Al Next Nearest Neighbor, Ring Occupation, and ProximityStatistics in ZSM-5

The distribution of framework Al in ZSM-5 was simulated for various Si/Al ratios and the results used to determine the fraction of Al atoms in next nearest neighbors (NNN) T sites. All the 4-, 5-, and 6-membered rings were identified in the unit cell and the fraction of these rings with 0, 1, 2, and 3 Al was calculated. Lastly, the radial distribution function of Al–Al pairs, the number of Al’s expected within a sphere of radius, r, centered around an Al (E), and the probability of finding at least one Al within a sphere of radius, r, centered around an Al (P) were calculated for different Si/Al ratios. Based on these results, the probability of locating NNN pairs of Al atoms situated at a distance suitable for the stabilization of M2+ and [M–O–M]2+ cations were carried out and then used to determine maximum values for M2+/Al and [M–O–M]2+/Al. The value of M2+/Al is 0.12 for Si/Al= 12 and 0.07 for Si/Al= 24, and the value of [M–O–M]2+ is 0.30 for Si/Al= 12 and 0.19 for Si/Al= 24. The values of M2+/Al obtained theoretically are in reasonable agreement with those observed experimentally for Pd–ZSM-5. A significant finding of our simulation is that Löwenstein’s rule is the dominant factor governing short-range correlations of framework Al atoms, and hence the distribution of NNN pairs of Al atoms. As a consequence, analytical theories that include consideration of Löwenstein’s rule provide rather accurate estimates of the probability of finding Al NNN pairs. c © 1999 Academic Press