Relaxational behavior of the piezoelectric constant and the electrostriction constant in polymers

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Abstract
Piezoelectricity in polymer films is classified by its mechanism into three groups: A-1, intrinsic piezoelectricity due to internal strain in nonpolar crystals; A-2, intrinsic piezoelectricity due to the strain-dependence of the spontaneous polarization in polar crystals; and B, piezoelectricity due to the heterogeneity of macroscopic strain. The relaxational behavior of piezoelectricity in Type A-1 is discussed for two cases: (a) the piezoelectric phase is relaxing, and (b) the piezoelectric phase is nonrelaxing but the nonpiezoelectric phase is relaxing. For Case a, a thermody-namic theory is developed, yielding relations among relaxation strengths of piezoelectric constant, dielectric constant, and elastic modulus. For Case b, on the other hand, the inequalities e″/e′ < 0 and d″/d′ > 0 are verified for a generalized composite model of two phases, where e′ — ie” and d′ — id″ are complex piezoelectric stress and strain constants, respectively. Relaxational behavior of the piezoelectric constant for Type A-2 and Type B is expected to reflect that of the electrostriction constant as suggested by theories. The complex electrostriction constant in a range from 30 Hz to 500 kHz is presented for unrolled and rolled poly(vinylidene fluoride) films. The frequency dependence of the complex electrostriction constant can explain the relaxational behavior of the piezoelectric constant of Types A-2 and B, and at the same time gives a new aspect of the relaxational character of polymers, the strain-dependence of the relaxation time, and its anisotropy.