Transport coefficients of the Lennard-Jones fluid close to the freezing line

Molecular dynamics simulations have been carried out along four Lennard-Jones (LJ) fluid isomorphs close to the freezing line, covering a
temperature, T, in the range of 0.8–350 and a number density, ρ, in the range of 1.1–3.0 in LJ units. Analysis of the transport coefficients is via
the Green-Kubo time correlation function method. The radial distribution function, percolation threshold connectivity distance, self-diffusion
coefficient, and shear viscosity are shown to be invariant along an isomorph to a very good approximation when scaled with Rosenfeld’s
macroscopic units, although there are some small departures for T ≃ 1 and lower temperatures. The thermal conductivity is shown for the
first time also to be isomorph invariant. In contrast, the Einstein and moment-based frequencies, and especially the bulk viscosity, ηb, show
poor isomorphic collapse at low T but not surprisingly tend to an “inverse power” potential limiting value in the high T limit. In the case of
the bulk viscosity, the significant departures from invariance arise from oscillations in the pressure autocorrelation function at intermediate
times, which scale for inverse power potential systems but not for the LJ case, at least in part, as the pressure and bulk elastic moduli are not
isomorph invariant.