Chapter 9 - Interfaces in Simple Fluids – Surface Tension

Abstract

This chapter is about liquid–gas surface tension: the excess free energy arising at interfaces between gas and liquid, or between different fluid phases in general. After recalling traditional approaches to surface tension, in terms of pressure, we show how the GvdW theory identifies the surface tension directly with free energy and nonlocal interactions in the fluid, primarily the binding energy resulting from attractions but also the steric interactions which are repulsive. Even an extremely simple GvdW treatment employing stepfunction density profiles and neglecting nonlocal entropy can provide a useful analytical expression for the surface tension of a Lennard-Jones fluid. An extension to square well fluids allows the ranges of repulsive and attractive interactions to be independent parameters in the pair-potential. The binding energy contribution dominates but the negative steric contribution is also important and we show how it can be estimated approximately in the case of a stepfunction density at the interface. We then compare our analytical surface tension with experimental values for argon and eight small molecules all represented as Lennard-Jones fluids with potential parameters taken from the literature. The comparisons generally show good agreement, but in the case of methanol there is clear evidence that the Lennard-Jones model is insufficient to describe the structure and interactions in the interface. A range of improvements to the simple GvdW theory are pointed out. The classical theory of nucleation describing activated formation of drops or bubbles in supersaturated bulk fluids is derived. The stepfunction “energy only” surface tension γE for Lennard-Jones fluids is extended to account for curvature dependence in spherical drops or cavities and, finally, the Young–Laplace equation for the excess pressure in such a cavity is derived.