Self-diffusion in an isotopic fluid

An expression for the sixth-frequency sum rule of the velocity correlation function is derived for a two-component system. This, along with lower-orde r frequency sum rules and Mori's memory-function formalism, have been used to study the mass dependence of self-diffusion in an isotopic Lennard-Jones fluid. The effect of inclusion of the sixth-frequency sum rule on the mass dependence of a self-diffusion coefficient of a single heavy particle in a fluid has been studied explicitly. It is found that the ratio of the self- diffusion coefficient of a heavy particle to that of a fluid particle is no t affected by the inclusion of the sixth-order sum rule. It is also found t hat for very high mass ratios the self-diffusion coefficients of a heavy pa rticle can have a minimum value which is 1/root 2 times the self-diffusion coefficient of fluid particles. The mole fraction dependence and thermodyna mic state dependence of the mass dependence of self-diffusion of a heavy pa rticle in the host fluid are also studied. [S1063-651X(98)15812-9].