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, η_s, were also calculated. At intermediate to high densities, D ⁻¹ and η_s 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 η_s at fluid–solid coexistence are given as a function of n. We refine further simple formulae for D and η_s 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.

Keywords:

• soft-sphere fluids
• molecular dynamics
• diffusion
• viscosity

Acknowledgements

It is a pleasure to contribute an article to this Special Issue of Molecular Physics in honour of J.-J. Weis. We have read his articles over the years with great interest and admiration. These publications have contributed immensely to our understanding of the liquid state, and have provided an inspiration for our own work. We wish Professor Weis many rewarding years to come. The authors would like to thank the Royal Society (London) and the Polish Academy of Sciences for partly funding this collaboration. The work has been partially supported by the Polish Ministry of Science and Higher Education grant N20207032/1512.