A differential effective medium model for piezoelectret foams

Abstract

Polymer foams with piezoelectric properties, called piezoelectrets, have recently gained interest in the acoustics and scientific community. These foams are heterogeneous materials consisting of a continuous polymer containing electrically polarized elliptical voids. The macroscopically observable piezoelectric behavior results from the unique combination of the high void-polymer elastic contrast and the void polarization. Existing modeling methods to approximate the macroscopic piezoelectric properties of these foams are elementary one-dimensional noncoupled electrostatic models. In this study, a coupled mean field microelectromechanical model has been developed as a predictive tool of the macroscopically observed piezoelectric material behavior. This technique employs Green’s function solutions of the three-dimensional (3D) stress equilibrium equations and Gauss’ Law. The result is a multiscale differential effective medium model approximating the 3D effective stiffness, dielectric permittivity, and piezoelectric coupling coefficients as a function of the constituent material properties, void shape and orientation, and deposited charge density. The model is employed to study the sensitivity of macroscopic foam behavior to various constituent material and void variables. This approach improves the approximation of the true piezoelectret behavior by capturing the influence of microscopic material structure and properties on macroscopic piezoelectric performance.