Relations between transport coefficients in Lennard-Jones fluids and in liquid metals

Several simple approximate hard-sphere relations for transport coefficients are compared with the results of molecular dynamics (MD) simulations perfo rmed on Lennard Jones (LJ) fluids. Typically the individual transport coeff icients: self-diffusion coefficients, D, shear viscosity, eta(s), bulk visc osity, eta(B), and thermal conductivity, lambda, agree within a factor of t wo of the exact results over the fluid and liquid parts of the phase diagra m, which seems reasonable in view of the approximations involved in the mod els. We have also considered the ratio, lambda/eta(s), and the product, D e ta(s), for which simple analytic expressions exist in the hardsphere models . These two quantities also agree within a factor of two of the simulation values and hard sphere analytic expressions. Using time correlation functio ns, Tankeshwar has recently related the ratio lambda/D to thermodynamic qua ntities, in particular, to the differences in specific heats, C-p-C-v, and to the isothermal compressibility, kappa(T). Using D and thermodynamic valu es taken solely from LJ MD simulations, his relation was tested and found t o give typically better than similar to 20% agreement at liquid densities, deteriorating somewhat as density decreases into the gas phase. Finally liq uid metals are considered. In this case, lambda is dominated by its electro nic contribution, which is related approximately to the electrical conducti vity by the Wiedemann-Franz Law. Some theoretical results for the electrica l conductivity of Na are referenced, which allow a semiquantitative underst anding of the measured thermal conductivity of the liquid metal. Shear visc osity is also discussed and, following the work of Tosi, is found to be dom inated by ionic contributions; Nevertheless, at the melting temperature of Na, a relation emerges between thermal conductivity, electrical resistivity and shear viscosity.