Models for self-diffusion in the square well fluid

Abstract

Transport properties of moderately dense fluids reflect several effects not present at the Boltzmann level: excluded volumes, finite collision times, and bound states. The description and relative importance of these effects is illustrated here by a discussion of the self-diffusion coefficient for the square well fluid. At high temperatures the particles behave as hard spheres and the Enskog kinetic theory describing excluded volume effects is adequate. Generalizations of the Enskog theory for application at lower temperatures are discussed critically. One approach assumes partial (uncorrelated) collisions for initial conditions modified to account for excluded volume effects. Another describes completed binary collisions at the core and edges of the well for the same modified initial conditions. Although both reduce to the Enskog theory at high temperatures, neither is adequate outside this limit for prediction of either the temperature or the density dependence. The proper treatment of both temperature and density effects is found to require a more detailed description of interrupted binary collisions and bound states. Such a treatment is described and shown to be in good agreement with computer simulation results. We conclude that generalization of the hard-sphere Enskog theory to the square well, and probably other potential models, is more subtle than might be expected and requires dynamical as well as static many-body effects.