A Series of Electromechanical Measurements for Determination of Piezoelectric,
Dielectric and Elastic Tensor Components in Porous Polypropylene Electrets
H. Kodama, T. Osawa, Y. Yasuno and T. Furukawa
Kobayasi Institute of Physical Research, Tokyo, JAPANINTRODUCTION
The electromechanical properties of the Porous Polypropylene (p-PP) electrets by means of the precise dielectric measurements including the nonlinear responses.
1. The dielectric resonance gives the piezoelectric and the elastic factors without adding the Maxwell force.
2. The second order and the third order nonlinear permittivity becomes a function of d33 and of the elastic compliance s33 when the electrostriction generated by the Maxwell
force between electrodes of the sample were considered.
The piezoelectric and the elastic factors were determined by the nonlinear permittivity measured by various measurements and were compared with those given by the dielectricresonance measurements.

DIELECTRIC RESONANCES OF THE SAMPLESAMPLE

1.37

 1' /  0

1.38

1.375
1.370

4201920
21
2223
Frequency (kHz)10502430
20
10010045 50 55 60
Frequency (kHz)T = S(1+ kw2/(1- kw2) tan b/b)
(1+ kl2/(1- kl2) tan c/c)/(1+ kt2 tan a/a)a = h/2vh, b = w/2vw, c = l/2vl
T and S: permittivity of free and fixed conditions respectively
: angular frequency, h: thickness, w: width, l: length of the sample

1.34-3

 1" /  0(x10 )

6

1.36
1.35

1.360
15-3

 1' /  0-3

 1" /  0 (x10 )T= -E2/2
w0+w l0+lt0+t

T=0l0

T-mode

1.380

1.365

1.373
8200
300
400
Frequency (kHz)vh, vw and vl: the acoustic velocity of thickness, width and length directions
kt, kw and kl: the electromechanical coupling factor of thickness, width andlength directions

1.50

 1' /  0

w0

1.375
1.374

NONLINEAR PERMITTIVITY AND ELECTROSTRICTION

W-mode1.376

 1" /  0 (x10 )1.377

L-modeFit.

Meas.

 1' /  0

Porous polypropylene sheet (provided by YUPO Corporation, JAPAN)
Thickness: 85 m. Density: 470 kg / m3.
Aluminum electrodes were deposited on both surfaces of the sample.
Corona discharge was used to make electret of the sample.

-3

 1" /  0 (x10 )

t0Strain Si induced by Elecric Field E:
S1=l/l0 = s13T, S2=w/w0 = s23T, S3=t/t0 = s33T+d33E
Capacitance: Cap =  lw /t= l0 (1+S1) w0 (1+S2)/t0 (1+S3)
Measured Permittivity: ap= Cap t0/l0w0=(1+S1)(1+S2)/(1+S3)
Electric Displacement: D = 1E + 2E2 + 3E3 + …

ap = [1 - d33E -1/2s13 + s23 - s33)E2]
2=-d331 , 3=-12(s13+s23-s33)/2

UnpoledPoled1.40
1.301.202520151050-10123456log f (Hz)NONLINEAR PERMITTIVITY MEASUREMENTSi) harmonic distortion of electric displacement against electric fieldii) linear permittivity against bias electric field

Applied Field: E = Eb + E0 cos tElectric Displacement:
D =1(Eb+E0 cos t)+2(Eb+E0 cos t)2+3(Eb+E0 cos t)3=(1+2Eb+3Eb2) Eb+(1+22Eb+33Eb2) E0 cos t+･･･

Applied Field: E = E0 cos tElectric Displacement:
D =1E0 cos t+2E02 cos2t+3E02cos3t+･･･= 1E0 cos t + (1/2)2E02 cos (2t) + (1/4)3E03cos(3t)+ ･･･D()= Meas E0 cos t, Meas = 1+22Eb+33Eb2

D1() = 1E0, D2(2) = (1/2)2E02, D3(3) = (1/4)3E03
100Hz
140-300140

=1kHz, Bias: 300s/cycle

Meas. Fit.

Sin WavePower
AmplifierElectric
Field

ChargeAmplifier40-10021.384

D1'
D2'
D3'

100

PC
GPIB

60

Impedance
Analyzer

40-50

2000024681012Parameter

Noteby e33/c33-4000400

800

Eb (kV/m)

Result12.1-5.12
2.93

EBParametertime

1’ (pF/m)
2’ (x10-21F/V)

Result12.2-5.51

SUMMARYi) dielectric resonance (without applying Maxwell force)
Result-0.75
-1.47
444
240
0.011
0.014
0.094

22Eb

1.380
-800

6PIEZOELECTRIC AND ELASTIC COMPONENTS
DETERMINED BY DIELECTRIC MEASUREMENTS

Parameter
d31 (pC/N)
d32(pC/N)
d33(pC/N)
e33 (C/m2)
k31
k32
kt

E

E0 (x10 V/m)

1’ (pF/m)
2’ (x10-21F/V)
3’ (x10-28Fm/V2)

1.382

1.381

Sample0

MeasuredFitted

1.383

80

20

DielectricResponse

Sample-150-6260-200

D1' (x10 C/m )A/DComberter

Function
Generator

80-92-9GPIB

D2' (x10 C/m )100

D3' (x10 C/m )PC

120-250

 Meas' /  0120

Parameter ResultNote
0.357
s11 (nPa-1)
0.645
s22 (nPa-1)
c33 (kPa)
540 1/c33 = 1.85(Pa-1)
0.17 by sw,and s22
s12 (nPa-1)
s13 (nPa-1)-3.125 by d31/e33
s23 (nPa-1)-6.125 by d32/e33

When the electrostriction is generated by the Maxwell force…
2 depends on the piezoelectric constant d33
3 depends on the elastic compliance s33
d33 determined by 2 showed a good agreement with the result of thedielectric resonance.
s33 determined by 3 was about two times larger than the result by thedielectric resonance. The result suggests an existence of frequency
dependence of s33.
The piezoelectric response of the p-PP electret
Mainly induced by the size effect.

ii) nonlinear permittivty (with applying Maxwell force)a) harmonic distortion measurementsb) DC bias voltage measurementsParameters33(Pa-1)
d33(pC/N)

Result Note
4.00 from 3’423
from 2’

Parameter Result450d33(pC/N)

Notefrom 2’

ACKNOWLEDGMENT
The authors thank to the Mr. Iida and Mr. Koike in YUPO Corporation
for kindly providing samples. This work is financially supported by theGrants-in-Aid for Scientific Research of Japan Society for the Promotionof Science.