Computation and analysis of the total dynamic structure factorS(k, ω) for small wave vectors

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Abstract
The total dynamic structure factor S(k, ω) has been studied by molecular dynamics simulations for three types of Lennard-Jones model mixtures at a thermodynamic state virtually comparable with the triple point state of argon. Most of the molecular dynamics calculations were performed with 2048 particles to include the region of small k-vectors. As in a recent work, the analysis of the data was carried out by means of hydrodynamic fit functions. However, in contrast to a pure fluid, in a mixture there are diffusion and thermal flow, which couple by cross effects. This leads to very complicated hydrodynamic equations containing many transport coefficients and thermodynamic quantities. Even for the density-density correlation function which is of interest here a very lengthy hydrodynamic expression arises not suitable for fit purposes. With several reasonable assumptions we were however able to cast this expression into a simple approximate form usable for our fit procedure. The transport coefficients of the mixtures, generated by this fit formula were found to be in fair agreement with those of liquid argon when scaled by the ratio of the characteristic times. Unfortunately our fit equation does not allow for the determination of the value of the mutual diffusion coefficient. A relative indication of this coefficient is however possible in terms of a general constant appearing in our fit equation which involves diffusion and cross effects. This constant varies in fact with the mutual diffusion coefficient of the mixtures considered.