Calculating the hopping rate for diffusion in molecular liquids: CS2

Abstract

We extend the cage correlation function method for calculating the hopping rate in Zwanzig’s model of self-diffusion in liquids [R. Zwanzig, J. Chem. Phys. 79, 4507 (1983)] to liquids composed of polyatomic molecules. We find that the hopping rates defined by the cage correlation function drop to zero below the melting transition and we obtain excellent agreement with the diffusion constants calculated via the Einstein relation in liquids, solids, and supercooled liquids of CS2. We also investigate the vibrational density of states of inherent structures in liquids which have rough potential energy surfaces, and conclude that the normal mode density of states at the local minima are not the correct vibrational frequencies for use in Zwanzig’s model when it is applied to CS2.

Direct Observation of Stretched-Exponential Relaxation in Low-Temperature Lennard-Jones Systems Using the Cage Correlation Function

“…The primary result of this paper is the observation that the cage correlation functions in the defective crystals cannot be fit with a simple exponential function at long times, as was done for the liquids [2,3]. The cage correlation functions shown in Fig.…”

“…We have recently developed a method to obtain estimates of the hopping rate between basins for Zwanzig's model of self-diffusion [1], in atomic [2] and molecular liquids [3]. We approached the problem by introducing the cage correlation function which measures the rate of change of atomic surroundings in a computer simulation [2].…”

“…The hopping rate was associated with the long-time exponential decay of this function. The cage correlation concept has proven itself to be a useful tool in understanding the mechanisms of self-diffusion, and as such was used to test the limits of the Zwanzig model [2,3], which is built on the foundation of Goldstein's activated jump model [4], and also on the rearranging regions model due to Adam and Gibbs [5].…”

“…Only those events which result in irreversible changes to the surroundings will cause the cage to decorrelate at long times. The mathematical formulation of the cage correlation function was given in previous publications [2,3], and is not repeated in this paper. A graphical representation of the cage correlation idea is shown in Fig.…”

“…We have used the cage correlation function to predict the hopping rates in liquids [2,3], and below we discuss the results for this correlation function when the liquid is cooled well below the melting temperature.…”