Diffusional anisotropy of simple sorbates in silicalite

Microcanonical ensemble molecular dynamics simulations are used to study anisotropy in diffusional and related dynamical properties for five spherical sorbates of varying size and polarizability in silicalite. Silicalite has straight and zigzag channels, parallel to the y and x-axes of the unit cell, respectively, which are interconnected in such a way that diffusion along the z direction is possible only by alternation of the sorbate between straight and zigzag channel segments. Helium, the smallest and most weakly bound sorbate, is found to comply most closely with the behavior expected on the basis of the simple random walk model developed to understand the geometrical correlation between the principal elements of the diffusional tenser in silicalite (J. Karger, J. Phys. Chem. 1991, 95, 5558). The larger and more strongly bound sorbates, Ne, Ar, CH4, and Xe, show significant deviations from this model. The diffusion of these particles along the z direction is distinctly subdiffusional with the mean square displacement growing as approximate to t(0.8). The randomization and anisotropy parameters for all four sorbates are similar but differ significantly from the predictions of the random walk model. The relative rates of diffusion along the straight and zigzag channels are more sensitive to the nature of the sorbate than the anisotropy and randomization parameters. For all five sorbates, the subdiffusional behavior along the z direction, as well as deviations from the predictions of the random walk model, are more pronounced at higher concentrations. The anisotropy in the short-time dynamics has been examined by studying the velocity autocorrelation functions and the instantaneous normal mode spectra. For very short times of less than 0.5 ps, the velocity autocorrelation function and its directional analogues are virtually identical, but divergences are seen by times of the order of 1 ps. The instantaneous normal mode spectra show the expected correlation between the diffusion coefficient, the Einstein frequency, and the fraction of imaginary modes. There is no significant anisotropy in the INM spectra that is consistent with the behavior of the velocity autocorrelation functions for short time scales.