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/Ai = 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.
Bibliographical noteFunding Information:
We thank Richard Borry, III and Enrique Iglesia for many helpful discussions of this work. This work was supported by the Office of Industrial Technology of the U.S. Department of Energy under Contract DE-AC03-SF7600098.