A novel method to describe the interaction pressure between charged plates with application of the weighted correlation approach

Abstract

Based on the Euler-Lagrange equation for ion density distribution in an inhomogeneous, charged, and hard-sphere fluid, a novel method is proposed to determine the interaction pressure between charged plates. The resulting expression is a sum of distinct physical contributions to the pressure, which involves different contributions to the single-particle direct correlation function. It can, therefore, be conveniently used in any density functional approach to facilitate analysis of the pressure components. In this study, the so-called fundamental measure theory (FMT)∕weighted correlation approach (WCA) approach is applied to estimate both the hard-sphere and the electric residual contributions to the single-particle direct correlation function, upon the calculation of the ionic density profiles between charged plates. The results, against the Monte Carlo simulations, show that the FMT∕WCA approach is superior to the typical FMT∕mean spherical approximation approach of the density functional theory in predicting the interaction pressure between charged plates immersed in an electrolyte solution upon various conditions in the primitive model. The FMT∕WCA approach can well capture the fine features of the pressure-separation dependence, to reproduce not only the shoulder shape and the weak attractions in monovalent electrolytes but also the strongly oscillatory behavior of pressure in divalent electrolytes where pronounced attractions are observed. In addition, it is found that the FMT∕WCA approach even has an advantage over the anisotropic, hyper-netted chain approach in that it agrees with the Monte Carlo results to a very good extent with, however, much less computational effort.