Computation and analysis of the transverse current autocorrelation function, Ct(k,t), for small wave vectors: A molecular-dynamics study for a Lennard-Jones fluid.

Abstract

Molecular-dynamics (MD) calculations are reported for three thermodynamic states of a Lennard-Jones fluid. Systems of 2048 particles and ${10}^{5}$ integration steps were used. The transverse current autocorrelation function, ${C}_{t}$(k,t), has been determined for wave vectors of the range 0.5l\ensuremath{\Vert}k\ensuremath{\Vert}\ensuremath{\sigma}l1.5. ${C}_{t}$(k,t) was fitted by hydrodynamic-type functions. The fits returned k-dependent decay times and shear viscosities which showed a systematic behavior as a function of k. Extrapolation to the hydrodynamic region at k=0 gave shear viscosity coefficients in good agreement with direct Green-Kubo results obtained in previous work. The two-exponential model fit for the memory function proposed by other authors does not provide a reasonable description of the MD results, as the fit parameters show no systematic wave-vector dependence, although the ${C}_{t}$(k,t) functions are somewhat better fitted. Similarly, the semiempirical interpolation formula for the decay time based on the viscoelastic concept proposed by Akcasu and Daniels fails to reproduce the correct k dependence for the wavelength range investigated herein.