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 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.

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• Incorporating Ion-Specific van der Waals and Soft Repulsive Interactions in the Poisson-Boltzmann Theory of Electrical Double Layers
• Adsorption of polyelectrolytes in the presence of varying dielectric discontinuity between solution and substrate
• In-plane structure of the electric double layer in the primitive model using classical density functional theory
• Interactions between polyelectrolytes mediated by ordering and orientation of multivalent non-spherical ions in salt solutions
• Brownian dynamics simulations of electric double-layer capacitors with tunable metallicity
• Absence of anomalous underscreening in highly concentrated aqueous electrolytes confined between smooth silica surfaces
• On the electrical double layer capacitance of the restricted primitive model: a link between the mesoscopic theory and the associative mean spherical approximation