Structure of a planar electric double layer containing size-asymmetric ions: density functional approach

We have studied the structure of the electrolytes with asymmetries in charge and size near a charged planar electric double layer by a density functional theory. In the present theory, the hard-sphere contribution has been approximated as the direct pair correlation function with the coupling parameter, whereas the electronic contribution has been approximated as the mean-spherical approximation in the bulk phase. This theoretical approach for the size-symmetric and size-asymmetric electrolytes displays a good agreement with the simulation results over a wide range of surface charge densities and electrolyte concentrations. However, the accuracy between the present theory and the simulation results slightly deteriorates for the highly size-asymmetric electrolytes and the multivalent electrolytes. In these cases, the performance of the present theory is comparable to those of the simplified extension of the Poisson-Boltzmann theory and the modified Poisson-Boltzmann theory. The calculated result indicates that the surface charge distribution function, which was introduced as an indicator for studying the charge reversal, layering effect, and surface charge amplification in a planar electric double layer, describes the electronic properties of a planar electric double layer well.