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Mechanical and Electrical Models for Piezoelectric Dispersions in Oriented Polymers

A complex piezoelectric modulus d*=d′−jd″ is defined as a ratio of electrical polarization to mechanical stress. In a number of oriented polymers such as polyglutamates and in polarized piezoelectric ceramic powders molded in resins, characteristic temperature variations of d′ and d″ have been observed. d′ takes a maximum and d″ changes from positive to negative at a temperature where the thermal relaxations in mechanical and dielectric properties take place.The externally applied stress produces a mechanical strain of crystallites, which is accompanied by piezoelectric polarization. The strain of crystallites is influenced by mechanical relaxation in amorphous regions surrounding the crystallites. The polarization in crystallites induces polarization observed on the surfaces of the specimen. The induced polarization is also affected by the dielectric relaxation in amorphous regions surrounding the crystallites. Therefore the phase difference between the applied stress and the resulting polarization is the sum of viscoelastic and dielectric phase differences.A mechanical model consisting of a spring for crystallites and a spring and two dashpots for amorphous regions is proposed. An electric circuit consisting of a capacitance for crystallites and a capacitance and two resistances for amorphous regions is also proposed. The combination of the two models gives a qualitative representation of the piezoelectric dispersion curves.