Transport properties of supercritical methane

The experimental results on molecular diffusion in supercritical methane in a wide pressure range reported by [U. Ranieri et al., Nat. Commun. 15, 4142 (2024)] are compared with the theoretical expectations based on the Lennard-Jones model. In the low-pressure low-density limit, the kinetic approach within the Chapman-Enskog approximation is shown to be adequate. At higher pressures and densities, the freezing density scaling approach becomes appropriate. In this approach, the properly reduced transport coefficients along isotherms appear as quasi-universal functions of the density divided by the density at the freezing point. We analyze the transition from gaslike to liquidlike dynamical behavior from the perspective of the Stokes-Einstein-Sutherland relation linking self-diffusion and shear viscosity coefficients. This analysis locates the dynamical crossover close to the transition from gas- to liquidlike molecular diffusion in methane, which is observed experimentally. We emphasize the importance of distinguishing between two separate transitions: the intersection of gaslike and liquidlike asymptotes of transport-related properties and the onset of the rigid-fluid regime. These transitions occur at significantly different locations on the phase diagram, which explains the conflicting criteria often used to define the gas-to-liquid-like dynamical crossover and the Frenkel line. In addition, our results offer a practical and predictive framework for estimating the transport properties of supercritical methane in pressure and temperature regimes where experimental data are currently unavailable.