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

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 concentration, 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 $$C_N$$ C N at fixed number of ions and $$C_\mu $$ C μ at fixed ionic chemical potential. Furthermore, we derive and exploit their thermodynamic relations. In the future these relations will also be useful for comparing and contrasting experimental data with theories for supercapactitors and other systems. The quantitative agreement between simulation and theory indicates that the presented DFT is capable of accounting accurately for coupled Coulombic and packing effects. Hence it is a promising candidate to cheaply study room temperature ionic liquids at much lower dielectric constants than that of water.

A molecular perspective on induced charges on a metallic surface

“…In particular, the fluctuation-dissipation relation linking the variance of the charge distribution to the differential capacitance of the system has already been considered in DFT-based ab initio molecular dynamics simulations, 41 classical Monte Carlo, 42 and molecular dynamics [43][44][45][46] simulations and more recently in Brownian Dynamics with an implicit solvent. 47 In the present work, we investigate the charge distribution induced on an atomically resolved metallic surface by a single ion in a vacuum or in the presence of a molecular solvent. Using classical molecular simulations, we consider the Na + cation and the Cl − anion in water at various distances from a (100) surface of a model gold electrode.…”

The Electrode-Electrolyte Interface from the perspective of Density Functional Theory

“…This approach will, for instance, be used in the BD simulations in Chapter 3. In that chapter, we also show, by comparing BD simulations with DFT calculation, that the atomic details of the surface of the electrode do actually not have a significant effect on the density profiles of the ions [2].…”

“…of which the first c (1) and second direct correlation c (2) function are the most important ones (within this thesis)…”

“…The simplest approach would be a mean-field approximation for which ⟨ qtot (r) qtot (r ′ )⟩ = q tot (r)q tot (r ′ ). However, a more general notion would be to introduce a pair charge distribution function q (2) (r, r ′ ) = q tot (r)q tot (r ′ )g q (r, r ′ ), similar to the pair distribution function ρ…”

“…The argument laid out above is deceptively simple. It implies that knowledge of the exact c (2) (r; ρ b ) is sufficient to determine the exact asymptotic decay of the one-body density profiles at a planar wall, and, indeed, of the solvation force for the liquid confined between two planar walls, provided the external potential is sufficiently short-ranged. In practice, one never has the exact c (2) (r; ρ b ) and it is not always clear what physics is omitted in employing an approximate c (2) (r; ρ b ).…”