Velocity autocorrelation functions of particles and clusters in liquids. A possible criterion for correlation length of incipient glass formation

Abstract

We have carried out molecular-dynamics simulations over a range of densities in two and three dimensions for particles that interact through soft repulsive potentials. We have also carried out calculations of the corresponding systems in which all particles except a tagged particle and its neighbors within a certain distance are frozen. Velocity autocorrelation functions for a single particle, for clusters containing the particle, and for the velocity of the particle relative to an embedding cluster were obtained. The single-particle velocity autocorrelation function can be resolved into correlation functions describing the local rattling in a cage or a cluster, the motion of the cluster itself, and a small cross-correlation term; the function for the single particle is sensitive to the structure of the fluid over a much shorter time scale than are those of clusters, and the shape of the single-particle velocity autocorrelation function comes primarily from rattling motion within a cage. We show that the velocity autocorrelation functions of clusters are probably better probes than that for the single particle for investigating incipient glass formation since they can be used to establish a correlation length which increases when a liquid is cooled. The dynamics of clusters at a given state point depend upon their sizes, and the nature of their motions changes qualitatively from "rattling" for small to "diffusional" for large clusters, the "critical" size at which the change occurs increasing with decreasing temperature. A simple model for this cluster behavior is presented.