In a paper recently published by Professor Lennard-Jones and the author (Lennard-Jones and Devonshire 1937) the equation of state of a gas at high concentrations has been calculated in terms of the interatomic fields. The equation found had the right kind of properties and, in particular, using the interatomic fields previously determined from the observed equation of state at low concentrations (Lennard-Jones 1931), the critical temperature was given correctly to within a few degrees for the inert gases. In this paper we shall apply the same method to determine the equation of state of a two-dimensional gas. Although such a gas cannot strictly be obtained in practice, an inert gas adsorbed on a surface (or in fact any gas held by van der Waals’ forces only) would probably behave very much like one, the fluctuations of the potential field over the surface not being of much importance. In confirmation of this it may be noted that the specific heat of argon adsorbed on charcoal was found by Simon (Simon 1935) to be equal to that of a perfect two-dimensional gas down to 60° K. A gas adsorbed on a liquid would be an even better representation of a two-dimensional one. Some measurements on the adsorption of krypton and xenon on liquid mercury have been made by Cassel and Neugebauer (Cassel and Neugebauer 1936), and they found no trace of any critical phenomena though they worked at temperatures considerably below the critical temperature of xenon. Our results are in agreement with this, for they show that the critical temperature of a two-dimensional gas should be about half that of the corresponding three-dimensional one.
Orientational order and solid-liquid coexistence in the two-dimensional Lennard-Jones system
