Electrostriction constant

There are several methods of measuring the electrostriction constant of a polymer film. 

Hayakawa and Wada (2) (1971) have designed a new apparatus to operate Method (C). The block diagram of the apparatus is illustrated in Fig. 8. 

Since C = s Cvac and G = a e Cvac(Cvac = capacitance in vacuum), 

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Table 4J. Electrostrictive constants (after Davison and Graham [79D01]).

As will be shown in the theory, the electrostriction effect plays an important role in the piezoelectric effect of polymer films. Moreover, a knowledge of the complex electrostriction constant as a function of frequency reveals a new aspect of the relaxational behavior of polymers. In this review a new method for measuring complex electrostriction constant with varying frequency will be presented with some results for poly(vinylidene fluoride). 

In the usual experiment where E0 = 0, the term kSE in Eq. (9) does not make any contribution as far as the electrical response with the same frequency as the mechanical excitation is concerned. However, as will be described in 2.2 and 2.4, the piezoelectric constant of a polymer film is sometimes a function of the electrostriction constant which plays an important role in the anisotropy and relaxational behavior of the piezoelectric effect. 

It must be noted that the above consideration for Case (A) assumes that the material is elastically heterogeneous but homogeneous in its dielectric property. If we assume heterogeneity in the electrostriction constant, CJC changes with strain, keeping //(//2 — ) constant, and hence another possibility of piezoelectricity may be introduced however, we will not take this complication into account in the following. 

III. Methods for Measuring the Piezoelectricity and Electrostriction Constant of Polymer Films 3.1. Measurement of the Piezoelectric Constant... 

A) When an alternating voltage (frequency = to) is applied to the film, the film is strained with frequencies to and 2 to. The former is the inverse piezoelectric effect and the latter the electrostriction effect. By measuring the strain amplitude of the 2to component, we can obtain the electrostriction constant (Oshiki and Fukada, 1971). 

In Table 2, the electrostriction constant is given for various polymer films (Nakamura and Wada, 1971 Kawai (2), 1970). The values by Nakamura and Wada were obtained at the strain frequency f0 —130 Hz and electric field frequency / = 1 MHz. Values by Kawai were measured at /=/0 = 150 Hz. The values are negative because the density decreases during elongation. 

Table 2. Electrostriction constant of as-cast polymer films at room temperature...

Fig. 16. Complex electrostriction constant, k — in", for elongational strain in as-cast polyfvinylidene fluoride) film plotted against frequency (Hayakawa and...

Now, the electrostriction constant opens up new aspects of relaxation phenomena. We can obtain as by use of a very small strain of the order of 10-4 and we can expect the anisotropy of this quantity for oriented polymers. 

As would be expected from Eq. (29) (eint=0 in this ease), the anisotropy should be ascribed to the electrostriction constant k. It should be noted that e and k in Eq. (29) refer to the elongational strain along the x-axis, Su whereas e in Fig. 24 is related to the elongational strain S in the yz-plane. If the film is assumed to be elastically isotropic,... 

The electrostriction constant of roll-drawn PVDF was measured by Nakamura and Wada (1971) and the result is given in Fig. 25. The value of k is greatest when stretched along the draw-axis. The ratio of e values at 6 = 0° and 0 = 90°, (e13/e12), is about 8 for the film of draw ratio a = 1.6,... 

Fig. 25. Ratio of electrostriction constant to dielectric constant of roll-drawn poly(vinylidene fluoride) film (draw-ratio = 2.3) plotted against angle 0 between elongational strain and draw-axis. Drawn after Nakamura and Wada [J. Polymer Sci. A-2,9,161 (1971)] by permission of John Wiley Sons, Inc.

Fig. 28. Piezoelectric stress constant obtained from inverse piezoelectric effect and electrostriction constant of drawn and polarized poly(vinylidene fluoride) film plotted against temperature. Draw ratio = 7. Polarized at 90° C under the field of 400 kV/ctn for 3 hours. Frequency of applied voltage = 37.5 Hz. (Oshiki and Fukada, 1971) Broken line represents dielectric constant at 21.5 Hz for roll-drawn poly (vinylidene fluoride) film (Peterlin and Eiweil, 1969)...

The electrostriction effect, beside its effect on the piezoelectricity, gives a new insight onto relaxations in polymers when the electrostriction constant is obtained over a wide frequency range. It provides us with a knowledge of the strain dependence of relaxation time. 

Polarisation dependent electrostrictive constant Lateral force Mass density... 

From tensor algebra, the tensor property relating two associated tensor quantities, of rank / and rank g, is of rank (/-b g). Hence, the physical property connecting /, and aj is the third-rank tensor known as the piezoelectric effect, and it contains 3 = 27 piezoelectric strain coefficients, dyk. The piezoelectric coefficients are products of electrostriction constants, the electric polarization, and components of the dielectric tensor. 

EFFECTS OF POISSON S RATIO AND ELECTROSTRICTION CONSTANT ON PIEZOELECTRICITY IN POLY(VINYLIDENE FLUORIDE)... 

In this paper, we report experimental results of the Poisson s ratio and electrostriction constant of PVDF and discuss the role of their constants to the piezoelectric effect by using the theory developed by Wada and Hayakawa. 

The dielectric constant e and piezoelectric constant eai were measured by using the apparatus developed by Furukawa et al The electrostriction constant K3i=Oe3/8S) was calculated by measuring an apparent piezoelectric constant under low frequency A.C bias (0.004 Hz). 

Figure 3. Plots of electrostriction constant K31 and dielectric constant 83 vs. roll ratio for films rolled at 80°C.

In order to clarify the effects of annealing temperature on electrostriction constant and Poisson s ratio, some samples were prepared by annealing in the range of 120°C to 180°C (2 hrs) for films drawn 4.2 times. Figure 6 shows... 

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