12 - Liquid-vapour surface

Summary

This chapter begins with a relatively brief discussion of the thermodynamics of liquid surfaces. Then the statistical mechanics of inhomogeneous systems, already developed for treating freezing in Chapter 6, are used to obtain some formally exact results for the surface tension of a liquid. These formulae will then, essentially, be developed by gradient expansion methods to yield an interesting relation between bulk and surface properties, related by the “width” of the liquid-vapour interface.

Thermodynamics of liquid surfaces

The atomic density profile, denoted by ρ(z), must vary continuously across the interface from the value ρ₁ of the bulk liquid to the value ρ_v of the bulk vapour. This variation can be expected to take place over a few atomic distances, at least when one is far from the critical point.

The anisotropy of the profile implies a net attraction to the liquid phase of an atom in the transition region: One must perform work to bring an atom from the bulk of the liquid to the surface; i.e., an excess of free energy is associated with the creation of the interface, namely, the surface free energy. It also implies that the tangential pressure, defined as the force per unit area transmitted perpendicularly across an area element in the yz or xz plane is a function p_t(z) of position in the transition region. The difference between the components p_t(z) and p_n = p of the stress tensor in the transition region is negative, i.e., it has the nature of a tension, namely, surface tension.