Theory of ionic liquids with polarizable ions on a charged electrode

TL;DR

This paper develops a mean-field theory for electric double layers in ionic liquids with polarizable ions, providing new analytical expressions for capacitance and insights into ion behavior affecting electrochemical device performance.

Contribution

It introduces a generalized analytical expression for differential capacitance considering polarizable ions, extending previous models and exploring their impact on ionic concentration and capacitance behavior.

Findings

Derived a new expression for differential capacitance involving ionic charge density and electric field.

Showed how polarizability and dipole moments influence capacitance and ionic distributions.

Identified the balance between dielectrophoretic attraction and Coulomb repulsion in ion behavior.

Abstract

We formulate a general mean-field theory of a flat electric double layer in ionic liquids and electrolyte solutions with ions possessing static polarizability and a permanent dipole moment on a charged electrode. We establish a new analytical expression for electric double layer differential capacitance determining it as an absolute value of the ratio of the local ionic charge density to the local electric field on an electrode surface. We demonstrate that this expression generalizes the analytical expressions previously reported by Kornyshev and Maggs and Podgornik. Using the obtained analytical expression, we explore new features of the differential capacitance behavior with an increase in the static polarizability and permanent dipole moment of cations. We relate these features to the behavior of ionic concentrations on the electrode. In particular, we elucidate the role of the competition between the dielectrophoretic attraction and Coulomb repulsion forces acting on polarizable or polar cations in the electric double layer in the behavior of the differential capacitance. The developed theoretical model and obtained theoretical findings could be relevant for different electrochemical applications, e.g. batteries, supercapacitors, catalysis, electrodeposition, etc.