Statistical Mechanics of Binary Mixtures

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Abstract
The possibility of specifying both the enumeration of the complexions of an assembly and the evaluation of its configurational energy in terms of the numbers of closest neighbor pairs of sites of various kinds, without introducing parameters explicitly to specify the occupation of individual sites, is considered. The formula obtained on such a basis by Alfrey and Mark is examined. Their work depends on an assumption which at first sight appears plausible. Furthermore, if this assumption could be justified, it would imply that the quasi‐chemical equation, which has been introduced in the theory of regular assemblies as an ad hoc assumption, could be derived from the Boltzmann equilibrium law and the elementary formulas of algebraic combinations. If a pair of closest neighbor sites of which one is occupied by a molecule of species i and the other by a molecule of species j is called an i—j pair, then it is shown that the assumption made by Alfrey and Mark is equivalent to neglecting the restrictions on the free allocation (amongst the ½zN pairs available in all) of pairs of different kinds which are inherent in the interconnections of an assembly of interacting particles. It is concluded, therefore, that the assumption in question is unjustified and leads to an incorrect result, and that consequently the quasi‐chemical equation is correctly introduced as an ad hoc assumption.

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