Refinement of the Lennard-Jones and Devonshire Theory of Liquids and Dense Gases

Abstract

The Lennard-Jones and Devonshire (LJD) theory of liquids represents an advance over the early free-volume theories, in that each molecule is assumed to move in a potential field generated by its neighbors. However, this potential is the static field computed with each neighbor at its equilibrium position (cell center), so that the LJD theory does not take account of the correlation of the motion of neighboring molecules. This correlation problem is treated in the present paper by recasting the exact classical partition function in a form in which the LJD potentials appear in the principal terms, while certain correlation potentials appear in correction terms. The resulting integrals are analogous to those appearing in the conventional theory of an imperfect gas, but with the correlation potential playing the role of the usual intermolecular potential, and the range of integration of each molecule limited to its own cell (where it is also subject to the static LJD potential). A practical method of evaluation of the integrals is developed, based on power series expansions of the factors containing the correlation potentials. The limitation of each molecule to a single cell (single occupancy) is not an essential feature of the theory. The allowance for multiple occupancy of the cells leads to the communal entropy correction, which has been treated by Pople and others. The present correction for correlation of neighboring molecules is applicable even for single occupancy, and is thus an addition to the communal entropy correction. The method is compared with Kirkwood's self-consistent field modification of the LJD theory, which takes some account of correlation, but only in an average sense. Comparison is also made with the recent cell-cluster theory of de Boer, which was in fact antedated by the present work (see footnote). The two theories are basically equivalent, in spite of their different formulations. It is felt that the present method puts the integrals in a form more practical for calculation.