cccccccccc#2 thermal and temporal stability of...

Thermal and temporal stability of ferroelectret films made from

cellular polypropylene/air composites

Axel Mellinger1, Michael Wegener, Werner Wirges, Rajendar Reddy Mallepally2,

and Reimund Gerhard-Multhaupt

Department of Physics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany

Abstract:

Ferroelectrets are thin films of polymer foams, exhibiting piezoelectric properties after electrical

charging. Ferroelectret foams usually consist of a cellular polymer structure filled with air. Polymer-

air composites are elastically soft due to their high air content as well as due to the size and shape of

the polymer walls. Their elastically soft composite structure is one essential key for the working

principle of ferroelectrets, besides the permanent trapping of electric charges inside the polymer

voids. The elastic properties allow large deformations of the electrically charged voids. However, the

composite structure can also possibly limit the stability and consequently the range of applications

because of, e. g., penetration of gas and liquids accompanied by discharge phenomena or because of a

mechanical pre-load which may be required during the application. Here, we discuss various stability

aspects related to the piezoelectric properties of polypropylene ferroelectrets. Near and below room

temperature, the piezoelectric effect and the stability of the trapped charges are practically

independent from humidity during long-time storage in a humid atmosphere or water, or from

operating conditions, such as continuous mechanical excitation. Thermal treatment of cellular

polypropylene above 10°C leads to a softening of the voided structure which is apparent from the

decreasing values of the elastic modulus. This decrease results in an increase of the piezoelectric

activity. Heating above 60°C, however, leads to a decrease in piezoelectricity.

1 Introduction

Ferroelectrets are polymer-air composites with piezoelectric properties [1, 2]. They are formed by

foaming charge-storing electret polymers, have void sizes of tens of µm in length and several µm in

height and exhibit a typical cellular structure as shown in Fig. 1 (left). As most of the voids are

closed, cellular ferroelectrets may described as 0-3 void-polymer composites in the connectivity nota-

tion employed by Newnham et al. [3]. Applications of a high electric field leads to Paschen break-

1 Email of corresponding author: [email protected] Present address: Lehrstuhl für Thermische Verfahrenstechnik der Universität Erlangen Nürnberg, Egerlandstr. 3,

91058 Erlangen, Germany

1

This manuscript was published in Ferroelectrics 331, 189–199 (2006)

down, thereby depositing an internal charge at the top and bottom of the void surfaces as schematical-

ly shown in Fig. 1 (right). These charges of opposite polarity form macroscopic dipoles. Due to the

morphology, the void heights and thus the dipole moment can be easily changed by applying a me-

chanical stress, leading to an electric signal. Through this mechanism, ferroelectrets obtain their

piezoelectric properties. In the most widely studied ferroelectret, polypropylene (PP) foams, typical

d33 coefficients of several hundred pC/N and pm/V have been determined for the direct and inverse

piezoelectric effect, respectively (see for instance the reviews [1, 2] and references therein). These

values are comparable to the piezoelectric activity of many electroceramics [5]. The polarity of the

trapped charges (and thus the polarization) can be switched by successively applying high electric

fields of opposite sign. The electric field must be above a threshold value [6, 7] in order to initiate the

micro-plasma discharges as basis for the internal charging process [8]. Thus, ferroelectrets are dis-

cussed as ferroic materials because of the following features: at least two stable polarization states (i),

which can be switched (ii) with electric fields above a threshold (iii). These properties are comparable

with those of ferroelectric materials; the underlying mechanisms, however, are completely different.

During the last five years, the preparation of voided polymer structures, the electrical charging via

electric breakdown phenomena within the voids as well as the resulting elastic and piezoelectric prop-

erties have been studied and optimized in several laboratories, as summarized in References [1] and

[2]. This work was mainly done on cellular polypropylene films, the “workhorse” of ferroelectret re-

search. Recently, the material base for ferroelectrets has been enlarged to other polymers, such as

Teflon® AF [9], polyethylene terephthalate (PETP) [10, 11] as well as cyclo-olefin polymers and

copolymers [12-14]. However, at present these materials require expensive matrix polymers or suffer

from d33 coefficients that are inferior to those of cellular PP.

In some kinds of PP and PETP ferroelectrets (those prepared by extrusion and stretching of a filler

loaded polymer) the piezoelectric properties are strongly dependent on their elastic properties, which

in turn depend on the morphology of the material [10, 15-17], as is schematically shown in Fig. 2.

Variation of the elastic properties is usually achieved by changing the void heights in various types of

inflation processes, as described in detail in, e.g., [4, 18-20]. Typical values for the elastic stiffness

and the piezoelectric coefficient of cellular PP and PETP are summarized in Tab. 1.

Despite the high relevance for applications, only a few investigations on the stability of ferroelec-

trets have been published. Investigations of the stability against ultraviolet light showed that irradia-

tion of PP ferroelectrets at wavelengths shorter than 210 nm decreases the piezoelectric activity

through partial photostimulated discharge [22]. The thermal stability of PP ferroelectrets strongly de-

pends on preparation and pre-aging procedures. Based on the pyroelectric properties of (non pre-

aged) cellular PP, a thermal stability up to 60°C was discussed [23]. Some recently published mea-

2


surements show a similar dependence for the piezoelectric properties [24, 25]. With PETP ferroelec-

trets the thermal stability (currently at lower piezoelectric activity) is slightly enhanced [10]. The ther-

mal stability can be significantly enhanced by using cyclo-olefin polymer compounds (COC and

COP) with high glass transition temperatures as basis for ferroelectrets. In COC and COP ferroelec-

trets the piezoelectric activity exhibits long-term stability up to at least 100 °C, depending on the used

polymer compounds [14]. However, no systematic investigations covering the elastic properties dur-

ing heat treatment have yet been published.

In the present work, we investigate the elastic and piezoelectric properties of PP ferroelectrets dur-

ing thermal treatment at different temperatures. Furthermore, we describe the influence of a mechani-

cal load on the piezoelectric properties of PP ferroelectret films. These investigations are accompa-

nied by dynamic fatigue measurements by continuous excitation of the transducer films for at least

15 h as well as repeated measurements of piezoelectric activity during 200 days after sample prepara-

tion. In addition, we study changes in the electrical and mechanical parameters during exposure to a

humid environment.

2 Experimental Procedures

2.1 Thermal and electrical treatment of cellular polypropylene film

Cellular polypropylene films of different thickness (nominal values 37, 70, 100 and 130 µm) were

supplied by VTT Processes, Tampere, Finland. All samples were charged in a point-to-plane corona

discharge using corona-tip voltages above 20 kV to ensure a poling field above the threshold for ini-

tiating micro-discharges in the internal voids. The charged films were coated with metal electrodes

(50 nm thickness) in high vacuum. In most cases, the electrode material was aluminum, except for the

humidity studies, where gold electrodes were used. Long-term heat treatment in wet and dry atmo-

spheres was performed in a Heraeus Instruments oven. In order to measure the piezoelectric coeffi-

cient, the samples were removed from the oven and cooled down to room temperature. After the de-

termination of the d33 coefficient at room temperature, the samples were again exposed to the elevated

temperature. All treatment times given in section 3 are the accumulated exposure time to the elevated

temperature, excluding the time for the cooling procedure and the piezoelectric measurement.

2.2 Measurement of quasistatic and dynamic piezoelectric coefficients

Dynamic piezoelectric d33 coefficients were determined by means of dynamic mechanical excita-

3


tion of the sample with a stress amplitude of 10 kPa at a frequency of 2 Hz with a Brüel & Kjaer mod-

el 4810 shaker. In addition, a mechanical bias stress in the range of 10 to 90 kPa was applied to the

sample. The resulting electric response of the sample was amplified by means of a Brüel & Kjaer

model 2635 amplifier and recorded with a digital storage oscilloscope. The direct piezoelectric d33 co-

efficient was then calculated from the applied force and the resulting electrical signal. Quasistatic

piezoelectric d33 coefficients were determined with a mechanical load of 500 g.

2.3 Dielectric resonance spectroscopy

Assessing the long-term stability of ferroelectrets under ambient and humid conditions requires a

reliable method for determining their piezoelectric coefficients. Standard electromechanical methods

rely on applying a mechanical stress to the sample, which may cause irreversible or slowly reversible

creep in materials with a low elastic modulus [25], thus limiting the accuracy of the measurements.

Therefore, the all-electrical method of dielectric resonance spectroscopy was used instead. As an ad-

ditional benefit, other device and material parameters, such as the resonance frequency, the elastic

modulus and the electromechanical coupling constant could be determined from a single measure-

ment. The principles of this method have been discussed extensively in a recent review [26], so that

only a brief summary will be given here. Upon application of an oscillating electric field

0iωtE t = E e the sample exhibits length-, width- and thickness-extension resonances at its eigenfre-

quencies. For the thickness extension resonance of free-standing thin planar films, the complex capac-

itance is given by [27]

33

2

1( )

tan( 4 )1

4

TEa TE

ta TE

AC fh

kf

%(1)

where A and h are the area and thickness (height) of the film, ε33 is the 33 component of the permittivi-

ty tensor and fa,TE is the antiresonance frequency, calculated from the sample density and the elastic

modulus c33 via

331.a,TE

cf =

hρ(2)

kt is the electromechanical coupling constant and is related to the piezoelectric coefficient d33 via

3333

33t

ck d

(3)

4


Thus, a change in the elastic stiffness of piezoelectric materials results in a change of the thickness-

extension resonance frequency. The dielectric spectra were acquired with a Novocontrol® ALPHA

spectrometer under isothermal conditions (in a Novocontrol® Quatro cryostat) in the frequency range

between 200 kHz and 2 MHz. In order to accommodate mechanical losses, c33 and kt were assumed to

be complex. The measured dielectric spectrum was normalized with the spectrum of a precision low-

loss reference capacitor with a capacitance closely matching that of the sample film. This procedure

eliminated electrical artifacts in the 10…20 fF range caused by the switching of internal spectrometer

components.

3 Results and Discussion

3.1 Temporal stability and influence of a bias stress

At room temperature in ambient atmosphere, the piezoelectric activity of PP ferroelectret films de-

creases slightly within the first several days as shown in Fig. 3 (left). This decay is about 25, 36 and

20% for the films with a nominal initial thickness of 37, 70 and 100 µm, respectively. Apart from this

initial decay, however, the d33 coefficient is stable for periods of at least 200 days [28]. The decrease

during the first few days after charging may have different origins: (i) possible charge relaxations that

will reduce the amount of charges in the electric (macroscopic) dipoles, and (ii) structural modifica-

tions which may lead to thickness relaxations and thus to changes of the dipole size. Changes in the

film thickness (and thus of the film density) also modify the elastic properties as discussed above and

as schematically shown in Figure 2.

A change in the elastic properties also occurs when a static bias stress is applied to the relatively

soft PP ferroelectrets. The static stress reduces the thickness (and increases the density) of the trans-

ducer films. However, taking into account the dependence shown in Fig. 2, the piezoelectric activity

in films with different initial structures may either decrease or increase if a static bias stress is applied.

Figure 4 shows this behavior for a sample with maximum piezoelectric activity (and lowest elastic

stiffness). The bias stress leads to an increase of the elastic stiffness and to reduced piezoelectricity.

However, during long-term experiments, the d33 coefficients decreased only slightly when the bias

stress was applied for at least 14 hours.

5


3.2 Thermal stability

Cellular PP films are known to lose their piezoelectric properties if heated to temperatures above

50 °C for extended periods of time (typically, several days) [25, 29] as the increased electrical con-

ductivity leads to a gradual charge neutralization. This is clearly visible in Fig. 3 (right), where the d33

coefficient drops to 60 and 30% of the initial value in films with a thickness of 100 and 37 µm, re-

spectively, during annealing at 50 °C. The difference in the decay rates may be explained by the dif-

ferent morphology of the films.

The situation is different, however, for short-term (up to several hours) heating to 60…70 °C . The

short-term thermal stability of PP foam with a thickness of 70 µm is demonstrated by the dielectric

resonance map shown in Fig. 5. The frequency scans were acquired under isothermal conditions in

10 °C increments over a period of several hours. The strongest loss peak around 600 kHz is caused by

the thicknesses extension resonance while the weaker peak near 50 kHz results from a radial reso-

nance mode of the film coated with circular electrodes. Above room temperature, both resonance fre-

quencies decrease with increasing temperature, indicating a gradual softening of the material. For a

quantitative analysis, the temperature dependence of the material parameters was calculated via Eqs.

(1) – (3). The elastic modulus c33 shows a gradual decrease with temperature between 100 and

10 °C and a substantially accelerated decrease above 10 °C (cf. Fig. 6, right). The transition point is

located between 10 and 0 °C, slightly higher than the glass transition temperature Tg of atactic PP,

commonly quoted as 14 °C [30]. The small difference probably indicates a slight increase in Tg,

probably due to the mechanical stretching.

The change in the elastic modulus is not accompanied by qualitatively similar changes in thick-

ness, as shown by the plot of capacitance versus temperature in Fig. 7. As the samples form a parallel

plate capacitor, their capacitance is given by C' = εε0A/h where ε is the dielectric constant and ε0 is the

permittivity of free space. Since A can be considered virtually temperature-independent (any changes

in A would have a substantial effect on the radial extension resonance mode in Fig. 5) and ε is only a

weak function of temperature for both air and PP [31], a nearly temperature-independent capacitance

indicates that the thickness, too, is not a strong function of temperature.

The softening of the films at elevated temperatures has a profound effect on their piezoelectric co-

efficients. Films with higher sensitivity (film thicknesses 70 and 100 µm in Fig. 6) show a strong in-

crease in d33 if heated up to 60 °C for periods of a few hours (Fig. 6, left), in good agreement with the

results of Taylor and Fernández [25]. The increase is caused by a softening of the cellular structure

(Fig. 6, right) allowing for a larger deformation when an electric field or mechanical stress is applied.

Above 60 °C, d33 declines rapidly, marking the onset of irreversible charge decay. From the tempera-

6


ture dependence of c33 and d33, relative temperature coefficients

33c

cα =

T

(4)

and

33d

dα =

T

(5)

were calculated. The room-temperature (20 °C) values listed in Tab. 2 are as high as 0.012 K1, an im-

portant consideration in the design of device applications. It should be noted that thermal aging may

enhance the service temperature of cellular PP to about 80 °C. While this thermal aging lowers the

piezoelectric activity, the remaining piezoelectric coefficients of some kinds of cellular PP films are

still significantly higher than those of classical ferroelectric polymers.

3.3 Humid environments

For the investigation of material parameters in humid environments, charged cellular PP samples

(nominal thickness 100 µm) were coated with gold electrodes (50 nm thickness). One batch of these

films was immersed in distilled water and subjected to elevated temperatures, while another batch

from the same polymer sheet was subjected to the same temperatures in ambient atmosphere. Their

electrical and mechanical properties were measured in intervals of 3-10 days by recording and analyz-

ing the dielectric resonance spectra. After removing the samples from storage, two dielectric spectra

were recorded at room temperature approximately 15 min apart. All samples within their respective

batch exhibited a similar behavior; Fig. 8 shows the piezoelectric coefficient d33 and the elastic modu-

lus c33 of one sample each from the “wet” and “dry” group, respectively. In both cases, the piezoelec-

tric activity exhibits a slight (<15%) decline during the first 41 days, during which the temperature did

not exceed 45 °C. At 50 °C, a stronger 25% decrease in d33 is observed during a time span of 12 d.

This coincides with the onset of a thermally stimulated open-circuit discharge current [29]. The pres-

ence of water does not significantly accelerate the decay of d33. However, the humidity appears to

have a short-term softening effect, even though the sample masses showed no increase which might

be caused by the absorption of water. In Fig. 8, the elastic modulus at the time of removal from stor-

age is systematically lower compared to the values 15 min later. Correspondingly, a higher piezoelec-

tric activity is observed. The same effect is much weaker in the “dry” samples.

7


4 ConclusionsFerroelectret films have a great potential for many sensor and actuator applications due to their

high piezoelectric activity, mechanical flexibility, large area and low manufacturing cost. The current

“work horse” material, cellular polypropylene, excels with d33 coefficients of several hundred pC/N. It

also exhibits a high stability in humid environments, as well as under mechanical stress. The softening

of the films above the glass transition temperature around 10 °C gives rise to higher piezoelectric co-

efficients, with relative temperature coefficients of up to 0.01 K1. This temperature dependence must

be taken into account in may device applications.

For applications in environments above 50 °C, the limited long-term stability of PP ferroelectrets

becomes a problem. The present study did, however, shed some light on the stability of PP ferroelec-

trets under various conditions. With the significantly improved understanding of the mechanisms un-

derlying the decrease of piezoelectricity, it becomes possible to employ pre-aging procedures in order

to enable the use of ferroelectrets in more demanding applications.

8


References[1] Bauer S, Gerhard-Multhaupt R, and Sessler GM: Ferroelectrets: Soft electroactive foams for

transducers. Phys Tod. 2004;57 (2): 37-43.[2] Wegener M and Bauer S: Microstorms in cellular polymers: A route to soft piezoelectric trans-

ducer materials with engineered macroscopic-dipoles. ChemPhysChem 2005;6: 1014-1025.[3] Newnham RE, Skinner DP, and Cross, LE: Connectivity and Piezoelectric-Pyroelectric Com-

posites. Mat. Res. Bull. 1978;13: 525-536.[4] Wegener M, Wirges W, Fohlmeister J, Tiersch B, and Gerhard-Multhaupt R: Two-step inflation

of cellular polypropylene films: Voidthickness increase and enhanced electromechanical prop-erties. J Phys D Appl Phys. 2004;37: 623-627.

[5] Tressler JF, Alkoy S and Newnham RE: Piezoelectric Sensors and Sensor Materials. J. Electro-ceramics 1998;2: 257-272.

[6] Wegener M, Paajanen M, Wirges W, and Gerhard-Multhaupt R: Corona-induced partial discharges, internal charge separation and electromechanical transducer properties in cellular polymer films. In: Proceedings, 11th International Symposium on Electrets (ISE 11). Piscataway NJ: IEEE Service Center; 2002:54-57.

[7] Gerhard-Multhaupt R, Wegener M, Wirges W, Giacometti JA, Altafim RAC, Santos LF, Faria RM, and Paajanen M: Electrode poling of cellular polypropylene films with short high-voltage pulses. In: Proceedings, Annual Report Conference of Electrical Insulation and Dielectric Phenomena (CEIDP). Piscataway, NJ: IEEE Service Center; 2002:299-302.

[8] Lindner M, Hoislbauer H, Schwödiauer R, Bauer-Gogonea S and Bauer S: Charged cellular polymers with ‘‘Ferroelectretic’’ behavior. IEEE Trans Dielectr Electr Insul. 2004;11: 255-263.

[9] Mellinger A, Wegener M, Wirges W and Gerhard-Multhaupt R: Thermally stable dynamic piezoelectricity in sandwich films of porous and nonporous amorphous fluoropolymer. Appl. Phys. Lett. 2001;79: 1852-1854.

[10] Wegener M, Wirges W, and Gerhard-Multhaupt R: Piezoelectric polyethylene terephthalate (PETP) foams Specifically designed and prepared ferroelectret films. Adv Eng Mat. 2005;7: 1128-1131.

[11] Wegener M, Wirges W, Dietrich JP, and Gerhard-Multhaupt R: Polyethylene terephthalate (PETP) foams as ferroelectrets. In: Proceedings, 12th International Symposium on Electrets (ISE 12). Piscataway NJ: IEEE Service Center; 2005:28-30.

[12] Saarimäki E, Paajanen M, Savijärvi A-M, and Minkkinen H: Novel heat durable electromechanical film processing: Preparations for electromechanical and electret applications. In: Proceedings, 12th International Symposium on Electrets (ISE 12). Piscataway, NJ: IEEE Service Center; 2005:220-223.

[13] Savijärvi A-M, Paajanen M, Saarimäki E, and Minkkinen H: Novel heat durable electromechanical films: Cellular film making from cyclic olefin polymers. In: Proceedings, 12th International Symposium on Electrets (ISE 12). Piscataway, NJ: IEEE Service Center; 2005:75-78.

[14] Wegener M, Paajanen M, Voronina O, Schulze R, Wirges W, and Gerhard-Multhaupt R: Voided cyclo-olefin polymer films: Ferroelectrets with high thermal stability. In: Proceedings 12th International Symposium on Electrets (ISE 12). Piscataway NJ: IEEE Service Center; 2005:47-50.

[15] Wegener M, Wirges W, Gerhard-Multhaupt R, Dansachmüller M, Schwödiauer R, Bauer-Gogonea S, Bauer S, Paajanen M, Minkkinen H, and Raukola J: Controlled inflation of voids in cellular polymer ferroelectrets: Optimizing electromechanical transducer properties. Appl Phys Lett. 2004;84: 392-394.

[16] Wegener M, Tuncer E, Wirges W, Gerhard-Multhaupt R, Dansachmüller M, Bauer-Gogonea S, Schwödiauer R, and Bauer S: Ferroelectrets: Highly anisotropic electrically charged polymer foams for electromechanical transducer applications. In: Proceedings IEEE Ultrasonics

9


Symposium 2004. Piscataway, NJ: IEEE Service Center; 2004:1138-1141.[17] Hillenbrand J, Sessler GM, and Zhang X: Verification of a model for the piezoelectric d33

coefficient of cellular electret films. J Appl Phys. 2005;98: 064105.[18] Paajanen M, Wegener M, and Gerhard-Multhaupt R: Understanding the role of the gas in the

voids during corona charging of cellular electret films – A way to enhance their piezoelectricity. J Phys D Appl Phys. 2001;34: 2482-2488.

[19] Paajanen M, Minkkinen H, and Raukola J: Gas diffusion expansion – increased thickness and enhanced electromechanical response of cellular polymer electret films. In: Proceedings, 11th

Intern. Symposium on Electrets (ISE 11). Piscataway, NJ: IEEE Service Center; 2002:191-194.[20] Zhang X, Hillenbrand J, and Sessler GM: Improvement of piezoelectric activity of cellular

polymers using a double-expansion process. J Phys D Appl Phys. 2004;37: 2146-2150.[21] Ohigashi H: Electromechanical Properties of Polarized Polyvinylidene Fluoride Films as Stud-

ied by the Piezoelectric Resonance Method. J. Appl. Phys.1976;47: 949-955.[22] Mellinger A, Camacho Gonzalez F, and Gerhard-Multhaupt R: Ultraviolet-induced discharge

currents and reduction of the piezoelectric coefficient in cellular polypropylene films. Appl Phys Lett. 2003;82: 254-256.

[23] Neugschwandtner GS, Schwödiauer R, Bauer-Gogonea S, Bauer S, Paajanen M and Lekkala J: Piezo- and pyroelectricity of a polymer-foam space-charge electret. J Appl Phys. 2001;89: 4503-4511.

[24] Fernández O and Taylor DM: Effect of temperature on electroactive films of cellular polypropylene. In: Proceedings, International Conference on Solid Dielectrics. Piscataway, NJ: IEEE Service Center; 2004:784-787.

[25] Taylor D. M., Fernández O: Thermal instability of electromechanical films of cellular polypropylene. IEEE Trans. Dielectr. Electr. Insul. 2005;12: 768-778.

[26] Mellinger A: Dielectric resonance spectroscopy: a versatile tool in the quest for better piezoelectric polymers. IEEE Trans. Dielectr. Electr. Insul. 2003;10: 842-861.

[27] IEEE Standard on Piezoelectricity. ANSI/IEEE Std. 176, New York: The Institute of Electrical and Electronics Engineers; 1987.

[28] Wegener M, Mellinger A, Wirges W, Mallepally RR, and Gerhard-Multhaupt R: Ferroelectret cellular polypropylene films: Piezoeletric properties and thermal and temporal stability. In: Proceedings, 2nd International Workshop on Piezoelectric Materials and Applications in Actuators (IWPMA). Paderborn, Germany: Heinz Nixdorf Institute; 2005:27-34.

[29] Lekkala J, Paajanen M: EMFi – New Electret Material for Sensors and Actuators. In: Proceedings, 10th International Symposium on Electrets. IEEE Service Center, Piscataway, NJ; 1999: 743-746.

[30] Menczel JD, Jaffe M and Bessey WE: Films. In: Turi, E. A., eds. Thermal Characterization of Polymers. Academic Press; 1997: 1955-2089.

[31] McCrum NG, Read BE and Williams G: Anelastic and Dielectric Effects in Polymeric Solids. New York: Dover Publications; 1967.

10


11

Figure 1: Scanning-electron micrograph of a cross section of a PP ferroelectret film (left, after [4]) and schematic figure of the cellular structure with trapped charges (right).


12

Figure 2: Piezoelectric activity and elastic stiffness as function of the foam density: Schematic sketch of typical behavior found on ferroelectret PP and PETP foams prepared by extrusion and stretching of

a filler loaded polymer sheet (after [10])


13

Figure 3: Temporal stability of piezoelectric cellular PP films. Left: room-temperature quasistatic piezoelectric coefficient d33 of 37, 70 100 μm thick films. Right: decay of the quasistatic d33 coefficient at

50 °C in ambient atmosphere.


14

Figure 4: Changes in the dynamically measured piezoelectric d33 coefficient, recorded on a 70 µm cellular PP film with different static bias stresses.


15

Figure 5: Dielectric loss (C'') of a 70 µm cellular PP film as a function of frequency and temperature. The frequency spectra were acquired under isothermal conditions at temperatures between -100 and

+120 °C in 10 °C increments. The strong loss peak around 600 kHz results from the thickness extension resonance.


16

Figure 6: Piezoelectric d33 coefficients (left) and elastic moduli c33 (right) of three different PP ferroelectret films as a function of temperature. The data was obtained from piezoelectric resonance

measurements.


17

Figure 7: Change in capacitance of three cellular PP samples (same as in Fig. 6) during heating.


18

Figure 8: Piezoelectric coefficient d33 and elastic modulus c33 as a function of storage time in distilled water (left) or in ambient atmosphere (right) at successively higher temperatures. The open and solid symbols denote the results from the first and second dielectric resonance measurement, performed

immediately after removing the sample from storage and approx. 15 min later.


Table 1: Elastic and piezoelectric properties of PP and PETP ferroelectrets compared to non-cellular polyvinylidene fluoride (a ferroelectric polymer). Resonance frequencies are given for a sample thickness found in typical device applications.

elastic stiffnessc33 (MPa)

piezoelectric coefficientd33 (pC/N)

resonance frequencyfres (MHz)

reference

cellularPP 1.3 ... 14 up to 340 0.6 … 2 [15]cellular PETP 7 up to 23 0.56 [10]

PVDF 9470 17.4 10 … 30 [21]

19


Table 2: Material parameters for three types of PP foam, obtained with dielectric resonance spectroscopy. The temperature coefficients c and d are defined in Eqs. (4) and (5).

PP foam type

#1 #2 #3nominal expanded thickness [µm] 37 70 130elastic modulus c33 at 20 °C [MPa]temperature coefficient c at 20 °C [K-1]

10.70.0064

2.7

9.3

piezoelectric coefficient d33 at 20 °C [pC/N]temperature coefficient d at 20 °C [K-1]

23--

2080.0086

270.012

20


cccccccccc#2 thermal and temporal stability of...

Documents