The mutual diffusion coefficient D₁₂ in binary liquid model mixtures. Molecular dynamics calculations based on Lennard-Jones (12-6) potentials

Abstract

Molecular dynamics calculations have been performed to determine the mutual diffusion coefficient D ₁₂ i.e. the dynamic cross correlations in a binary model mixture. The mean square displacement as well as the velocity-correlation function of the centre of mass of particles of kind 1 have been used for the determination. From various pilot runs it turned out that using runs of a length of 10⁵ time-steps the cross correlations can be very accurately evaluated in terms of D ₁₂/D ₁₂ ⁰, where D ₁₂ ⁰ is the pure mutual diffusion coefficient available through the two self diffusion coefficients of the mixture. Whilst the overall error for this quotient D ₁₂/D ₁₂ ⁰ is found to be 3 per cent, the inaccuracy in D ₁₂ itself is slightly larger because of the additional evaluation of the thermodynamic factor for non-ideal mixtures.

Systematic errors have been discovered in earlier molecular dynamics calculations of the D ₁₂, which are primarily due to the use of too short runs. Our calculations resulted in positive cross correlations of 5 per cent for the Ar/Kr model system. This is in contrast to previous molecular dynamics results which yielded 9 per cent negative cross effects for this system.

Extended computations of the D ₁₂/D ₁₂ ⁰ will be reported in the subsequent paper, where a series of very different model systems is discussed.