Non-mean-field theory of anomalously large double-layer capacitance

TL;DR

This paper introduces a non-mean-field theory explaining how double-layer capacitance can exceed traditional limits by considering discrete ion binding and interface dipoles, supported by simulations and applicable to asymmetric ion liquids.

Contribution

The paper presents a novel non-mean-field model accounting for large capacitance via ion-image charge binding and interface dipoles, challenging existing mean-field limitations.

Findings

Capacitance can be significantly larger than mean-field predictions due to bound ion dipoles.

At small voltages, capacitance is limited by dipole-dipole interactions, leading to large values.

Capacitance collapses at high voltages, aligning with experimental observations.

Abstract

Mean-field theories claim that the capacitance of the double-layer formed at a metal/ionic conductor interface cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments the apparent width of the double-layer capacitor is substantially smaller. We propose an alternate, non-mean-field theory of the ionic double-layer to explain such large capacitance values. Our theory allows for the binding of discrete ions to their image charges in the metal, which results in the formation of interface dipoles. We focus primarily on the case where only small cations are mobile and other ions form an oppositely-charged background. In this case, at small temperature and zero applied voltage dipoles form a correlated liquid on both contacts. We show that at small voltages the capacitance of the double-layer is determined by the transfer of dipoles from one electrode to the other and is therefore limited only by the weak dipole-dipole repulsion between bound ions, so that the capacitance is very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the much smaller mean-field value, as seen in experimental data. We test our analytical predictions with a Monte Carlo simulation and find good agreement. We further argue that our ``one-component plasma" model should work well for strongly asymmetric ion liquids. We believe that this work also suggests an improved theory of pseudo-capacitance.