The central cell model: A mesoscopic hopping model for the study of the displacement autocorrelation function

摘要

On the mesoscale, the molecular motion in a microporous material can be represented as a sequence of hops between different pore locations and from one pore to the other. On the same scale, the memory effects in the motion of a tagged particle are embedded in the displacement autocorrelation function (DACF), the discrete counterpart of the velocity autocorrelation function (VACF). In this paper, a mesoscopic hopping model, based on a lattice-gas automata dynamics, is presented for the coarse-grained modeling of the DACF in a microporous material under conditions of thermodynamic equilibrium. In our model, that we will refer to as central cell model, the motion of one tagged particle is mimicked through probabilistic hops from one location to the other in a small lattice of cells where all the other particles are indistinguishable; the cells closest to the one containing the tagged particle are simulated explicitly in the canonical ensemble, whereas the border cells are treated as mean-field cells in the grand-canonical ensemble. In the present paper, numerical simulation of the central cell model are shown to provide the same results as a traditional lattice-gas simulation. Along with this a mean-field theory of self-diffusion which incorporates time correlations is discussed. © 2011 American Institute of Physics Article Outline INTRODUCTION LOCAL RANDOMIZATION AND PROPAGATION Randomization Propagation JUMPS AND TIME CORRELATIONS THE CENTRAL CELL MODEL Generating the initial configuration Time evolution ANALYSIS OF THE SELF-DIFFUSION PROCESS: THE DISPLACEMENT AUTOCORRELATION FUNCTION Contribution at the initial time Contribution after one iteration: A probabilistic interpretation of the normalized DACF Contribution after several iterations MEAN-FIELD DACF: THEORETICAL PREDICTION OF SELF-DIFFUSIVITY Exact DACF in the limit of infinite dilution Approximated mean-field DACF and self-diffusivity at arbitrary loading Mean-field jump randomization Mean-field propagation Mean-field jump probabilities DISCUSSION OF THE MEAN-FIELD RESULTS Memory preserved in exit and inner sites Memory-preserving backscattering CONCLUSIONS