Three-dimensional Ising system with long-range interactions: A computer model of Vycor glass.

Abstract

A computer model for Vycor glass using the three-dimensional Ising model with long range interactions is presented. The effect of the interaction range on the resulting Vycor microstructure is also investigated by measuring the pore size distribution for the q=6 (nearest neighbor) as well as longer-range interaction, i.e., q=26 and 124 Ising models. The discrepancy between the nearest-neighbor Ising model and the experimental results is interpreted in terms of a lattice-induced interfacial energy anisotropy. The influence of the range of interaction on the degree of interfacial energy anisotropy is illustrated by means of two- and three-dimensional Wulff plots (interfacial energy versus interface orientation) for each of the ranges of interaction considered. The shape of the pore size distributions obtained from the longer range Ising models is in agreement with the experimental results. However, the simulation distributions display a shift in the peak location observed as compared to the experimental distribution. The shift in peak location present in the simulation results is explained by a relative abundance of short chords combined with a lack of the large chords, with respect to the experimental results. This abundance of short chords is attributed to the interface roughness introduced by the longer range interaction, while the lack of large chords is attributed to the finite lattice sizes used in this study. A minimum system size and maximum interaction range are suggested, which should lead to a pore size distribution in close agreement with experimental results.