Piezoelectricity of Polymer Films

Some polymer crystals have no symmetry center and hence exhibit intrinsic piezoelectricity (Rez, 1962). However, since the polymer film is in general composed of numerous crystallites, the piezoelectricity 

Polymer chains generally form a helix in the crystal and are aligned in parallel with each other. Let us consider a crystal of cellulose, for example. 

This crystal, which belongs to the space group monoclinic C2, is associated with the piezoelectric tensor (chain axis = c-axis)  

In the following, letters with bar and without bar represent the quantities for crystallite and film, respectively. 

In an uniaxially oriented film in which the c-axes of crystallites are oriented equally along the z- and — z-axes of the film (draw-axis) but the other two axes of the crystallites (a, b) are randomly oriented around the z-axis, the tensor related to the film coordinates is reduced to a simple form (Fukada and Yasuda, 1964), 

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The piezoelectricity of polymer films and its inverse effect, strain induced by applied voltage, have been observed for as-cast films, oriented films, and films which has been polarized under a static field. It is at present believed that all kinds of polymer films exhibit more or less piezoelectricity. 

These facts suggest that the origin of the piezoelectricity in polymer films is not the same in all polymers. In this review, a general description and classification of the piezoelectricity of polymer films will be presented, and the results hitherto obtained will be interpreted along the lines of the theory. 

The above theory reveals that the piezoelectricity of polymer film can be classified into four cases at its origin (A) The intrinsic piezoelectricity due to internal strain in the crystal, (B) the intrinsic piezoelectricity due to strain-dependence of spontaneous polarization, (Q the piezoelectricity originated from the polarization charge qp arising from strain-independent persistent polarization P0, and (D) the piezoelectricity from the true charge gt embedded in the film. It must be emphasized that in cases (Q and (D) heterogeneous strain Au = (u — Sl/T) must exist in the film. 

It must in any case be noted that the piezoelectricity of polymer films due to charges is not an intrinsic property of polymers it varies from sample to sample and can be remarkably enhanced by drawing and/or poling, as will be described in following sections. 

Hayakawa,R., Wada,Y. (1) A general description of piezoelectricity of polymer film. Rep. Progr. Polymer Phys. Japan 14,467 (1971). 

Hayakawa,R. and Wada, Y. Piezoelectricity and Related Properties of Polymer Films. Vol. 11, pp. 1-55. 

When a polymer film is deformed sinusoidally with time with an angular frequency to, an open-circuit voltage or a short-circuit current of the same frequency is observed across the electrodes on both surfaces of the film. This phenomenon is called the piezoelectricity of the film. The deformation is usually the elongational vibration along an axis in the film plane and sometimes the bending vibration. 

The piezoelectric constant of polymer films is usually a function of the frequency of the applied strain, and the constant is expressed by a complex quantity. In other words, the open-circuit voltage across the film surfaces is not in phase with the applied strain and the short-circuit current is not in phase with the strain rate. This effect, first pointed out by Fukada, Date and Emura (1968) and designated piezoelectric relaxation or dispersion, will be discussed in this review in terms of irreversible thermodynamics and composite-system theory. 

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). 

Introductory Remarks on the Origin of Piezoelectricity in Polymer Films... 

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

Fig. 4. Block diagram of the apparatus for measuring complex piezoelectric stress and strain constants of polymer films with varying frequency (Furukawa and...

As stated in the Introduction, as-cast polymer films in general show a weak piezoelectric effect in both elongation and bending. The results by Furukawa, Uematsu, Asakawa and Wada (1968) for five kinds of polymer films are illustrated in Figs. 18 and 19. The effect is ascribed to space charges embedded in the film. 

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