Hybrid density-potential functional theory of electric double layers

We present a field theoretic derivation for the free energy of the electrolyte solution. A reference system is introduced to describe non-electrostatic interactions, notably hard-sphere interactions, between charged particles in the electrolyte solution. The reference system is described by the Bikerman theory — a local density approximation, and the fundamental measure theory (FMT) — a nonlocal density approximation. Combining the classical part for charged particles in electrolyte solution and a quantum mechanical part for interacting electrons, we obtain a hybrid density-potential functional for the grand canonical potential of the electric double layer (EDL). Variation analysis of the hybrid density-potential functional leads to two controlling equations in terms of the electron density and the electric potential, respectively. Numerical implementation of the developed model is demonstrated for a simple EDL without specific adsorption. Particularly, oscillating density of counterions occurs near the metal surface when the FMT is used for the reference system.