On the Theory of the Thermal Diffusion Coefficient for Isotopes

Abstract

Enskog's general theory of thermal diffusion holds for a gas of spherically symmetrical molecules which is sufficiently dilute that collisions of more than two molecules at a time are of negligible importance. The first approximation to the thermal diffusion constant of a mixture of two isotopes is derived from this theory. The result is presented in terms of suitably defined cross-section integrals, in which the intermolecular forces are not yet specialized. This general formula for the thermal diffusion constant $\alpha$ is then worked out explicitly for several well-known molecular models: the elastic sphere model, the inverse power model, the Sutherland model, and the Lennard-Jones model. The various limitations on the accuracy of the theory are discussed, and the theoretical results are compared with the very few experimental data which are as yet available. The comparison indicates that the customary molecular models of kinetic theory are hardly adequate to give a satisfactory account of thermal diffusion. These models are relatively satisfactory for the elementary free-path phenomena to which they are usually applied, but they are not sufficiently precise to meet the more exacting test of thermal diffusion. The best check between theory and experiment is obtained for neon with the Sutherland model. The use of this model, however, places the entire burden of accounting for the observed decrease of $\alpha$ with temperature on the attractive part of the intermolecular forces, whereas in view of the smallness of this attractive force as determined by other methods, it can hardly be doubted that the decrease is actually due to the increased "softness" of the repulsive force at low temperatures.