OFFICE OF NAVAL RESEr\RCH

Gov't Order NAONR 27-73

Task No. NR 356-522

TECHNICAL REPORT NO. 1

PIEZO- AND PYROELECTRICITY IN POLYMER ELECTRETS

by

M. G. Broadhurst, C. G. Malmberg, F. I. Mopsik and W. P. Harris

Prepared for Publication

in the

Symposium Volume of the Electrochemical

Society - Conference on Electrets, Charge

Storage and Transport in Dielectrics - Miami Beach, Fla. October 8-13, 1972

Institute for Materials Research, National Bureau of Standards

Washington, D. C. 20234

March 1, 1973

Reproduction in whole or in p'art is permitted for

any purpose of the United States Government

Approved Public Release; Distribution Unlimited
(Proc. Gonf. on Eleotrets, Charge

Storage and Transport in Dielectrics,

Miami Beach, Fla., Oct. 1972),

Chapter in Electrets, Charge Storage

and Transport in Dielectrics, pp. 492-

504 (Electrochemical Society, New

York, N. Y., 1975)^
OFFICE OF NAVAL RESEARCH

Gov't Order NAONR 27-73

Task No. NR 356-522

TECHNICAL REPORT NO. 1

PIEZO- AND PYROELECTRICITY IN POLYMER ELECTRETS

by

M. G. Broadhurst, C. G. Malmberg, F. I. Mopsik and W. P. Harris

Prepared for Publication

in the

Symposium Volume of the Electrochemical

Society - Conference on Electrets, Charge

Storage and Transport in Dielectrics - Miami Beach, Fla. October 8-13, 1972

Institute for Materials Research, National Bureau of Standards

Washington, D. C. 2023A

March 1, 1973

Reproduction in whole or in p*art is permitted for

any purpose of the United States Government

Approved Public Release; Distribution Unlimited

DEPARTMENT OF THE NAVY

OFFICE OF NAVAL RESEARCH

ARLINGTON, VIRGINIA 22217 IN REPLY REFER TO

i47 2:GAlJ:mDl

31 ATig 1972

NR 356-522

Dr. M. G. Broadhurst

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ENCLOSURE Tl^y

PIEZO- AND PYROELECTRICITY IN POLYMER ELECTRETS

"M. G. Broadhurst, C. G. Malnberg, F. I. Mopsik and W. P. Harris

Institute for Materials Research, National Bureau of Standards

Washington, D. C. 2023A

ABSTRACT

A model for a polymer electret, based on an elastically isotropic solid with orientationally frozen molecular dipoles, was

developed and tested experimentally'. Tliis electret is shown to be

both piezoelectric and pyroelectric. The polarization is shown to

change with mechanically and thermally induced strains in the polarization direction. The currents generated by the electret will be

proportional to the strain rate and, for thin contact electrodes and

uniform strains, unaffected by the presence of . real charges. Poly

(vinyl chloride) films were poled at SO^C, just above their glass

transition temperature. The pressure-and temperature-induced shortcircuit currents in the polarization direction equalled 0 . 15 (pA/cm^)

/

(bar/min) and 2.2 (pA/cm'^) / (K/min) respectively for a specimen poled

at 320 kV/cm. These currents were 1) reversible and proportional to

the rate of temperature or pressure change, 2) proportional to

poling voltage" up to 320 kV/cm, 3) in the direction corresponding to

increasing polarization with increasing pressure and decreasing

temperature, 4) stable with time without special storage conditions,

5) about 1.6 times as great for temperature induced strains as for

equivalent pressure induced strains and 6) about 2-4 times as great

in magnitude as expected from dielectric constant measurements. The

apparent polarization from temperature measurements for the 320 kV/cm

specimen was about 1.7 uC/cm^, or about 1/3 the value expected for

maximum alignment of dipoles. In the same specimen the pyroelectric

coefficient was found to be P3 = - 0.39 nC/cva.^ K and, assuming

elastic isotropy, the piezoelectric strain coefficients Were found

to be d3i=d32=d33 = - 0.89 pC/N.

Introduction

Oliver Heaviside first postulated the existence of a permanent

electric monent in a dielectric solid [1]. Experinental confimation

came in the early 1920 *s with the work of Eguchi on wax and rosin

mixtures which were solidified in the presence of a strong electric

field [2]. It was recognized early [3], that two types of polarization were generally present in electrets - one due to a homocharge

having the same polarity, the other due to a heterocharge having the

opposite polarity to that of the adjacent polarizing electrode. It

is generally agreed that the heterocharge arises fron a more or less

uniform vola^e polarization of the dielectric by means of a permanent

dipole orientation, by charge diffusion, or by a not-yet-understood

charge separation and trapping mechanism. The homocharge is thought

to be real charge very near the dielectric surface and due to con- duction between dielectric and electrode, to field emission to or from the electrodes, or to breakdown in the electrode-specimen gap.

Contact electrif icatiop (due to rubbing the surface of the specimen)

is also a known source of surface charge.

Soon after their discovery, electrets were shown to be both

piezoelectric and pyroelectric [4], However, work on these effects

focused on crystalline solids and little work was done on amorphous

electrets'. In 1960 Gubkin [5] published an electrostatic theory of

piezoelectricity which did not involve the microscopic structure of

the electret. This approach would seem to be a much better description of the phenomenon of piezoelectricity in pol>'mer materials,

many of which are partially or completely amorphous, than the

classical approach [6] which is concerned with structure in the

dielectric. Fukada and coworkers [7] have reported results of a large number of measurements of piezoelectricity in biological and

synthetic pol>—lers and have emphasized the importance of structure

in interpreting the data. Other investigators have reported

measurements of piezoelectricity [8,9] and pyroelectricity

(9,10,11,12] in poly (vinylidene fluoride) (PVF2) films. The pyroelectric activity in polymers seems to be closely related to piezoelectric activity, and PVF2 is one of the most active of the pol\Tners

yet studied. As yet there seems to be no systematic experimental

approach to piezoelectric pol>'mers based on bulk theory such as that proposed by Gubkin. Below we give a brief summary of Gubkin's

theory and apply it to the piezo- and pyroelectric effects in

poly (vinyl chloride) (PVC) films.

•

Gubkin's Phenomenological Theory

Consider the dielectric-electrode assembly in figure 1. Assume

the thicknesses of the disk, L, and air gaps, 2., are small with

respect to their widths so that edge effects are negligible. The

dielectric disk has a dielectric constant k* and an arbitrary

charge distribution o(z) assumed to be a function only of the co- ordinate (z) perpendicular to the disk surface. p(z) is made up

of both real, (z) , and induced p^ (z) charges and the polarization is given by

dlv P(z) = - p^(z) (1)

Taking a very simple case of no net charge on the disk

L

(i... e. /f pp^(z) (z) dz=0) and of charges on the opposite surfaces of

the disk equal in magnitude but opposite in sign, one can write the

surface charge density on the electrodes as

a =

e <*V

(2)

where a is the apparent real surface charge due to p^(z), V

is the potential difference between the electrodes, z 'is the

permittivity of free space, P is the frozen-in part of the

(uniform) polarization and a is the real surface charge

density [13]. Gubkin [5] identified the piezoelectric effect with

the pressure derivative of the electrode surface charge density,

da/dp. We will be concerned with the response to both hydrostatic pressure and temperature, 6 . The above equation is equivalent but simpler for our purposes than that derived by Hayakawa

and Wada [14]

.

Application to Isotropic Amorphous Solids With Rigid Dipoles

Since we will restrict our measurements to a specific set of

experimental conditions, we can simplify Eq. (2). These conditions

are

:

1) We measure changes in surface charge at nearly zero

potential (V=0)

.

2) We use thin evaporated metal electrodes so that

£/L « 1, and the electrodes change area in accord with changes

in specimen area, A.

3) We consider only amorphous specimens which we assume to be

clastically isotropic.

A) We assume the free charges to be frozen in the solid and to

move in proportion to macroscopic strains, and the polarization

charges to be rigid molecular dipoles whose positions move in proportion to macroscopic strains but whose effective total moment, M,

remains constant as long as the strains are isotropic.

Under these conditions , with a = Q /A and P = M/AL, we

r r s can write the electrode charge as.

We will use a coordinate system fixed in the specimen such that

the + 2 axis is normal to the film surface in the direction of the

poling field and x and y are in the plane of the film. The

charge ,Q , is that on the surface which was maintained at a positive

potential during poling (bottom electrode in figure 1). The

electrode charge depends only on sample thickness, L , and will change

with isotropic volume strain d(ln v) according to

(3)

the

(A)

(9Q/3p)v=o,e

^''^ P3B/3, (5a)

and

(5b)

and the currents from this electrode resulting from a varying

pressure or temperature are given by

(6a)

and

(6b)

In the above a = (3 (In v)/39) is the coefficient of thermal

expansion and 3 = - (3 (In v)/3^)g is the compressibility, and

V*=0 means at constant near-zero voltage.

The piezoelectric strain coefficient d..iisiiV = (3P ./3T.)„ is

the change in the polarization along the i

direction with respect to stress T. at constant electric field.

Thus, for the elastically isotropic electret

d = - oil. V/3T )y = - B/3 (7)

The pyroelectric coefficient at zero field p.=(3P^/38)^

is the change in polarization at constant stress aiong

the i axis with respect to temperature. Thus,

P3 = - PgOln v/39)^= - P^a = 3 (3Q/ 39)y^Q^p/A. (9)

One can estimate the expected value of P during poling from

dielectric constant data. If at room temperature the static

dielectric constant is <^ and at some elevated temperature, f rom _ which the sample is coolea under an applied field, ^^^-^ » the

dielectric constant is <^ , then the poling procedure can be

expected to freeze in a dipolar polarization

P = (<o - E - . (10)

p e R o pole .

In general, for a non-crystalline polar material like PVC, P

is considerably less than the maximum value of P possible by ^ complete dipole alignment, and is usually linear with E up

to breakdown fields. Crystalline materials such as ?VF2^

are reported capable of a much higher degree of orientation than

PVC [15] . It is convenient to use a reduced polarization

P /e E , to describe a particular polymer. This quantity gives

S O pole ^ 1 . y to the apparent freezeable dielectric increment and is comparable to

the reduced heterocharge used to describe thermally stimulated

current results [16].

Specimens

The specimens used in this study were made from 5 mil (127 ym)

commercial rigid PVC film with a glass transition near 70°C. The

material was quite stable with respect to weight loss, as determined by repeated weighings after temperature cycling and

evacuation. After the films were cleaned with detergent and water

and dried, circular gold electrodes of 6.35 cm^ area were evaporated

on both sides of each specimen. Some measurements were also made on

a commercial film of PVF2.

Poling

Specimens were placed between 1/A" thick glass plates to

prevent distortion and heated to (80 + I)°C in an oven. A high

voltage DC power supply was used to apply (3.9 + .0.2)kV across a series of wire-Tv'ound resistors (with 4^ 1% nominal accuracy) having

a total of 9.6 MiT resistance. These resistors were arranged so that taps were available at 1/2, 1/A, 1/8 and 1/96 of the total

resistance. These resistance ratios had a measured accuracy of

better than + 1%. The taps were used to apply voltages of 3.9,

3.9/2, 3.9/4 and 3.9/8 kV across specimens Al, A2, A3 and A4

respectively. The voltage from ground to the 1/96 total resistance

tap was monitored with a precision voltmeter and recorder.

Immediately following application of the poling voltage the

oven was cooled from 80°C to room temperature in 1/2 hour. During

this, time the poling voltage gradually increased by about 2%.

Specimen Bl (PVF2) "was poled under similar conditions.

Measurements of Piezo- and Pyroelectric Currents

The specimen holder shown in figure 2 was machined from solid

copper 10.2 cm in diameter and 8.9 cm high. The specimen chamber

is 5.1 cm in diameter and 3.2 cm high. (A minimum of 2.5 cm wall

thickness surrounds the chamber) . One thermocouple hole is located

in the copper just below the center of the chamber and pressuretight fittings are used to admit a second thermocouple and a shielded current-measuring lead to the chamber. A copper tube in

the lid allows helium gas to be added to and removed from the

chamber and the lid is sealed with a rubber "0" ring and secured

with cap screws. Pressure is controlled by allowing helium gas

from a cylinder to leak into and out of the chamber through a metering valve and is monitored with an accuracy of better than + 1%

with a pressure transducer and strip-chart recorder (all shown in

figure 3)

.

To change and control its temperature, the holder is placed on

the copper block shown in figure 3. Streams of warm and cool water

from thermostated baths pass through the block, and the rate of

heating and cooling is controlled by the positions of the valves

shown in figure 3. The temperatures in the block and chamber are

measured with a precision voltmeter and monitored on a chart

recorder. A double chromel-constantan thermocouple in the chamber

gives an emf of 120 yV/K. The holder is conveniently used up to

14 bar (200 psi) and within + 10 K of room temperature.

The poled specimens are placed in the bottom of the chamber

with the "plus" electrode up. The "plus" electrode is the one maintained at positive potential during poling. A specimen is in

place in figure 2. The specimen's bottom electrode is in contact

with the grounded copper can. A spring and foam sponge provide the

force necessary to maintain contact between the upper specimen

electrode and a thin brass strip connected to the shielded currentmeasuring lead. This lead is connected to a low- impedance current

amplifier which is specified to operate with a maximum of AOO yV

across the input leads. The current amolifier is operated on a (10^1 + A%)V/A range and the amplifier output drives a strip-chart

recorder with a calibrated (+ 1%) full scale sensitivity of from

100 to 0.01 V. The chart recorder is typically used to measure

10*"^^ A full scale, with a nominal accuracy of + 5%.

Pressure, temperature and current data are recorded simultaneously on chart recorders and are then analyzed by measuring from

the chart records several values of the slopes of the pressuretime curves and corresponding currents at constant temperature and

of the temperature-time slopes and corresponding currents at

constant pressure. Data taken in this way from a single specimen

loading yield a standard deviation of + 2%. Values for different

loadings of the same specimen show a variation of about 5%.

Including uncertainties in specimen thickness, electrode area, time,

poling voltage, etc., we found the precision to be about 5% and

estimated the accuracy to be about 10%.

Typical Data

Strip chart recording traces for specimen Al are shown in

figures 4 and 5. In figure A the specimen is first cooled, heated

and cooled again in the region of 23°C. The magnitude of the

current increases as the rate of temperature change, d6/dt.

Increases, reverses with a reverse in temperature change and is

constant when d9/dt is constant and zero when d9/dt is zero. Cooling produces a negative current from the "plus" electrode.

Figure 5 shows the results of increasing and decreasing the

pressure through two cycles around 120 psi (about 8 bars). Here

the current response is more complex because of adiabatic

temperature effects in the helium pressurizing gas during pressure

change. As the metering valve is opened the helium enters the

chamber causing a piezoelectric response. Heating by the gas causes an opposite pyroelectric response which gradually diminishes

as the specimen temperature equilibrates (in about 30 s). The'

piezoelectric current then predominates and gradually decreases in

magnitude as the rate of pressure change falls off and the pressure

approaches the fixed pressure head. The direction of the piezoelectric current is such that an increase in pressure produces a negative current from the "plus" electrode. The polarization of

the sample thus increases with either a decrease in temperature or an increase in pressure as expected from the electret model.

Results of the Measurement

The results of the measurements are shown in Table 1. The

values of P (p) and P (9) were calculated from Eq . (6) using

values of ^ S/3 = o!86 x 10~5/bar and a/3 = 0.78 x lO"'* /K

which we measured for one of the PVC films in the z direction

with a capacitive strain gauge to be described elsewhere. These

values are in reasonable accord with published values for bulk.

PVC of B/3 = 0.80 X 10-=/bar and a/3 = 0.67 x lO^^/K [17],

indicating that large anisotropic effects are not present.

Assuming isotropy we can reduce the piezoelectric results further

with the aid of Eq. (8). Values of the piezoelectric strain

constants so calculated are shown in Table 2, with some values

chosen from the literature for other materials.

The pyroelectric coefficients, pyo£ PVC are proportional to

the poling field from 320 to AO kV/cm. The values obtained are about p^ = 1.2 x E , nC/cm^ where E , is in MV/cm. These

. vole . , ,pole ^ « ^ , „i 9„ values are quite comparaole to reported values of 0.3 - 2.4 nC/cm'^K

for PVF2 films poled at 1 MV/cm. The pyroelectric coefficients in

Table 1 showed no indication of decay after 6 weeks for the A series

of PVC samples nor after 4 months for some comparable specimens

prepared earlier.

Discussion of the Results

The apparent reduced polarization of the A specimens of PVC

from Table 1 is 61.8 from temperature measurements and 38.3 from

pressure measurements. Dielectric constant data [21] indicate that

cooling from 80°C to room temperature under an applied field should

yield a reduced polarization of only about 10. Measurements on the

PVC used in this study gave essentially the same result. It is not

clear where the extra apparent polarization comes from or why the

temperature and pressure data yield different values. Very slow

cooling near 80°C would allow more polarization as shown by

Reddish [21] because of the gradual stiffening of the polymer chain

just above the glass transition temperature. However, it is

difficult to see from Reddish 's data how this effect could give a reduced polarization greater than about 15. Another possible source

of the enhanced polarization is anisotropic thermal expansion and

compressibility in the films which might allow, the dipoles to tilt

during strain.. A third possibility is that some as-yet-not-underStood charge separation - trapping mechanism sometimes proposed for

electrets [22] enhances the polarization. A reduced heterocharge

of 16.1 has been reported from TSD measurements on PVC [16], in

agreement with the value expected from dielectric data.

If one calculates the maximum polarization possible in PVC

assuming complete dipole alignment one finds, with a dipole moment

of 3.6 x 10~^'^C»m (1.1 Debye) per repeat unit and a density of

1.4 g/cm^ [21], a P of 5 x 10"°C/cm^ . This value is roughly

triple the apparent " polarization from temperature data for the

Al specimen. If specimen Al is at one third maximum dipole alignment, non-linear effects due to saturation would still be within

experimental error in our measurements.

Conclusions

The piezo- and pyroelectric currents generated in PVC films due

to changing temperature and pressure are found to be quite stable,

reproducible and well behaved. The measured effects are accounted

for quite well by a model of a simple elastic solid with partially

ordered rigid dipoles. These results indicate that this model

is a good basis for understanding and studying piezo- and pyroelectric effects in polymers.

Acknowledgment

The partial support of this work by the Office of Naval

Research is gratefully acknowledged.

REFERENCES

1. 0. Heaviside, Electrical Papers, Macmillan, London, _1» ^88

(1892).

2. M. Eguchi, Phil. Mag. 178 (1925).

3. S. Mikola, Z. Phys. 32, 475 (1925).

4. E. P. Adams, J. Franklin Inst. 204 , 469 (1927).

A. Meissner and R. Bechnann, Z. tech. Phys. 9^, 174 and 430 (1928).

5. A. N. Gubkin and W. S. Sorokin, Izv. Akad. Nauk SSSR, Ser.

fiz. 24, 246(1960). (Trans. Bull. Acad. Sciences 24_, 246 (1960).

6. W. G. Cady, Piezoelectricity, McGraw-Hill Book Co., Inc.,

N. Y. (1946).

7. E. Fukada, Ultrasonics, 6^, 229 (1968), T. Furukawa and

E. Fukada, Kept. Progr. Polymer Phys. Japan 12, 401, (1969),

T. Takamatsu and E. Fukada, ibid, p. 417.

8. H. Kawai, Japan, J. Appl. Phys. 8_, 975 (1969).

9. K. Nakamura and Y. ^^ada, J. Polymer Sci. A-2 , 9_, 161 (1971).

10. J. G. Bergman, Jr., J. H. McFee and G. R. Crane, Appl. Phys.

Letters, 18, 203 (1971).

11. A. M. Glass, J. H. McFee and J. G. Bergman, Jr., J. Appl. Phys.

42 , 5219 (1971)

.

12. G. Pfister, M. Abkowitz and R. G. Crystal, Bull. Am. Phys. Soc.

II r7, 318 (1972). (Papers DL 11 and DL 12).

13. C. W. Reedyk and M. M. Perlman in Electrets , p. 97, edited by

L. M. Baxt and M. M. Perlman (The Electrochemical Society, New York,

1967).

14. R. Hayakava and Y. Wada, Rept. Progr. Polymer Phys. Japan 14 , 467, (1971).

15. J. H. McFee, J. G. Bergman, Jr. and G. R. Crane, Ferroelectrics

3, 305 (1972).

16. J. van Turnhout, Pol>T2er J. 2^, 173 (1971).

17. P. Heydemann and H. D. Guicking ,- Kolloid-Z . 193 , 16 (1963).

18. J. Cohen and S. Edelman, J. Appl. Phys. 42_, 3072 (1971).

19. E. Fukada and T. Sakurai, Polymer J. (Japan) 2, 656 (1971).

20. D. A. Berlincourt, D. R. Curran and H. Jaffe, Physical Acoustics

Vol. 1 Part A, Academic Press p. 183 (1964).

21. W. Reddish, J. Pol>-mer Sci. C14, 123 (1966).

22. M. M. Perlman, J. Appl. Phys. 42_, 2645 (1971).

Table 1. Suzaaary of Plezo- and Pyroelectrlc Data on PVC

Sp«claeo 'pole 3

(kV/cffl) (nC/aa2K) (pC/N)

P

B o pole

from T from p from T from p

Al

Ml (repeat after 2 weeks)

A2

A3

A3

(inverted)

A4

Bl (PVF2)

320

320

1(0

80

80

40

320

-0.402

-0.384

-0.214

-0.104

-0.100

-0.0537

-0.885

-0.873

-O;909

-0.510

-0.244

-0.111

-0.704

1.72 1.02

1.64 1.05

0.912 0.593

0.445 0.284

0.428

0.229 0.129

60.6 35.8

57.9 37.3

64.4

62.8

60.4

41.9

40.0

64.8 36.4

Average for FVC aaaples 61.8 38.3

Table 2. Piezoelectric Strain Coefficients

Material

PVC

PVC

PVC

PVF

PVF2

PVF2

BeO

ZnO

CdS

CdSe

BaTiO,

pole

(kV/cn)

E <320

P

180

200

320

300

31

(pC/N)

-0.93 E /320

P

0.3-0.5

11-80

1-1.3

3-7

2

-0.12

-4.7

-5.18

-3.92

-34.5

33

(pC/N)

-0.93 E /320

P

0.24

12

10.32

7.84

85.6

Reference

this work

8

18

8

8

19

20

20

20

20 . 20

Figure 1. Specimen electrode arrangement

Figure 4. Temperature and current for PVC specimen Al poled at

320 kV/cm. Cooling produced a negative current from

the "plus" electrode.

Figure 5. Pressure and current for PVC spe^^imen Al poled at

320 kV/cm. Pressurizing produced a negative current

from the "plus" electrode.

I

'igure 2. Specrnien holder showing specimen in place in botton

'of chamber.

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itigure 3. -Specimen holder, pressure and temperature control devices

and current measuring and recording equipment.