Molecular association at the microscopic level

For the molecular equilibrium A + B ⇔ AB occurring in a dilute solution or gas, the two-particle Helmholtz free energy, W, is used to evaluate the association constant, KAB, which, for ionic A and B, is identical to the Bjerrum result. The criterion defining the bound species AB is not arbitrary; the cutoff separation distance in the configuration integral used to calculate KAB arises directly from the definition of W. For a one-component dense fluid, W permits the derivation of the phase-condensation temperature, which, for a gas, is the critical temperature and for a liquid the freezing temperature. For ionic A and B (e.g., molten salt), the Kosterlitz–Thouless expression for the freezing temperature is obtained.

Statistical Mechanics of Almost One-dimensional Systems

A method is described whereby the classical configuration integral of statistical mechanics can be evaluated with any desired accuracy for almost one� dimensional systems with forces of finite range. The systems contemplated are those in which the molecules or atoms can in any given configuration be ordered serially in such a way that a given molecule may be considered as mteracting only with a definite number of neighbours. This kind of model would be appropriate for example for adsorption of gas molecules in very fine Clipillaries. The results are also of importance in connection ith the " tunnel" model for dense fluids and may have other applications as a basis for approximate treatments of real three�dimell8ional systems.