The Stokes-Einstein relation for simple fluids: From hard-sphere to Lennard-Jones via WCA potentials

Abstract

The Stokes-Einstein (SE) relation is examined for hard-sphere (HS) and Weeks-Chandler-Andersen (WCA) fluids by the molecular dynamics method on temperatures and densities corresponding to the saturated vapor line of Lennard-Jones (LJ) liquids. While the self-diffusion coefficient, D, and shear viscosity, ηsv, increases and decreases, respectively, with increasing steepness in interaction potentials, the same SE relation holds for HS and WCA fluids as that obtained for LJ liquids, i.e., Dηsv = (kBT/C)(N/V)1/3, where kB is the Boltzmann constant, T is the temperature, and N is the particle number included in the system volume V. The coefficient C is almost constant at about 6 to 2π for η > 0.3, where η is the packing fraction. The results show that the SE relation for simple liquids and fluids does not need to bear any concepts of both the hydrodynamic particle size and the boundary condition. In light of this SE relation, the Enskog, Eyring-Ree, and Zwanzig theories are quantitatively tested. In addition, the cause of deviation from unity of the exponent in the fractional SE relation for simple fluids is clearly accounted for. The present results show that applying both the original and the fractional SE relations to simple liquids and fluids does not lead to any meaningful discussions.

Thermodynamic and dynamical properties of the hard sphere system revisited by molecular dynamics simulation

“…Accurate representations of the compressibility factor of the HS fluid and solid branches in analytic form are presented in Eqs. (4) and 7, respectively. Consequently, the Helmholtz free energy, F, at any density on the phase diagram can be obtained directly by thermodynamic integration if the free energy of fluid and solid reference states are known.…”

“…The self-diffusion coefficient and shear viscosity data are presented and discussed in Sec. 4. The main conclusions are summarized in Sec.…”

“…Many theories of the dynamics of the molecules in the liquid state also require accurate values of the fluid self-diffusion coefficient, D, and shear viscosity, η, in the thermodynamic limit, to test adequately (e.g., the applicability of the Stokes-Einstein relationship, 4 ). It is known that D has a significant system size dependence which can be reduced significantly by taking about 1 million particles in a simulation.…”

Elastic properties of dense hard-sphere fluids

“…This dependence is very weak: α is just above 0.14 in the entire densities range considered. Recent MD simulations [39] reported α in the range from 1/2π 0.159 to 1/6 0.167 for a similar range of φ, which is somewhat above the theoretical expectations. It should be noted, however, that the effect of a finite particle number in simulations of the transport coefficients of HS fluids and the way how these coefficients are approaching the thermodynamic limit are not very thoroughly investigated (note, however, a very recent paper [43], where this thematics has been addressed).…”

“…The ratio of sound velocities can also be important in the context of the Stokes-Einstein (SE) relation. For selfdiffusion of atoms in simple pure fluids the SE relation takes the form [37][38][39][40][41][42]…”