High-Frequency Shear Modulus and Relaxation Time of Soft-Sphere and Lennard–Jones Fluids

The high-frequency shear modulus, G∞, and shear relaxation time, τshear, are obtained using the Zwanzig–Mountain equation for soft-sphere and Lennard- Jones potentials. The Hansen and Weis soft-sphere radial distribution function and the Matteoli–Mansoori Lennard-Jones radial distribution function are used in the equation. The shear relaxation times of different isotherms for both of these fluids pass through a minimum at a reduced density of about 0.7, which indicates a change from fluid-like behavior to viscoelastic behavior. The origins of this common density point are discussed. It is also shown that for the Lennard-Jones fluid, if the ratio of the reduced relaxation time to a power of the reduced temperature is plotted as a function of the reduced density, all isotherms become superimposed on a single curve.