Generalized Helmholtz model describes capacitance profiles of ionic liquids and concentrated aqueous electrolytes

Abstract

In this work, we propose and validate a generalization of the Helmholtz model that can account for both “bell-shaped” and “camel-shaped” differential capacitance profiles of concentrated electrolytes, the latter being characteristic of ionic liquids. The generalization is based on introducing voltage dependence of both the dielectric constant “ϵr(V)” and thickness “L(V)” of the inner Helmholtz layer, as validated by molecular dynamics (MD) simulations. We utilize MD simulations to study the capacitance profiles of three different electrochemical interfaces: (1) graphite/[BMIm+][BF4−] ionic liquid interface; (2) Au(100)/[BMIm+][BF4−] ionic liquid interface; (3) Au(100)/1M [Na+][Cl−] aqueous interface. We compute the voltage dependence of ϵr(V) and L(V) and demonstrate that the generalized Helmholtz model qualitatively describes both camel-shaped and bell-shaped differential capacitance profiles of ionic liquids and concentrated aqueous electrolytes (in lieu of specific ion adsorption). In particular, the camel-shaped capacitance profile that is characteristic of ionic liquid electrolytes arises simply from combination of the voltage-dependent trends of ϵr(V) and L(V). Furthermore, explicit analysis of the inner layer charge density for both concentrated aqueous and ionic liquid double layers reveal similarities, with these charge distributions typically exhibiting a dipolar region closest to the electrode followed by a monopolar peak at larger distances. It is appealing that a generalized Helmholtz model can provide a unified description of the inner layer structure and capacitance profile for seemingly disparate aqueous and ionic liquid electrolytes.