Quantum and Classical Characteristics of the Capacitance of Electrode-Electrolyte Interfaces from Joint Density Functional Theory

Abstract

Quantifying the interfacial response towards addition of charge, the capacitance of electrode-electrolyte interfaces is a key property for the functioning of electrochemical devices. The rich electronic properties of two-dimensional electrode materials strongly affect their electrochemical behavior, giving rise to their so-called quantum capacitance CQ. It is well-accepted that the quantum capacitance is essentially equal to the electronic density of states (DOS) of the electrode. However, the total capacitance Ctot of the electrode-electrolyte interface is also determined by the "classical" double-layer capacitance Cdl. Typically, both contributions are assumed to act in series, resulting in the commonly employed partitioning 1/Ctot = 1/CQ + 1/Cdl. However, in spite of its fundamental relevance, the motivation of this partitioning remained vague to date.I will show how both quantum and classical characteristics of the capacitance of complex electrode-electrolyte interfaces rigorously derive ab initio from joint density functional theory that provides a framework for the combined description of both the electronic density of the electrode and the ionic and dielectric densities of the electrolyte. Whereas the quantum capacitance is determined by the DOS of the Kohn-Sham single-particle orbitals, the double-layer capacitance is determined by the interaction between the local density of states (LDOS) of the electrode and the Fukui function of the electrode-electrolyte system. The derived relation precisely yields the known partitioning of the total interface capacitance, but it also shows that additional capacitive contributions arise, e.g., from the electronic exchange-correlation interaction.This analysis provides a clear perspective on the influence of the electrode material and thickness, as well as temperature, on the charging response of the interface, which is particularly relevant for two-dimensional electrode materials where all capacitive contributions are significant and non-trivial. Moreover, the presented approach makes the transition from thin two-dimensional to thick bulk electrodes mathematically traceable and shows how the classical electrochemical double-layer capacitance is recovered in the limit of a bulk metal electrode. The findings will be exemplified by computational results for a single-layer graphene electrode, and for bulk and single-layer gold electrodes.[1] T. Binninger, Piecewise nonlinearity and capacitance in the joint density functional theory of extended interfaces, Phys. Rev. B 103 (2021), L161403.