Sechν(bt) FORM OF THE MEMORY FUNCTION

Abstract

An expression for the memory function appearing in the Mori's memory function formalism has been derived using two plausible approximations. The resulting expression is of the [Formula: see text] form. The parameters a, b and ν are such that sum rules up to the sixth order of an appropriate time correlation function are exactly satisfied. The sech (bt) and the [Formula: see text] forms of the memory function have been used and derived earlier. But these satisfy sum rules only up to the fourth order and are special cases corresponding to ν = 1 and ν = 2. It is found that ν varies from 1.1 to 1.7 for Lennard–Jones fluids, investigated over wide ranges of densities and temperatures for the velocity auto-correlation function. We have also derived expressions for the shear viscosity and the thermal conductivity by using this approach. The results obtained for the shear viscosity and the thermal conductivity for Lennard–Jones fluids at various densities and temperatures have been found to be in good agreement with molecular dynamics (MD) results.