Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids

Abstract

Molecular Dynamics, MD, simulations were used to compute physical properties of model fluids in which the particles interacted via the soft-sphere or inverse power pair potential, φ(r) = ε(σ/r) n . n dictates the steepness or stiffness of the potential, and ε and σ are a characteristic energy and distance, respectively. A wide range of n values were considered, from the hard-sphere (n → ∞) limit down to (the latter for the first time). A linear isotherm relationship for dense fluids observed by Parsafar and Mason for supercritical compressed gases [J. Phys. Chem. 97, 9048 (1993)], was found to apply to the data for n ∼ 12 (values typical of simple fluids). For smaller n, there is a change in sign of the slope, and the data exhibited more curvature. The self-diffusion coefficient, D, and shear viscosity, ηs, were also calculated. At intermediate to high densities, D −1 and ηs depend to a very good approximation linearly on pressure, as was found by van der Gulik [Physica A 256, 39 (1998)] on treatment of experimental shear viscosity data for simple molecules. Values for D and ηs at fluid–solid coexistence are given as a function of n. We refine further simple formulae for D and ηs proposed in our previous publication [Phys. Chem. Chem. Phys. 10, 4036 (2008)]. The glass transition packing fraction and pressure for the fluid are estimated by extrapolation of the self-diffusion coefficient data. In contrast to the n = 12 case, the shear stress correlation function correlation time shows only a weak density dependence near coexistence for the very soft interactions (e.g. ). It is shown that for the very soft interactions close to n = 3, the increase in viscosity is largely determined by the infinite frequency shear modulus rather than the relaxation time, which hardly changes with density at high density.