No abstract

Recent simulation work has established that the widely accepted mode-coupling theory for the strain rate dependence of the pressure and energy of simple fluids under shear (i.e., energy and pressure are functions of strain rate to the power 3 / 2) is observed in the vicinity of the triple point. Away from the triple point, the scaling exponent of the strain rate was seen to be closer to 2 than 3 / 2, suggesting a possible analytic behavior. In this paper, we accurately determine the scaling exponent behavior for a Lennard-Jones fluid in the dense fliud region and find that it varies continuously between approximately 1.2 and approximately 2 as a function of density and temperature, thus confirming its nonanalyticity. We furthermore find that the behavior is characterized by a simple linear function of density and temperature.

The solid–liquid equilibrium phase transition of a one-component Lennard-Jones system is determined by equilibrium and nonequilibrium molecular dynamics simulation methods. One method uses the observation that the scaling exponent of the pressure or energy of a shearing Lennard-Jones liquid is approximately 1 at the solid phase. This enables us to locate the density of the coexisting solid phase. The coexisting liquid phase density is then obtained by constructing a tie line between the coexisting solid phase point and the liquid phase curve. Alternatively, the coexisting liquid phase density can be efficiently obtained by observing the change in pressure as a function of strain rate and density. The coexisting solid phase density can be then obtained from a tie line from the liquid curve to the solid curve. These calculations are the first reported use of combined equilibrium and nonequilibrium molecular dynamics methods for phase coexistence at equilibrium. Our results are in very good agreement with those obtained by alternative simulation methods for phase equilibria.

Nonequilibrium molecular dynamics simulations are reported at different strain rates (gamma) and thermodynamic state points for a shearing atomic fluid interacting via a Lennard-Jones potential. Our simulations are performed at the Lennard-Jones triple point, a point midway between the triple point and the critical point, and a high point closer to the critical temperature. We find that, for the mid-point and high point, the energy and hydrostatic pressures have strain-rate dependencies of gamma(2), in contrast to the gamma(3/2) dependencies predicted by mode coupling theory. This analytical dependence is consistent with a Taylor series expansion of these quantities as powers of the strain rate tensor. Only at the triple point does the pressure and energy display a nonanalytical dependence on gamma(3/2).