Charge and electric field distributions in the interelectrode region of an inhomogeneous solid electrolyte

TL;DR

This paper models charge and electric field distributions in an inhomogeneous solid electrolyte under external electric fields, extending previous homogeneous models to account for inhomogeneity and calculating related capacitance.

Contribution

It introduces a new approach combining collective variables and mean cell potentials to analyze inhomogeneous ionic conductors under external electric fields.

Findings

Charge and electric field distributions depend on electrode charge.

The model predicts differential electric capacitance behavior.

Extension of previous homogeneous models to inhomogeneous cases.

Abstract

A solid ionic conductor with cation conductivity in the interelectrode region is studied. Due to their large size, the anions are considered fixed and form a homogeneous neutralizing electric background. The model can be used to describe properties of ceramic conductors. For a statistical mechanical description of such systems, which are characterized by short-range Van der Waals interactions and long-range Coulomb interactions, an approach combining the collective variables method and the method of mean cell potentials is used. This formalism was applied in our previous work [Bokun G., Kravtsiv I., Holovko M., Vikhrenko V., Di Caprio D., Condens. Matter Phys., 2019, 29, 3351] to a homogeneous state and in the present work is extended to an inhomogeneous case induced by an external electric field. As a result, mean cell potentials become functionals of the density field and can be described by a closed system of integral equations. We investigate the solution of this problem in the lattice approximation and study charge and electric field distributions in the interelectrode region as functions of plate electrode charges. The differential electric capacitance is subsequently calculated and discussed.