The shear viscosity of n-butane by equilibrium and non-equilibrium molecular dynamics

Abstract

The shear viscosity of n-butane has been computed by the method of molecular dynamics (MD), by both the Green-Kubo technique and a non-equilibrium method employing a weak fictitious external field inducing a symmetric velocity gradient (pure deformational flow). In this last case, non-equilibrium segments, starting from equilibrium configurations, were averaged, the subtraction technique being used to measure the signal out of noise.

The stress autocorrelation functions, provided independently by these two techniques, agree remarkably well with each other over the period of time investigated, i.e. the length of the non-equilibrium segments (0·76 ps). This function presents a long positive tail at two definitely different thermodynamical states: a dense liquid and a supercritical fluid. This tail, which is difficult to interpret, extends over 3·0 and 1·5ps respectively and gives a non-negligible contribution to the viscosity coefficient.

In this particular case where the correlation time is relatively long, the use of Green-Kubo formula at equilibrium is more advantageous than the subtraction method despite the fact that, as a statistical analysis shows, the stress autocorrelation function obtained by this last method is far more precise at times shorter than 0·5 ps.

These calculations illustrate the agreement, at weak gradients, of the non-equilibrium fictitious field methods with the Green-Kubo equilibrium method, for a rather complex molecular system subject to periodic boundary condition. This result is important as it is a necessary condition for the non-equilibrium MD methods to be generally valid for arbitrary shear rates beyond the linear region.