Space-charge polarization by confined ion migration in microstructured solid dielectrics

Abstract

A continuum formulation for the effective electrostatic response of microstructured solid dielectrics undergoing intrinsic and extrinsic polarization is presented. The extrinsic polarization is produced by space charges resulting from the presence of confined mobile ions unable to migrate across microstructural interfaces. To ease the presentation, attention is restricted to rigid material systems containing a single species of dominant mobile ions. The relevant field equations of electrostatics are recast in the form of a minimum energy principle for the electrostatic and chemical potentials, and an effective response in terms of the energy density of a representative volume element is then proposed. Elementary bounds and approximate estimates for the effective energy density are also provided. By way of example, the formulation is used to explore the dependence of the macroscopic response upon microstructural morphology in multiphase layered media, with focus on constitutive nonlinearity and microstructural size effects.