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

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