Frequency-Dependent Elongational Viscosity by Nonequilibrium Molecular Dynamics

The elongational viscosity of a liquid describes the response of the liquid to simultaneous stretching and compression in various directions, subject to the restriction that the trace of the rate of the strain tensor is zero (or the density is constant). Despite the growing popularity and usefulness of nonequilibrium molecular dynamics methods in studies of the shear viscosity of simple and complex fluids, the elongational viscosity remains a relatively neglected property in computer simulation studies. This stems from some significant technical difficulties that arise when standard methods such as the constant strain rate SLLOD algorithm are applied to elongational flow. For example, if planar elongational flow with a constant elongation rate is applied in a computer simulation with periodic boundary conditions, the box size in the contracting direction quickly becomes smaller than twice the range of the potential, violating the minimum image convention. The time at which this occurs may be less than the time required for the system to reach a steady state, making it impossible to compute the steady-state elongational viscosity. This difficulty can be avoided by applying an oscillating elongational strain rate to the liquid, and computing frequency dependent elements of the stress tensor, which can then be extrapolated to zero frequency to evaluate the steady-state elongational viscosity. We have used this method to compute the elongational viscosity of a simple atomic liquid and discuss its possible application to a model polymeric liquid.