An Introduction to Microscopic Theories for Inhomogeneous Liquids: Getting Started with Density Functional Theory

TL;DR

This paper introduces classical density functional theory (DFT) for inhomogeneous liquids using a lattice-gas model, making the complex theory accessible to students with basic statistical mechanics knowledge and demonstrating practical calculations of density profiles.

Contribution

It provides an accessible introduction to DFT for inhomogeneous liquids based on a lattice-gas model, linking it to undergraduate thermodynamics and statistical mechanics.

Findings

Derived a simple DFT for the lattice-gas model.

Presented typical results of density profiles near interfaces.

Demonstrated practical calculations accessible to students.

Abstract

Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example. to calculate the density distribution of the molecules in the vicinity of a confining wall, the interfacial tension, the wetting behaviour and many other properties of nonuniform liquids. DFT can however be somewhat daunting to students entering the field, because of the many connections to other areas of liquid-state science that are required and used to develop the theories. Here we give an introduction to some of the key ideas, based on a lattice-gas (Ising) model fluid. This builds on knowledge covered in most undergraduate statistical mechanics and thermodynamics courses and so students can quickly get to the stage of calculating density profiles, etc for themselves. We derive a simple DFT for the lattice-gas and present some typical results that can readily be calculated using the theory.