Linear and angular velocity autocorrelation functions for two-dimensional systems of repulsive and Lennard-Jones diatomics

Abstract

The method of molecular dynamics has been employed to study the autocorrelation functions (ACF's) of the linear velocity and of the angular momentum for two two-dimensional systems of diatomic molecules. The anisotropic potential used is built from four atom-atom interactions. These are either purely repulsive (R), or repulso-attractive (LJ). Emphasis has been put on the long-time behaviour; for this we have used large systems (1600 molecules). The density lies in the intermediate range. The linear velocity ACF exhibits, for system R, an initial decay which is exponential and whose characteristic time has been checked to be of the order of the mean ‘collision’ time. For system LJ (where collisions cannot be usefully defined) the decay does not follow a simple law, and lies above a single exponential. After an intermediate regime which lasts a long time-span for both systems, the ACF's adopt a t ^-1 decay in agreement with theoretical predictions based on hydrodynamics or other approaches. The mean square displacement has also been extracted from the data. Its ratio to time, i.e. the apparent coefficient of diffusion, increases logarithmically with time, so that the two kinds of data are in accord. This asymptotic regime starts after about 11 collision times for the repulsive system, and about as soon for the other one. The angular momentum ACF's, after an initial decay which is closer to an exponential for system R than for system LJ, adopt a t ^-3 behaviour for a very long time-span; this possibly masks a final t ^-2 decay predicted by several theories based on the coupling of the intrinsic momentum with the vorticity of the fluid.