Critical phenomena in gases. II. Vapour pressures and boiling points

Abstract

The object of the first paper on “Critical Phenomena in Gases” (referred to in this paper as Paper I) was to develop a simple method of dealing with dense gases and to calculate critical temperatures in terms of atomic fields of force. Each atom in a dense gas was pictured as caged for most of its time by a cluster of neighbours, equal in number to those which surround it in the solid (and presumably also in the liquid) phase. The model was intended to provide a general average of the potential field in which any one atom moved by replacing its varying environment by an arrangement of neighbours which could be regarded as typical. This arrangement was taken to be the one in which the neighbours were situated at their mean positions as determined by the density of the gas. The potential energy of any one atom could thus be expressed as a function of the volume of the gas—a step which is probably the crucial one in a theory of critical phenomena. This point of view brings the process of condensation within the category of those described by Fowler (1936) as co-operative phenomena. In passing we may observe that the derivation of van der Waals’ equation provides a particular example of this method, for in it the potential energy of each atom is assumed to be inversely proportional to the volume. The present theory goes beyond this simple model, for the potential energy of an atom is considered to be not only a function of volume but also a function of the position of the atom relative to its neighbours. The probability of finding an atom in any assigned position can be calculated by statistical means and its average potential energy and its available free volume easily deduced. The equation of state can then be deduced by thermodynamic methods, as has been pointed out elsewhere (Lennard-Jones 1937).

A theory of solid solutions and solid-fluid equilibria for mixtures

“…The most ambitious approach has been to calculate the properties of both phases within the context of a single theory, This is exemplified by the order-disorder theory of Lennard-Jones and Devonshire [ 1 ] which treats the fluid as a disordered solid and, more recently, by the density functional theory [2--4], which treats the solid as a highly inhomogeneous fluid, an idea originating from the work of Kirkwood and Monroe [ 5 ]. The densityfunctional-theory work has attracted considerable interest in recent years since it seems to provide a quite accurate picture of the solid structure while being based on accurate approximations for the fluid properties [2][3][4].…”

Influence of temperature, molecular weight, and molecular weight dispersity on the surface tension of polystyrene, polypropylene, and polyethylene. II. Theoretical

“…An expression of the surface tension as a function of microscopic parameters is then obtained. The lattice considered has been described in detail in several references1–3 and is based on the formalism developed by Lennard‐Jones and Devonshire13 to describe the properties of small‐molecule liquids. Figure 1 shows a two‐dimensional cross section of the lattice considered in both models.…”

Effect of Temperature Dependence of the Langmuir Constant Molecular Pair Potentials on Gas Hydrates Formation Mechanism

“…The SC model was also introduced by vdWP, inspired by an analogous approximation made by Lennard-Jones and Devonshire in the case of liquids [36,38]. Using chemical potentials for water, Eq.…”