Remarks on Piezoelectric Relaxation

The piezoelectricity of polymeric materials has in general a relax-ational nature and the piezoelectric stress constant e is a function of the frequency of the applied strain in a similar way to the elastic modulus and dielectric constant. The induced polarization has in-phase and out-of-phase components to the strain and the e-constant is expressed as a complex quantity, as in Eq. (32). 

However, in contrast to the cases of complex elastic modulus G and dielectric constant e, the imaginary part of the piezoelectric constant, e , does not necessarily imply an energy loss (Holland, 1967). In the former two, G /G and e /e express the ratio of energy dissipation per cycle to the total stored energy, but e /e does not have such a meaning because the piezoelectric effect is a cross-coupling effect between elastic and electric freedoms. As a consequence, e is not a positive definite quantity in contrast to G and e . In a similar way to e, however, the Kramers-Kronig relations (Landau and Lifshitz, 1958) hold for e  

The relaxational behavior of the intrinsic piezoelectricity of a polymer film arises from two origins. 

In Case (A), as will be discussed in 4.3, the piezoelectric relaxation is described as a coupling of dielectric relaxation and mechanical relaxation. In Case (B), on the other hand, the mechanical relaxation in the amorphous phase plays an important role in the piezoelectric relaxation ( 4.4). 

Thermodynamic Description of Piezoeletric Relaxation in a Single-Phase System 

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