Harmonic modes in a hard sphere fluid

Effective separation of forces in a mode coupling theory of self-diffusion

A mode coupling theory (MCT) expression for the self-diffusion coefficient follows simply when the soft fluctuating intermolecular forces are projected along a collective densitylike variable. The projected forces separate into two parts: from the gradient of the direct correlation function (dcf), and from the short range forces. The time correlation function of the dcf-derived forces is related to the excess entropy, as shown by Ali [J. Chem. Phys. 124, 144504 (2006)], and this relationship is evaluated for two variations of MCT. As for hard spheres, the derivation of an analogous MCT is beset by a number of singularities that kinetic theory could not remove. A justifiable MCT for hard sphere fluids may not exist.

Momentum and stress relaxation in fluids illustrating caging

The self diffusion coefficient, shear viscosity, and velocity time correlation function are calculated for a hard sphere fluid under a severe assumption, namely, the friction arises from uncorrelated binary collisions and from correlated backscattering (caging) collisions as represented in the memory function. Relaxation of the memory function from its zerotime caging value is described as a diffusion process. Derived diffusion coefficients and the shear viscosities, relative to their Enskog values decrease and increase with density, respectively, in a monotonic and gradual fashion in contrast with simulation values that show a precipitous change near the fluid-solid transition. In the present pair diffusion model, the velocity time correlation function vanishes at the proper time but its tail is overly damped relative to the simulation data. A weak breakdown of the Stokes-Einstein relation is also predicted.