratio of DMF to methanol was 1:3. Upon contact of the suspension with the methanol,

216

the PVDF chains retracted and precipitated instantly, due to their insolubility in methanol. The

retracted chains entrapped the fillers and prevented them from reagglomeration.

The mixtures were then filtered and placed in an evaporation dish for 24 hr in a fume hood.

Next, the MWCNT/PVDF nanocomposites were dried at 80 ºC for 24 hr in a vacuum oven;

whereas, the CuNW/PVDF nanocomposites were dried for 96 hr at room temperature under

vacuum. Finally, the MWCNT/PVDF and CuNW/PVDF nanocomposites with the

concentrations between 0.4v% and 1.5v% were produced by the compression molding of the

prepared materials at 200 ºC for 10 min under pressure of 35 MPa.

8.4.3. Characterization

Characterizations of the MWCNT and CuNW were carried out by scanning electron

microscopy (SEM) and transmission electron microscopy (TEM) techniques using a XL 30 FEG

and a CM120 microscope operating at 120kV, both from Philips, respectively. For those

analyses, diluted solutions of MWCNT and CuNW were prepared by sonication in methyl

alcohol for 15 min with subsequent dripping on copper grids. The average diameter of both

fillers was measured using the Image-Pro® Plus 4.5 software. The oxidation of CuNWs was

studied by wide-angle x-ray diffraction (WAXD), using a Rigaku diffractometer, model Ultima

IV, with CuK radiation (= 1.542 Å), operated at 40 kV and 40 mA.

The morphology of the nanocomposites was also characterized by the SEM and TEM

techniques employing the above-described microscopes. For the SEM analysis the samples were

cryo-fractured using liquid nitrogen, while for the TEM analysis the samples were prepared by

217

cryo-ultramicrotomy. Direct current (DC) conductivity was measured by two different setups

with 90 V as applied voltage. For the samples with conductivities lower than 10-2

S·m-1

, a

Hiresta UP (MCP-HT450 model) resistivity meter connected to an URS probe ring was used; for

the samples with electrical conductivities higher than 10-2

S·m-1

, a Loresta GP resistivity meter

(MCP-T610 model) connected to an ESP four-pin probe was used. Both instruments were from

Mitsubishi Chemical Co., Japan. The broadband dielectric properties were measured using an

impedance/gain-phase analyzer (Solartron SI 1260) in the frequency range of 101 and 10

6 Hz.

Prior to the measurements, electrodes of silver were painted on the samples.


8.5.1. Oxidation of CuNWs

Luo et al. [20] demonstrated that the oxidation reaction of CuNW synthesized by AC

electrodeposition in PAO templates can be divided in two stages, in which the degree of

oxidation is determined by the presence of Cu, Cu2O and CuO. Before oxidation the CuNW

presents only metallic Cu and Cu2O; after stage 1 the composition of CuNW consists of Cu2O

and CuO and after stage 2 oxidized CuNWs present only CuO.

As shown in Figure 8-2, the WAXD analyses of the CuNW powder displayed diffraction

peaks at 2θ values of 43.2˚, 50.4˚ and 74.1˚ corresponding to (111), (200) and (220) planes of Cu

[21], respectively. The diffraction at 61.4° corresponds to the (220) crystalline planes of the

cubic phase of Cu2O [22] and the peaks at 2θ values of 35.5˚, 38.7˚, 48.8˚, 58.2˚, 61.5˚, 66.2˚ and

81.2˚ correspond to the (002), (-111), (111), (200), (-202), (202), (-113), (-311), (310), (313)

crystalline planes of CuO, respectively [23]. Therefore, it can be claimed that the CuNWs used in

218

this work were partially oxidized (with oxidation being in stage 1) and had possibly a non-

conductive shell (oxide layer) and a conductive core (fresh copper).

Figure 8-2: WAXD diffractogram of the CuNW.

8.5.2. Morphological Characterization of the Nanocomposites

Figure 8-3 shows the SEM micrographs of the solution-mixed MWCNT/PVDF and

CuNW/PVDF nanocomposites, both at concentration of 1.5v%. These images revealed a

segregated structure for both types of nanocomposites. The segregated structure has been

reported by other researchers, and led to CPCs with lower percolation threshold [24, 25]. In fact,

to obtain a low percolation threshold, a non-uniform distribution of nanofiller network is

preferred [26, 27]. In this way, conductive fillers just occupy some preferred areas to make a

conductive network, thereby resulting in lower percolation threshold.

219

Figure 8-3: SEM images: a) MWCNT/PVDF nanocomposites; b) CuNW/PVDF nanocomposites,

both with 1.5v% of filler.

The segregation could be the result of weak interactions between the nanofillers and the

PVDF chains, which prevents significant incorporation of the fillers. As a matter of fact, when

the suspension of conductive filler/PVDF/DMF was dripped into methanol, the polymer chains

precipitated instantly and the coagulated chains captured the conductive fillers and prohibited

them from reagglomeration. The vivid networks of conductive filler without any significant

agglomerates, seen in Figure 8-3, confirm this idea. However, due to inhomogeneous dispersion

of conductive filler in suspension, the polymer chains created some filler-free areas during the

coagulation. This led to the morphology of segregated structure for both MWCNT/PVDF and

CuNW/PVDF composites. Comparing both structures, it is observed that the MWCNT/PVDF

composite was formed by segregated structures smaller than the CuNW/PVDF composites; this

can be ascribed to higher affinity of MWCNT to PVDF chains, and in consequence better

dispersion and distribution of MWCNTs in PVDF matrix.

220

TEM micrograph of MWCNT/PVDF shows that MWCNT were well dispersed in PVDF

matrix. Individual MWCNTs are easily observable without creating any significant agglomerate.

It is worth noting that the observable lengths of MWCNT in the TEM micrograph do not present

the whole length of MWCNTs due to curvy structure of this nanomaterial. The TEM micrograph

of CuNW/PVDF shows that CuNWs were relatively well-dispersed in the polymer matrix;

however, bundles of CuNWs are also discernible. This can be related to high van der Waals

forces between CuNWs and also their low affinity to PVDF matrix.

Figure 8-4: TEM images of: a) MWCNT/PVDF nanocomposites; b) CuNW/PVDF

nanocomposites, both with 1.5v% of filler.

8.5.3. DC and AC Conductivity

In general, energy dissipation within a dielectric in an alternating field is related to its

electrical conductivity. Accordingly, it is important to have a profound understanding of the

electrical conductivity in an AC field. Generally, the AC conductivity * is calculated from the

dielectric permittivity and dielectric loss according to the relation: ( ) ,

where o is vacuum permittivity (8.854×10-12

F/m), is angular frequency and ɛ´ and ɛ are

221

dielectric permittivity and dielectric loss, respectively [28]. This equation shows that the real part

of AC conductivity is proportional to dielectric loss and occurs due to flow of charges through

the dielectric material (DC conduction). The imaginary part of AC conductivity is engaged with

dielectric permittivity and does not pass through the dielectric material, but is generated to

compensate for the charges which are polarized within the dielectric material (dielectric

dispersion).

For CPCs, AC conductivity is expressed as follows [28-30]:

( ) (8-1)

where σDC is DC conductivity and A and s are parameters dependent on concentration and type of

fillers, temperature and morphology of CPCs. It is well known that σAC is the sum of all

dissipative effects, including Ohmic conduction (σDC) created by free charges as well as

frequency-dependent dielectric dispersion (A(ω)s). Dielectric dispersion in CPCs originates from

interfacial, dipolar and/or electronic polarization mechanisms depending on the frequency range,

molecular structure of conductive filler and polymer matrix and morphology of CPCs [31].

Given the frequency range focused in this study, i.e., 101 to 10

6 Hz, interfacial polarization

played the main role in developing the dielectric properties of the MWCNT/PVDF and

CuNW/PVDF nanocomposites. Interfacial polarization is broadly observed in heterogeneous

systems with phases with different conductivities or dielectric permittivities, such as CPCs [32,

33]. Interfacial polarization takes place because of the accumulation of mobile charges at the

interface of unlike phases with different electrical conductivities or permittivities. As interfacial

polarization occurs at large scale (mesoscopic scale), it has usually been observed at low

frequencies, due to its large relaxation time with respect to electric field frequency at high

222

frequencies [8, 32]. It is notable to declare that the dipolar polarization occuring in the PVDF

matrix also contributes slightly to the dielectric properties of conductive filler/PVDF

nanocomposites over the freqyency range of study.

Figure 8-5 and Figure 8-6 present the DC conductivity and AC conductivity of the

MWCNT/PVDF and CuNW/PVDF nanocomposites, respectively. The electrical percolation

thresholds (c) of both nanocomposites were obtained by fitting the data to the power law

equation for electrical conductivity [34]. The percolation thresholds obtained from the

percolation theory were 0.13v% and 0.27v% for the MWCNT/PVDF and CuNW/PVDF

nanocomposites, respectively. This result can be related to the higher aspect ratio of MWCNTs,

which gives rise to higher probability of MWCNTs contacting each other, i.e., lower percolation

threshold.

Figure 8-5 and Figure 8-6 show a continuous increase in the AC conductivity of both

nanocomposites, with the increase of the amount of filler. This increase can be related to the

formation of further conductive paths (higher DC conductivity), and also larger dielectric

dispersion arising from the development of interfacial polarization. It was also observed that both

DC and AC conductivities of the MWCNT/PVDF nanocomposites were higher than of the

CuNW/PVDF nanocomposites, although Cu has higher intrinsic conductivity than MWCNT. It

seems that the oxide layer on the surface of CuNWs avoided the direct contact between them

leading to a lower electrical conductivity.

Pure PVDF and nanocomposites with low filler content displayed AC conductivity highly

dependent on frequency, indicating an insulating behavior. However, as the filler content was

increased, the AC conductivity became independent of frequency, indicating the formation of a

223

complete conductive network. In fact, in the insulative region and at low frequency range, due to

large insulative gaps between the conductive fillers, the AC (DC) conductivity was very low.

Nevertheless, with frequency increase, the role of dielectric dispersion arising from interfacial

polarization increased leading to a rise in AC conductivity. It is also evident that at high filler

loadings, the AC conductivity of the MWCNT/PVDF nanocomposite was independent of

frequency, showing the conquering role of Ohmic conduction and well-established conductive

network formation. Nonetheless, the CuNW/PVDF nanocomposites at high filler loadings still

demonstrated an ascending trend with frequency. We believe that the presence of oxide layer on

the surface of CuNWs precluded the direct contact between CuNWs averting the formation of a

well-established conductive network. Therefore, the dielectric dispersion still played an

important role in contributing to AC conductivity at high frequencies.

(a) (b)



MWCNT/PVDF nanocomposites as a function of frequency.

224

(a) (b)



CuNW/PVDF nanocomposites as a function of frequency.

8.5.4. Dielectric Permittivity and Dielectric Loss

The ability of dielectric materials to store energy is attributed to polarization, i.e. electric

field-induced separation and alignment of electric charges, which can result in an increase in

capacitance. As mentioned before, considering the frequency range of study (101 – 10

6 Hz),

interfacial polarization is the conquering polarization mechanism in developing the dielectric

properties of the MWCNT/PVDF and CuNW/PVDF nanocomposites.

Figure 8-7 (a) and (b) shows the dielectric permittivity of the MWCNT/PVDF and

CuNW/PVDF nanocomposites as functions of filler content and frequency. It is evident that the

dielectric permittivity grew drastically as the filler content was increased. This increase can be

related to the formation of nanocapacitor structures, conductive nanofiller as nanoelectrode and

225

polymer matrix as nanodielectric, experiencing interfacial polarization. The electric dipole has a

magnitude equals to strength of each charge times the separation between charges. Considering

the scale at which the charges are polarized in interfacial polarization, i.e. mesoscopic scale, the

interfacial polarization creates a large dipole momentum. Moreover, increase in conductive filler

content is associated with the formation of an abundance of nanocapacitor structures. Thus, the

high dielectric permittivity at filler loadings close to or above the percolation threshold can be

related to the presence of a large number of nanocapacitor structures together with large dipole

momentum of interfacial polarization.

It can be observed that at high filler loadings (conductive region), the dielectric permittivity

declined tremendously with frequency for both types of nanocomposites. For instance, the

dielectric permittivities of 1.5v% MWCNT/PVDF and 1.5v% CuNW/PVDF nanocomposite

were 618 and 1189 at 20 Hz, which decreased to 46 and 18 at 106

Hz, respectively. This is due to

the large retardation time of interfacial polarization with respect to the electric field frequency at

high frequencies (relaxation phenomenon) [1, 8]. In fact, with frequency increase, the electric

field is too fast not to let the free electrons pile up at the interface. However, in the insulative

region, due to absence of interfacial polarization, the dielectric permittivity was independent of

frequency.

226

(a) (b)

Figure 8-7: Dielectric permittivity (´): (a) MWCNT/PVDF nanocomposite; (b) CuNW/PVDF

nanocomposites.

It is interesting to observe that CuNW/PVDF nanocomposites presented higher dielectric

permittivity than MWCNT/PVDF nanocomposites. As shown in Figure 8-7, at filler

concentrations of 0.4, 0.8 and 1.5v% and at a frequency of 20 Hz, the MWCNT/PVDF

nanocomposites exhibited dielectric permittivities of 91, 290 and 618, respectively, while the

dielectric permittivities of the CuNW/PVDF nanocomposites were 230, 577 and 1189,

respectively. The higher dielectric permittivity of CuNW/PVDF nanocomposites can be related

to the higher conductivity of CuNWs compared to MWCNTs. The higher conductivity of

CuNWs provided the composites with greater amount of mobile charge carriers participating in

the interfacial polarization leading to larger dielectric permittivity. Thus, the CuNW/PVDF

nanocomposites presented superior dielectric permittivity to MWCNT/PVDF nanocomposites.

227

Figure 8-8 shows the dielectric loss () as functions of filler content and frequency for both

types of nanocomposites. It can be seen that the dielectric loss rose significantly with filler

content. The increase of dielectric loss with filler content can be attributed to enhanced Ohmic

loss and polarization loss. At higher filler contents, the amount of dissipating nomadic charges is

higher. Moreover, increase in filler content is associated with the developed conductive network

formation in which the electrons have greater mean free path to move in each half cycle of

alternating field, thereby dissipating more electrical energy [7, 35]. All these phenomena lead to

higher Ohmic loss, which is linked to dissipation of energy in phase with alternating field. In

addition, the augmented polarization loss arising from interfacial polarization is another

significant factor increasing the dielectric loss at higher filler contents.

(a) (b)

Figure 8-8: Dielectric loss () :(a) MWCNT/PVDF; (b) CuNW/PVDF nanocomposites.

228

The dielectric loss displayed a frequency-independent behavior in the insulative region, but it

dropped drastically with frequency in the conductive region. The decaying trend of dielectric loss

with frequency can be ascribed to reduced Ohmic loss and polarization loss. As a matter of fact,

frequency increase accompanies with reduced available times for free electrons to travel

throughout the conductive network in each half cycle of alternating field, i.e. reduced Ohmic

loss. Furthermore, due to interfacial polarization relaxation, the interfacial charge polarization

decays with frequency leading to lower dipole momentum and polarization loss.

As shown in Figure 8-8, it was surprisingly observed that the dielectric loss in CuNW/PVDF

nanocomposites was considerably lower than the MWCNT/PVDF nanocomposites, which is

significantly desirable for charge storage applications. At filler concentrations of 0.4, 0.8 and

1.5v%, the MWCNT/PVDF nanocomposites exhibited dielectric losses of 541, 7105 and

8.1106, respectively, while the dielectric losses of the CuNW/PVDF nanocomposites were

1020, 1142 and 4620, respectively, both at a frequency of 20 Hz. The lower dielectric loss of the

CuNW/PVDF nanocomposites is ascribed to the presence of oxide layer on the surface of

CuNWs avoiding the formation of a conductive network. In other words, oxide layer reduced the

Ohmic loss through shrinking the available free path of nomadic charges by decaying the

conductive network formation. It is worthwhile to mention that although polarization loss in the

CuNW/PVDF nanocomposite was higher (due to higher dielectric permittivity); however, the

Ohmic loss played the dominant role in enhancing the dielectric loss.

The dielectric permittivity and dielectric loss are related to each other with the term

dissipation factor, which is of great importance in industry since it includes the effects of both

dielectric permittivity and dielectric loss.

229

(8-2)

The lower the dissipation factor of a dielectric material, the better is its performance for charge

storage applications. Figure 8-9 depicts the dissipation factors of the MWCNT/PVDF and

CuNW/PVDF nanocomposites as functions of filler content and frequency. It can be observed

that the dissipation factors of the CuNW/PVDF nanocomposites are orders of magnitude lower

than the MWCNT/PVDF nanocomposite. For instance, at filler concentrations of 0.4, 0.8 and

1.5v% and at a frequency of 20 Hz, the MWCNT/PVDF nanocomposites presented dissipation

factors of 5.9, 2.4103 and 1.310

4, while the CuNW/PVDF nanocomposites showed the

dissipation factors significantly lower and equal to 4.5, 2.0 and 3.9, respectively. As a matter of

fact, high conductivity of fresh core of CuNWs (high dielectric permittivity) combined with the

presence of oxide layer on their surfaces (low dielectric loss) led to novel composites with

superior dielectric properties and reduced dissipation factors.

230

(a) (b)

Figure 8-9: Dissipation factor (tan ) as function of the frequency: (a) MWCNT/PVDF

nanocomposites; (b) CuNW/PVDF nanocomposites.

Figure 8-10 shows a scheme of the oxide layer formation on the outer surface of CuNWs.

This layer avoids the direct contact between the nanowires leading to very low energy losses.

The fresh core of the CuNWs provides the composite with high interfacial polarization.

Therefore, it can be claimed that we have used the formation of oxide layer, which is usually

assumed as a weakness for electronic applications, as a benefit to improve the dielectric

properties. This combined with high conductivity of fresh core of CuNWs draws a promising

future for CuNW/polymer composites as charge storage materials.

231

Figure 8-10: Scheme of core-shell structured CuNW, composed of a non-conductive shell (oxide

layer) and a conductive core (fresh copper), showing the blocking of the charge carriers at

internal interfaces of the individual CuNW.

8.6. Conclusions

The dielectric properties of the CuNW/PVDF and MWCNT/PVDF nanocomposites, prepared

by coagulation technique followed by compression molding, were compared. It was observed

that the dielectric permittivity and dielectric loss increased drastically with conductive filler

content for both types of nanocomposites. The ascending trend of dielectric permittivity with

filler content was ascribed to the formation of an abundance of nanocapacitor structures, i.e.

conductive nanofiller as nanoelectrode and polymer matrix as nanodielectric. The increase of

dielectric loss with filler loading was attributed to enhanced Ohmic loss and polarization loss

arising from conductive network formation and developed interfacial polarization, respectively.

The results also showed that the dielectric permittivity and dielectric loss declined with

frequency for both types of nanocomposites, which was attributed to polarization relaxation and

reduced Ohmic loss and polarization loss, respectively.

232

Comparing the dielectric properties of the MWCNT/PVDF and CuNW/PVDF

nanocomposites showed that the CuNW/PVDF nanocomposites presented higher dielectric

permittivity, lower dielectric loss and consequently significantly lower dissipation factor than of

the MWCNT/PVDF nanocomposites. Higher dielectric permittivity of the CuNW/PVDF

nanocomposite was attributed to greater intrinsic conductivity of fresh core of CuNWs relative to

MWCNTs, thereby providing the nanocomposites with more free charges taking part in

interfacial polarization. Lower dielectric loss in the CuNW/PVDF nanocomposites was ascribed

to the presence of oxide layer on the surface of CuNWs averting the direct contact between

CuNWs. In conclusion, it can be claimed that high conductivity of fresh core of CuNWs

combined with the presence of oxide layer on their surfaces led to novel composites with

superior dielectric properties.

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Chapter 9

Summary, Conclusions and Future Work

9.1. General Background and Project Objectives

In the current competitive market of electronics, companies are taking effort to produce

lighter weight and smaller electronic devices with enhanced functionality and design options.

Accordingly, conductive filler/polymer composites (CPCs) have attracted great attention to

satisfy these requirements, due to their tunable electrical conductivity, light weight, low cost,

corrosion resistance and easy processability [1, 2]. CPCs are made by incorporating conductive

filler into a polymer matrix. Conventional polymers such as polycarbonate (PC), polystyrene

(PS) and poly(vinylidene fluoride) (PVDF) are insulative; however, adding conductive fillers to

these polymer matrices can provide them with wide a range of conductivities through the

formation of a conductive network.

The ability to regulate the conductive network formation in CPCs enables them to present a

wide spectrum of conductivity, and to perform as insulative, semi-conductive or conductive

materials. The level of electrical conductivity defines the applications in which CPCs can be

used. Charge storage, ESD protection and EMI shielding are the major applications of CPCs,

requiring low, medium and high electrical conductivity, respectively.

Accordingly, this dissertation aimed to create unique morphologies of nanocomposites by

manipulating mixing methods and processing conditions employing different nanofillers, and

then relating the obtained morphologies to the final electrical properties, i.e., electrical

237

conductivity, electromagnetic interference (EMI) shielding and dielectric properties. In order to

perform do this, multi-walled carbon nanotube (MWCNT) was selected as the conductive filler,

due to its extraordinary electrical properties and increasing industrial usage; and PC, PS and

PVDF were employed as the polymer matrices.

In this dissertation, controlling the conductive network formation was the key aspect in

designing the morphology of CPCs for electrical applications. Improving the conductive network

formation enhances electrical conductivity and EMI shielding; whereas, deteriorating the

conductive network formation decreases the leakage current, thereby improving dielectric

properties [1-4]. Having the knowledge of controlling the conductive network formation enables

the manufacturers to employ cost-effective materials and proper processing conditions to attain

the desired properties. In this dissertation, two distinct techniques were employed to manipulate

the conductive network formation to improve the electrical properties including:


Changing the type of conductive filler (substituting MWCNTs with copper nanowires

(CuNWs))

This dissertation was directed to scrutinize the influence of the above-mentioned techniques

on electrical properties of CPCs. These techniques were manipulated to tailor the conductive

network formation to improve electrical conductivity and EMI shielding or dielectric properties.

238

9.2. Electrical Behaviors of CPCs and the Mechanisms Behind

Prior to exploring the influence of the above-mentioned techniques on the electrical properties

of CPCs, some studies were implemented on MWCNT/polymer composites to obtain a general

understanding of the realm of CPCs and their electrical behaviors. These studies investigated the

electrical behaviors of MWCNT/polymer composites, as typical CPCs, as functions of MWCNT

loading and composite thickness, and were used to describe the mechanisms behind the behavior.

9.2.1. Volume Resistivity

Volume resistivity is the reciprocal of electrical conductivity and defined as the electrical

resistance through a cube of a material. When expressed in ohmcm, it would be the electrical

resistance through a one-centimeter cube of a material. Volume resistivity is considered to be an

important factor when dealing with the bulk of materials, such as EMI shielding and charge

storage. Volume resistivity of materials is a property which spans a very wide range. The

resistivity of insulators is typically more than 1014

Ωcm, that of semi-conductive materials

covers the range 1014

to around 1 Ωcm, and for semi-metals and metals it is less than 1 Ωcm.

The results showed that the volume resistivity of MWCNT/polymer composites decreased

with increase in MWCNT content due to formation of conductive network. Generally speaking,

the descent of volume resistivity with MWCNT concentration can be better described by the

percolation curve (volume resistivity versus MWCNT content curve). The percolation curve of

CPCs can be divided into three distinct regions: 1) the region far below the percolation threshold

239

(insulative zone), (2) the region where percolation occurs (percolation zone) and (3) the region

far above the percolation threshold (conductive zone).

In the insulative region, the MWCNTs are far from each other and the polymer matrix

restricts the conductance, due to its insulative properties. By raising the filler loading further, the

fillers get closer and ultimately at a critical concentration range called the percolation threshold,

the first conductive network forms, which lets the current pass through. In the percolation region,

where percolation occurs, the free electrons in conductive filler will increasingly play the role of

charge carriers due to direct contact between MWCNTs; thus, the resistivity of nanocomposite

diminishes by several orders of magnitude. After percolation, as the filler concentration

increases, the clusters initiate connections with each other to form a 3-D network which leads to

further decrease in resistivity. Nevertheless, in the conductive region, the constriction resistance

of contact spots between MWCNTs leads the resistivity to decrease marginally. In fact, a

considerable amount of current dissipates at the contact spots between the conductive fillers

leading to a plateau in the percolation curve at high MWCNT concentrations.

9.2.2. EMI Shielding

Electronic devices inherently irradiate electromagnetic (EM) waves. As these waves can

interfere with the operation of other electronics, related agencies have applied regulations to

shield the EM waves. In order to perform effective shielding, electronics should be enclosed with

appropriate conductive shields. CPCs are promising candidates to shield electronics, due to their

low weight, low cost, and easy processability that improve design options and reduce or

eliminate the seams and penetrations in electronics’ enclosures.

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Conventional polymers, due to their insulative nature, are inherently transparent to incident

EM waves. However, CPCs due to presence of interacting mobile charge carriers in conductive

filler can shield the EM wave efficiently. EMI shielding in CPCs comprises three distinct

mechanisms; namely reflection, absorption and multiple-reflection. When an EM wave strikes a

medium with unlike intrinsic impedance from the space in which EM wave is propagating, a

portion of EM wave is reflected off from the shielding material surface; a portion of EM wave

penetrates through the material, which is attenuated through absorption mechanism; and the

remaining portion is transmitted out the material. The lower the power of the transmitted wave,

the higher is the efficiency of shielding material.

To study the shielding mechanisms of CPCs accurately, the contributions of absorption and

reflection to EMI shielding as functions of MWCNT concentration and material thickness were

investigated. It was observed that the values of both reflection and absorption increased with

increase in MWCNT concentration. The ascent in reflection with MWCNT loading is attributed

to higher amount of interacting mobile charge carriers on the surface of CPCs. However, the

ascending trend of absorption with MWCNT loading is more complicated to explain and is

attributed to higher imaginary permittivity (Ohmic loss) and real permittivity (polarization loss)

of the MWCNT/polymer composites [1, 2].

Real permittivity in MWCNT/polymer composites arises from the formation of a large

number of nanocapacitors, i.e., MWCNTs acting as electrodes and insulative polymeric layer

acting as dielectric material, and also presence of structural defects (polarization centers) in

MWCNTs [5-7]. Increasing MWCNT concentration results in an increase in both the number of

nanocapacitors and polarization centers, leading to higher real permittivity (charge polarization).

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In addition, increasing MWCNT concentration is accompanied with a reduction in the thickness

of insulative polymeric gaps between MWCNTs leading to greater electronic polarization of

polymeric layer. Hence, there is a direct relationship between MWCNT loading and the

polarization loss in AC field and shielding by absorption.

Imaginary permittivity of MWCNT/polymer composites originating from Ohmic loss also

contributes significantly to shielding by absorption, where energy is dissipated by movement of

the nomadic charge carriers along the MWCNTs. Increasing MWCNT concentration is

associated with an increase in the number of dissipating mobile charge carriers leading to higher

imaginary permittivity; and therefore, higher shielding by absorption. Moreover, as additional

networks are formed, the electrons have a greater mean free path in which to move according to

the direction of electric field in each half cycle and, consequently, could dissipate more electrical

energy, i.e. higher Ohmic loss.

Multiple-reflection is the third mechanism of shielding representing internal reflections inside

a conductive barrier. This mechanism usually occurs in materials with large interfacial areas,

such as filler-polymer systems. Multiple-reflection has a negative influence on overall EMI

shielding, since its resultant is an increment in transmitted wave. Multiple-reflection can be

ignored if the shield’s thickness is larger than the shield’s skin depth [3]. The skin depth is the

distance inside the conductive material at which the wave power decreases to of its incident

value and is defined as √ , where f is the wave frequency, μ is shield’s magnetic

permeability and σ is the shield’s electrical conductivity. As multiple-reflection cannot be

measured independently, its influence is inherent in shieldings by reflection and absorption. In

our samples, particularly at high shielding values, multiple-reflection can be ignored.

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9.2.3. Broadband Dielectric Spectroscopy of CPC

Generally, charge polarization in MWCNT/polymer composites arises from three sources,

namely 1) interfacial polarization, 2) MWCNT polarization, and 3) polymer polarization.

Interfacial polarization usually occurs in heterogeneous systems with phases with different

conductivities or real permittivities, such as MWCNT/polymer composites [8]. At the internal

phase boundaries of polymer and MWCNTs, nomadic charge carriers can be trapped and cause

charge polarization. As electric dipole has a magnitude equal to strength of each charge times the

separation between charges, the contribution of interfacial polarization to dielectric permittivity

can be orders of magnitude larger than other types of polarization, since the charge carriers are

separated over a considerable distance, i.e., at the mesoscopic scale. It is worthwhile to mention

that interfacial polarization diminishes greatly with increased frequency, due to the large

retardation time of interfacial polarization with respect to the electric field frequency at high

frequencies (relaxation phenomenon) [9].

MWCNT polarization also contributes to the real permittivity of MWCNT/polymer

composites, particularly at high frequencies where interfacial polarization is weak. It is believed

that the crystallographic defects in MWCNT structures may behave as polarized centers [10]. For

instance, a defect in the armchair-type CNT, which can conduct electricity, can cause the

surrounding region to be semiconducting. Therefore, in the molecular structure of MWCNTs,

there may be two regions with dissimilar conductivities that induce charge polarization on the

molecular scale.

The electronic polarization of polymer matrix also contributes to real permittivity, particularly

at high frequencies. In the narrow insulative gaps between MWCNTs, there may be a buildup of

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very high field strength, which is higher than the macroscopic field strength by a factor of M (i.e.,

M is the ratio of the average size of the conducting MWCNT aggregates to the average gap

width) [11]. This high field strength contributes significantly to the electronic polarization of

polymer matrix and, thus, real permittivity.

Real and imaginary permittivities of CPCs over the broadband frequency range are functions

of many parameters, including conductive filler and polymer matrix features, content of filler,

interaction of conductive filler and polymer matrix, frequency range, etc [12, 13]. The results

demonstrated that the real permittivity rose considerably, specifically at low frequencies, as the

MWCNT concentration approaches the percolation threshold or beyond. As a matter fact, huge

real permittivities close to or above the percolation threshold arose from the formation of a large

number of nanocapacitor structures experiencing interfacial polarization, i.e., MWCNTs as

nanoelectrodes and polymer matrix as dielectric material. It was also observed that the real

permittivity was frequency-independent in the insulative region (concentrations below the

percolation threshold); however, it was a strong function of frequency in the conductive region.

This phenomenon was related to relaxation phenomenon of interfacial polarization occurring at

higher frequencies. As a matter of fact, the accumulated charges at the interface did not adapt

themselves to increased frequency, resulting in the relaxation phenomenon.

Likewise, the results showed that the imaginary permittivity was very low at MWCNT

concentrations far below the percolation threshold; nonetheless, it increased considerably

(several orders of magnitude) as the MWCNT concentration approached the percolation

threshold. High imaginary permittivity at MWCNT concentrations close to or above the

percolation threshold was attributed to two mechanisms: (1) increase in the amount of interacting

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nomadic charges in the composite due to growth in the content of MWCNTs, and (2) the

formation of conductive network in the composite which provided the nomadic charges with

greater mean free path in which to move in each half cycle of alternating field. It was also

observed that imaginary permittivity was frequency-independent in the insulative region;

whereas it showed a very strong descending trend with frequency in the conductive region.

9.3. Effects of MWCNT Alignment, Induced by Injection Molding, on Volume Resistivity

and EMI Shielding

In order to explore the effects of MWCNT alignment, induced by an injection molding

machine, on the electrical properties of the injection molded MWCNT/PS composites, a series of

injection molding experiments were carried out on a 5.00 wt% MWCNT/PS composites using a

two-level, four-factor factorial design to study the impact of four processing parameters, i.e.,

mold temperature, melt temperature, injection/holding pressure and injection velocity on the

volume resistivity of the molded composites. An injection molding machine (Boy 12A) was used

to inject the MWCNT/PS nanocomposite melt into a rectangular cavity. The cavity was fed with

an edge gate and had dimensions of 22.86 × 10.16 × 2.0 mm.

The results showed a decrease of about ten orders of magnitude in the volume resistivity by

adding 5.00 wt% MWCNT, compared with pure PS. Interestingly, depending on the processing

conditions, differences in the volume resistivity up to six orders of magnitude was observed in

the thickness direction of the nanocomposites. The results revealed that the melt temperature

followed by the injection velocity had the greatest influence on MWCNT alignment and volume

resistivity, while the influences of mold temperature and injection pressure were unimportant. In

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other words, the composites produced at lower melt temperature and higher injection velocity

underwent higher shear rate, and thus presented greater MWCNT alignment. It was also

observed that the greater MWCNT alignment was associated with inferior conductive network

formation and higher volume resistivity.

To investigate the influence of MWCNT alignment on electrical properties at different

MWCNT concentrations, we used the results obtained from the experimental design of 5.00 wt%

MWCNT to select three processing conditions with the maximum possible variation in MWCNT

alignment, i.e., volume resistivity. In other words, knowing the considerable influence of melt

temperature and injection velocity on MWCNT alignment and volume resistivity of

MWCNT/PS nanocomposites, three different injection molding experiments (from sixteen

experiments in the experimental design) were employed to make samples with various MWCNT

alignments at different MWCNT concentrations. The selected injection molding experiments

were performed by manipulating just the melting temperature and injection velocity. The

samples made at different processing conditions were used to investigate the effects of MWCNT

alignment on the electrical properties of MWCNT/PS composites at different MWCNT

concentrations. To have a better comprehension of the effects of MWCNT alignment on the

electrical properties, the electrical properties of the injection molded samples were compared

with those of the compression molded samples, where MWCNTs were determined to be

randomly distributed.

The results displayed that the injection molded (MWCNT-aligned) samples showed a higher

volume resistivity and percolation threshold than the compression molded (randomly distributed

MWCNTs) samples. Using the Raman spectroscopy in conjunction with volume resistivity

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results, it can be claimed that the greater the alignment of MWCNTs, the higher are the

resistivity and percolation threshold of MWCNT/polymer composites. We contend that the

alignment of MWCNTs reduced the probability of MWCNTs being connected with each other,

which gave rise to a higher volume resistivity and percolation threshold.

It was also observed that the injection molded samples showed inferior EMI shielding than

the compression molded samples in the X-band frequency range (8.2 – 12.4 GHz). Moreover, the

results demonstrated that the higher MWCNT alignment corresponded to lower EMI shielding.

As there is an inverse relationship between MWCNT alignment and MWCNT connectivity, it

can be interpreted that greater MWCNT connectivity in the compression molded samples caused

higher EMI shielding. The obtained results are in agreement with researchers who believe that

EMI shielding does not require filler connectivity; nevertheless, it rises with filler connectivity

[2, 14].

To obtain more in-depth knowledge about the effect of MWCNT alignment on EMI shielding,

the impacts of MWCNT alignment on shielding by reflection and absorption were investigated.

We observed that at different MWCNT concentrations, the shielding by reflection of the

compression molded and injection molded samples were almost identical. This similarity was

described by the fact that the MWCNT surface projection normal to the incoming EM wave had

comparable area regardless of whether the MWCNTs were aligned or not. However, the

shielding by absorption was extremely sensitive to MWCNT alignment. The inverse relationship

between MWCNT alignment and conductive network formation says that the shielding by

absorption may be a strong function of MWCNT connectivity. To verify this hypothesis, the

effects of MWCNT alignment on real and imaginary permittivities were studied.

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It was interesting to observe that the real permittivity of the compression molded samples was

higher than injection molded samples in the X-band frequency range. This was attributed to

larger electronic polarization of polymer matrix in the compression molded samples. In fact, in

narrow insulative gaps between MWCNTs, very high field strength may build up, which is

higher than the macroscopic field strength by a factor of M (i.e., M is the ratio of the average size

of the conducting MWCNT aggregates to the average gap width) [15]. This high field strength

contributes significantly to the electronic polarization of the polymer matrix. Since the

possibility that MWCNTs neighbor each other in the compression molded samples was greater,

the insulative gaps of the polymer were thinner, resulting in a higher electric field and greater

electronic polarization of the polymer matrix. Therefore, the compression molded samples

showed greater real permittivity than injection molded samples. In conclusion, it can be claimed

that higher polarization of the polymer matrix in the compression molded samples played a

significant role in greater polarization loss and enhanced absorption.

We also observed that the imaginary permittivity of the injection molded samples was lower

than that of the compression molded samples and the level of this difference increased

tremendously with increase in MWCNT concentration. The higher imaginary permittivity of the

compression molded samples was ascribed to the enhanced conductive network formation, i.e.,

there was enhanced MWCNT network formation in the compression molded samples. At

enhanced conductive network formation, the electrons have a greater mean free path in which to

move according to the direction of electric field in each half cycle of alternating field, and

consequently, can dissipate more electrical energy. Greater electrons’ mean free path at lower

MWCNT alignments can be related to improved MWCNT network formation, leading to larger

248

conduction current. Thus, it can be concluded that the greater electrical energy loss by free

electrons in each half cycle of alternating field in the compression molded samples, due to

greater electrons’ mean free path, contributed considerably to higher shielding by absorption.

Since the electrical conductivity and EMI shielding of the compression molded samples were

greater than those of the injection molded samples, it can be concluded that in order to obtain

high electrical conductivity and EMI shielding in injection molding process, the mold and

processing conditions should be designed in such a way to obtain random distribution of

MWCNTs.

9.4. Effects of MWCNT Alignment, Induced by Injection Molding, on Dielectric Properties

The materials used for charge storage applications are required to present high real

permittivity with a low leakage current, i.e., imaginary permittivity. High real permittivity with a

low leakage current in CPCs can only be attained at filler contents very close to the percolation

threshold [16]. The enhanced real permittivity observed in CPCs near the percolation threshold

arises from the formation of a large number of nanocapacitors, i.e., conducting clusters isolated

by thin layers of polymer. These nanocapacitors entitle CPCs to store large amount of charges.

Nevertheless, the insulator-conductor transition that occurs in CPCs at the percolation threshold

leads to a drastic variation in the volume resistivity and imaginary permittivity; thereby it

prevents employing CPCs as charge storage materials above the percolation threshold. Hence,

there is a very narrow concentration window near the percolation threshold for high aspect ratio

fillers, such as MWCNTs, to regulate the dielectric properties.

249

In this dissertation, MWCNT alignment was introduced as an innovative technique to improve

the dielectric properties and to broaden the narrow concentration window used to regulate the

dielectric properties. Actually, the dielectric properties results used to justify the effects of

MWCNT alignment on EMI shielding were analyzed for another scenario, i.e., charge storage

applications. Comparing the percolation curve of the compression molded and injection molded

samples showed that the sharp decline in the volume resistivity of the injection molded samples

around the percolation threshold was muted in comparison to that of the compression molded

samples. Therefore, it can be asserted that the MWCNT alignment can provide a wider

concentration window around the percolation threshold to regulate the dielectric properties.

Wider insulator-conductor transition window decreases the challenges and risks in manipulating

CPCs around the percolation threshold to obtain the preferred dielectric properties.

We observed that the imaginary permittivities of the injection molded samples were

significantly lower than those of the compression molded samples. Lower imaginary permittivity

of the injection molded samples relative to the compression molded samples was related to

inferior network formation and lower Ohmic loss arising from MWCNT alignment. Nonetheless,

MWCNT alignment showed an adverse influence on the real permittivity. This was also related

to a lower chance of MWCNTs neighboring each other leading to a poorer electronic

polarization of polymer matrix.

Therefore, MWCNT alignment reduced both real and imaginary permittivities; however,

charge storage materials are required to present high real permittivity and low imaginary

permittivity. Hence, it is necessary to evaluate the overall impact of MWCNT alignment on the

dielectric properties. Hence, the dissipation factors (imaginary permittivity/real permittivity) of

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the compression molded and injection molded samples at different MWCNT concentrations were

compared with each other. The results showed that injection molded samples presented lower

dissipation factor than compression molded samples, thereby improving dielectric properties. In

other words, the positive effect of the MWCNT alignment on reducing the dissipative energy

dominated its adverse effect on decreasing the capacitive energy. In brief, this study shows that

injection molding process, as an industrial technique, can be creatively employed to improve the

dielectric properties of MWCNT/polymer composites for charge storage applications.

9.5. Novel CuNW/PVDF Nanocomposites for Charge Storage: Comparison of its Dielectric

Properties with MWCNT/PVDF Nanocomposite

The CPCs used for charge storage applications are needed to present high real permittivity

and low imaginary permittivity. In order to attain a high real permittivity, highly conductive

fillers are greatly appreciated, since greater amount of nomadic charges would be available for

charge polarization. The limited electrical conductivity of MWCNTs was the stimulation to

investigate the dielectric properties of CuNW/polymer composites, due to superior electrical

conductivity of CuNWs to MWCNTs.

Highly conductive CuNWs are prone to provide enhanced charge polarization. However,

unavoidable oxide layer formation on the surface of CuNWs acts as a barrier and significantly

reduces the electrical conductivity of CuNWs. Unavoidable oxide layer formation on the surface

of CuNWs, which has always been a disadvantage for electronics applications, was innovatively

employed as an advantage to decay the conductive network formation and reduce the imaginary

permittivity. In fact, the oxide layer around CuNWs has the potential to avoid the direct contacts

251

between CuNWs leading to inferior conductive network formation (lower energy loss). On the

other hand, the fresh core of CuNWs can provide the composite with considerable free charges

for interfacial polarization. The results showed that high conductivity of fresh core of CuNWs in

combination with the presence of oxide layer on their surfaces caused CuNWs to show superior

dielectric properties relative to MWCNTs.

9.6. Recommendations

Processing conditions, composite morphology and composite components are the three key

factors to be manipulated to obtain the desired electrical properties. In other words, obtaining

preferred electrical properties in CPCs is possible by tailoring the processing conditions and

composite morphology using proper conductive fillers. Given these factors, the following

subjects are recommended for future work:

Developing a comprehensive model to include the effects of alignment, dispersion,

conductivity of filler and wave frequency on electrical properties of CPCs. The starting

point for this model can be the equations developed for electrical properties of conductive

monolithic materials. It should be noted that in employing these equations for CPCs the

effects of real permittivity and charge polarization should be embedded.

Studying the influence of MWCNT alignment on the broadband EMI shielding and

dielectric properties of MWCNT/polymer composites. In this dissertation, the influence of

alignment on the electrical properties of MWCNT/polymer composites was just studied

over the X-band (8.2 – 12.4 GHz). Broadband spectroscopy of electrical properties will

252

provide further information about the EMI shielding mechanisms and their relationship

with real and imaginary permittivities.

Comparing the EMI shielding and dielectric properties of CPCs holding MWCNTs and

CuNWs over the X-band. This investigation can give further information about the

mechanisms behind the relationship between intrinsic conductivity of filler and EMI

shielding for high-frequency applications.

Investigating the effect of degree of CuNW oxidation on the electrical properties of

CuNW/polymer composites.

Manipulating the structure of MWCNTs in order to obtain desired electrical properties in

MWCNT/polymer composites, i.e., doping MWCNTs to improve electrical conductivity

and EMI shielding or creating structural defects to improve the dielectric properties.

Incorporating secondary ferroelectric filler such as BaTiO3, as insulating barrier, to

deteriorate conductive network formation and improve the dielectric properties of

MWCNT/polymer composites. Next, injection molding of the made composites to

examine the impacts of both MWCNT alignment and barrier layer in improving the

dielectric properties for charge storage applications.

Investigating the influence of novel nanofillers, such as exfoliated nanographene, on the

electrical properties of CPCs.

253

Employing injection-compression molding to produce CPCs with high electrical

conductivity and EMI shielding. In this way, we can combine the benefits of injection

molding, as a mass production technique, and compression molding to get random

distribution of MWCNTs. As shown in the thesis, unavoidable MWCNT alignment in

injection molding process has an adverse effect on electrical conductivity and EMI

shielding.

Incorporating MWCNTs into a blend with the following features to obtain enhanced

dielectric properties: a blend with one dispersed phase and one continuous phase; the

MWCNTs should have higher affinity to dispersed phase. Accordingly, we can obtain

high real permittivity originating from MWCNT within dispersed phase and low

imaginary permittivity due to lack of a conductive network throughout the composite.

The MWCNT concentration should be low enough to not let any network form in the

continuous phase.

It was mentioned that in conductive monolithic materials, the reflection loss is a function

of whereas the absorption loss is a function of , where is electrical

conductivity and is magnetic permeability. It is known that EM wave is composed of

two components; namely electric field and magnetic field. Thus, it is important to employ

a hybrid system of filler to shield both electric field and magnetic field. We recommend

using a hybrid system of a conductive filler and a magnetic filler. As listed in Table 2-3,

silver has higher electrical conductivity and nickel has higher magnetic permeability

relative to copper. This provides an opportunity to investigate the electrical properties of

254

composites comprising silver or nickel nanowires or their hybrid system. It is highly

recommended that the fillers used in hybrid composites have aspect ratios of the same

order of magnitude. The information obtained from this study can shed more light on the

relationships between filler intrinsic properties and electrical properties of composites.

Investigating the hybrid system of MWCNT and CuNW (CuNW is more conductive and

MWCNT has higher aspect ratio and surface area) to obtain enhanced dielectric

properties. It should be regarded that both electrical conductivity and surface area are

important factors in the final dielectric properties.

Studying the effects of foaming on dielectric properties due to its impact on decaying the

conductive network formation [17]. Foaming, like alignment, is a novel way to improve

dielectric properties, and to widen the typically narrow concentration window used to

regulate dielectric properties.

Injection molding of CuNW/polymer composites to take advantage of the influence of

oxidative layer on the surface of CuNWs together with CuNW alignment on the dielectric

properties.

Covering the surface of MWCNTs with an oxidative layer, such as polymer layer or

surfactant to decrease imaginary permittivity for charge storage applications.

Investigating the rheological properties of injection molded samples versus

compression molded samples. This will provide more information on the effects of

MWCNT alignment on viscosity and shear rate, which can be an important factor on

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aspect ratio loss and developed morphology in injection molded samples. Investigating

this concept is important due to significant impact of MWCNT aspect ratio on electrical

properties. (MWCNT aspect ratio is decreased by more sever processing.)

9.7. References



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[10] L. Qi, B.I. Lee, S.H. Chen, W.D. Samuels, G.J. Exarhos, High-dielectric-constant silver-

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[12] Huang Y, Li N, Ma YF, Feng D, Li FF, He XB, et al. The influence of single-walled

carbon nanotube structure on the electromagnetic interference shielding efficiency of its

epoxy composites. Carbon. 2007;45(8):1614-21.

[13] Higginbotham AL, Stephenson JJ, Smith RJ, Killips DS, Kempel LC, Tour JM. Tunable

permittivity of polymer composites through incremental blending of raw and

functionalized single-wall carbon nanotubes. Journal of Physical Chemistry C.

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[14] Al-Saleh MH, Sundararaj U. Electromagnetic interference (EMI) shielding effectiveness

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[15] Gusev AA, Guseva OA. Voltage breakdown in random composites. Adv Eng Mater

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[16] Jiang MJ, Dang ZM, Bozlar M, Miomandre F, and Bai JB. Broad-frequency dielectric

behaviors in multiwalled carbon nanotube/rubber nanocomposites. J Appl Phys 2009;

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[17] Mahmoodi M, Arjmand M, Sundararaj U, Park S. Broadband dielectric spectroscopy of

carbon nanotube filled polystyrene foamed nanocomposites. Extended abstracts, SPE-

ANTEC Tech. Cincinnati, April 22-24, 2013.

electrical conductivity, electromagnetic interference

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