Monolayers on water: I. A theoretical equation for the liquid expanded state

Abstract

A theoretical equation of state for monolayers of fatty acids on water has been developed for the liquid expanded state. The equation is Π + π∞md 2 4A 2 A 1 - πd 2 4A 2 = kT where Π is the surface pressure, A is the area per molecule, m is the number of carbon atoms in the chain, d is the diameter of the chain, and ϵ is the minimum Lennard-Jones potential energy. This equation is based on a very simple model with the CH 2 groups acting as a stack of hard disks. The theoretical term for van der Waals cohesion between CH 2 groups is combined with a co-area term developed for two-dimensional hard-disk fluids. The equation of state is tested with experimental data for many saturated fatty acids. In spite of the fact that there are no adjustable parameters, the theoretical equation predicts the experimental variables, A, m, and T to within about 15% at a given value of II. The equation is approximately valid for unsaturated fatty acids if m is replaced by 2.5 m 9, where m 9 is the number of carbon atoms to the double bond counting from the ninth carbon atom in the chain. Comparison is made with other equations of state reported in the literature.