Density dependence of the stress relaxation function of a simple fluid

We present accurate molecular dynamics calculations of the shear stress relaxation modulus of a simple atomic fluid over a wide range of densities. The high accuracy of the data enables us to study changes in the functional form of the shear relaxation modulus, and the properties that are derived from it, as the density is increased from the ideal gas limit to the upper limit of the fluid range. We show that the shear relaxation modulus of a dilute atomic fluid can be accurately described with a simple functional form consisting of a Gaussian plus a single exponential, whereas the dense fluid exhibits a more complicated relaxation function. The infinite-frequency shear modulus, the zero-shear viscosity, and the zero-shear first normal stress coefficient are calculated from the stress autocorrelation function. The ratio of the first normal stress coefficient to the viscosity is used to calculate the viscoelastic relaxation time. While the viscosity and the infinite-frequency shear modulus both increase monotonically with increasing density, the first normal stress coefficient and the viscoelastic relaxation time both decrease to a minimum at intermediate densities before increasing again. Our results for the viscosity and the first normal stress coefficient in the low-density limit both agree well with the predictions of kinetic theory.