Adsorption of mixtures of the Yukawa-ions near a hard wall: A density functional study based on the third-order Ornstein-Zernike relation

Abstract

We examine the adsorption of the primitive-model “ionic” mixtures modeled in terms of the screened Debye potentials on a hard structureless wall. It is well-known that the screened Debye potentials are of the Yukawa form. They could approach the Coulomb potentials when the screen parameter λ vanishes. Thus the study of the mixtures of repulsive and attractive Yukawa molecules can mimic the ionic fluid behavior at small λ. One of the advantages of using this Yukawa potential is that it avoids the long-range interactions and mitigates the complications inherent in the Coulomb potential.We have previously developed a third-order Ornstein-Zernike relation (OZ3) and have adapted it to the adsorption of many types of fluids on hard walls. Specifically, a new generation of closures was developed for use in the Euler-Lagrange equations of the density functional theory (DFT) for determining the non-uniform densities of various fluid types: such as the Lennard-Jones fluid, as well as the regular Yukawa fluids (with finite λ values) on an inhomogeneous substrate. In this work, we examine the applicability of the OZ3-inspired bridge functions to the adsorption of the “small-λ” Yukawa fluids. The mixtures of these Yukawa fluids are, for simplicity, called the Yukawa ions, in contrast to the Coulomb ions. The results shall mimic the electrical double layers in electrochemistry.The Euler-Lagrange equations for the binary mixtures are solved with new OZ3 closures. Two types of closures are investigated: one derived from the Jackson-Feenberg approximation, and the other derived from the linear cavity approximation. The results are compared with the Monte-Carlo results on primitive-model symmetric ions and asymmetric ions on a neutral hard structureless wall. Satisfactory agreements are obtained. It is noted that the contact value theorems (i.e. the hard-wall sum rules) play an instrumental role in obtaining the accurate results.