A systematic comparison of different approaches of density functional theory for the study of electrical double...

Based on the best available knowledge of density functional theory (DFT), the reference-fluid perturbation method is here extended to yield different approaches that well account for the cross correlations between the Columbic interaction and the hard-sphere exclusion in an inhomogeneous ionic hard-sphere fluid. In order to quantitatively evaluate the advantage and disadvantage of different approaches in describing the interfacial properties of electrical double layers, this study makes a systematic comparison against Monte Carlo simulations over a wide range of conditions. The results suggest that the accuracy of the DFT approaches is well correlated to a coupling parameter that describes the coupling strength of electrical double layers by accounting for the steric effect and that can be used to classify the systems into two regimes. In the weak-coupling regime, the approaches based on the bulk-fluid perturbation method are shown to be more accurate than the counterparts based on the reference-fluid perturbation method, whereas they exhibit the opposite behavior in the strong-coupling regime. More importantly, the analysis indicates that, with a suitable choice of the reference fluid, the weighted correlation approximation (WCA) to DFT gives the best account of the coupling effect of the electrostatic-excluded volume correlations. As a result, a piecewise WCA approach can be developed that is robust enough to describe the structural and thermodynamic properties of electrical double layers over both weak- and strong-coupling regimes.