Replica Density Functional Study of One-Dimensional Hard Core Fluids in Porous Media

TL;DR

This study compares two density functional methods to model one-dimensional hard core fluids in porous media, providing accurate bulk and interface properties and deriving the underlying replica density functional theory.

Contribution

It introduces and compares two density functional approaches for modeling fluids in porous media, including a derivation of the replica density functional theory.

Findings

Numerically exact results for bulk partition coefficient and density profiles.

The quenched-annealed functional approximates the exact results well.

Derivation of the underlying replica density functional theory.

Abstract

A binary quenched-annealed hard core mixture is considered in one dimension in order to model fluid adsorbates in narrow channels filled with a random matrix. Two different density functional approaches are employed to calculate adsorbate bulk properties and interface structure at matrix surfaces. The first approach uses Percus' functional for the annealed component and an explicit averaging over matrix configurations; this provides numerically exact results for the bulk partition coefficient and for inhomogeneous density profiles. The second approach is based on a quenched-annealed density functional whose results we find to approximate very well those of the former over the full range of possible densities. Furthermore we give a derivation of the underlying replica density functional theory.