The tunnel theory of fluids: the 12:6 fluid

Abstract

A theory of fluids is described based on a ‘tunnel’ model, in which lines of molecules are pictured as moving almost one-dimensionally in tunnels or fine capillaries, the walls of the tunnels being formed by neighbouring lines of molecules. This model is similar to the cell model in that the whole fluid is broken down into subsystem s sufficiently simple to permit explicit calculation of their properties; in the cell model the subsystems are single molecules moving in cages, in the tunnel theory they are whole lines of molecules moving in tunnels. The advantages of the tunnel model are that density fluctuations are permitted in a natural way, so that the difficulty of the ‘communal entropy’ is no longer insuperable; and that the basic ‘structure’ is a disordered one, since the molecules in different tunnels are randomly placed with respect to each other. This model has already been shown to give a good description of the ‘hard-sphere’ fluid; in this paper it is applied to the 12:6 fluid and shown to give values for liquid densities, compressibilities and vapour pressures which are satisfactorily close to the experimental values for simple liquids. The calculated critical constants are less satisfactory, probably because the approximation of treating the motion along the tunnels as one-dimensional is less accurate at low densities.