Capacitance and Structure of Electric Double Layers: Comparing Brownian Dynamics and Classical Density Functional Theory

TL;DR

This study compares Brownian Dynamics simulations and classical Density Functional Theory to analyze the structure and capacitance of electric double layers in electrolytes, finding excellent agreement across various parameters.

Contribution

It introduces a detailed comparison between BD and DFT methods for electric double layers, highlighting their agreement and clarifying ensemble differences.

Findings

Excellent agreement between BD and DFT results across parameters

Proper ensemble considerations are crucial for accurate capacitance calculations

Thermodynamic relations between capacitance types are derived and validated

Abstract

We present a study of the structure and differential capacitance of electric double layers of aqueous electrolytes. We consider Electric Double Layer Capacitors (EDLC) composed of spherical cations and anions in a dielectric continuum confined between a planar cathode and anode. The model system includes steric as well as Coulombic ion-ion and ion-electrode interactions. We compare results of computationally expensive, but "exact", Brownian Dynamics (BD) simulations with approximate, but cheap, calculations based on classical Density Functional Theory (DFT). Excellent overall agreement is found for a large set of system parameters $-$ including variations in concentrations, ionic size- and valency-asymmetries, applied voltages, and electrode separation $-$ provided the differences between the canonical ensemble of the BD simulations and the grand-canonical ensemble of DFT are properly taken into account. In particular a careful distinction is made between the differential capacitance $C_N$ at fixed number of ions and $C_\mu$ at fixed ionic chemical potential. Furthermore, we derive and exploit their thermodynamic relations. In the future these relations are also useful for comparing and contrasting.