Remarks on the Origin of Piezoelectricity in Polymer Films

Introductory Remarks on the Origin of Piezoelectricity in Polymer Films 

As has been well established, piezoelectricity in a non-polar crystal is brought about by the internal strain in the crystal. The internal strain means the displacement of atoms which is not affine to the deformation of crystal lattice. In the case of a polymer film which is not electrically conductive and where the charges are possibly embedded, a description of piezoelectricity can be reached by considering not only the internal strain in the lattice but also the displacement of these charges which is not affine to the average deformation of the whole system. 

Let us consider an atom at x = in the film which has an electric charge q (Fig. 1). Other atoms in the film are assumed to form a continuum with a uniform dielectric constant s. When the electrodes on the film are short-circuited, induced charges on the electrodes, and q2, respectively, are given by 

When the film is strained and the ratios CJC and C2/C are changed, qt and q2 are varied according to Eq. (12), which results in the piezoelectric current i — — dq1/dt = dq2/dt. Since CJC is proportional to 11(1/2 — ), no piezoelectricity would be expected if the strain is homo- 

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. 

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