Two- and N-step correlated models for the analysis of molecular dynamics trajectories of linear molecules in silicalite

Abstract

Recent molecular dynamics data on the diffusion of linear diatomic and triatomic molecules in the zeolite silicalite are analyzed in terms of a new correlated model ͓F. Jousse, S. M. Auerbach, and D. P. Vercauteren, J. Chem. Phys. 112, 1531 ͑2000͔͒ capable to account for both first-and higher-order correlation effects. This ''N-step'' model reproduces very well our calculated mean square displacements and diffusion coefficients of the molecules considered. The improvements with respect to the results obtained with our previous ''two-step'' model ͓P. Demontis, J. Kärger, G. B. Suffritti, and A. Tilocca, Phys. Chem. Chem. Phys. 2, 1455 ͑2000͔͒ are remarkable for all molecules except chlorine, showing that only in this case the effect of ͑negative͒ correlations spanning more than two jumps between channel intersections ͑ϳ20 Å͒ can be neglected. The basic trajectory analysis in terms of single-and two-step models, besides being an useful reference, provides all the input data needed for the application of the N-step model. Indeed, in its silicalite formulation, the N-step model is strongly linked to the two-step one because it calculates the probability of a sequence of jumps in the same channel by means of the correlations between any two consecutive jumps. Finally, the possibility to obtain qualitative insight into the diffusive mechanism through various kind of correlation coefficients is discussed.

Tracing Memory Effects in Correlated Diffusion Anisotropy in MFI-Type Zeolites by MD Simulation

“…This means that a molecule passing a channel intersection continues on its way independent of its past (i.e., independent of the channel intersection from where it has come). Although in numerous experimental , and simulation − studies eq 1 was found to serve as a reasonable estimate, in several cases the deviations were found to be physically significant.

1 Topology of the channels in silicalite-1.

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Modeling and Simulation of Structure, Thermodynamics, and Transport of Fluids in Molecular Confinements

“…In numerous experimental [127,185] and simulation studies [139,172,176,[180][181][182]186], (171) has in principle been confirmed, although some deviations have also been observed. In [139] these deviations were quantified by introducing a memory parameter…”

“…silicalite. The black dots show the intersections between straight channels and zigzag channels in the unit cell and the grey dots show intersections of the straight channels with zigzag channels that are outside the unit cell diffusion [180][181][182]. If such effects are neglected, the principal values of the diffusion tensor, i.e.…”

Modeling molecular diffusion in channel networks via displacements between the channel segments

“…There is no need anymore for including the correlation of subsequent displacements by introducing memory parameters. [16][17][18][19][20][21] This simplification, however, doesn't allow anymore the prediction of structurerelated diffusion anisotropy, as the prevailing feature of the original model presented in ref. 7.…”

“…In the extreme case of hardly any interchange the molecules essentially remain in one channel, so that D z approaches zero and b ) 1. Several papers [16][17][18][19][20][21] deal with the possibilities to account for correlations between subsequent dispacements and to derive the corresponding relations for the memory parameter b and, thus, for the interrelation of the principal elements D i of the diffusion tensor. In this paper (section 2) we develop a model for diffusion in MFI-type zeolites where the channel segments, i.e.…”