Studies on Mordenite by Monte Carlo Method Ⅰ. Si, Al Distribution in Framework of Parent Mordenite

The distribution of Al atoms in the framework of parent mordenites was simulated by two models. According to the first one, Model-Ⅰ, the distribution of Al atoms was constrained only by Loewenstein’s rule. In Monte Carlo simulation, the sampling configurations were created by using a random number generator which posits Al atoms in a representative portion of the framework （27 unit cells） randomly and does not allow the presence of any couple of nearest-neighboring Al-Al. For each sampling configuration, the numbers of five types of building unitsSi（n-Al）; n=0-4 were counted up by computerization. The populations of the building units for given Si/Al ratio were obtained by taking an average from a sample space with a big enough size.
Distribution Model-Ⅱ superim poses on Model-Ⅰ a second, weaker constraint which minimized the number of Al-Al next-nearest neighbors in its sampling configurations. The calculated populations of the building units Si（n-Al） could be compared with the relative intensities, (Ⅰ_Si（n-Al）, of the ²⁹Si MAS NMR spectrum of the parent mordenite sample with corresponding Si/Al framework ratio.
The Monte Carlo simulation based on distribution Model-Ⅱ gave much btter results than the Model-Ⅰ coinciding with ²⁹Si MAS NMR observations. And so we can conclude that the distributions of Al atoms in the framework of parent mordenites are subject to the constraint of Loewenstein’s rule, which fobbids the presence of Al-Al nearest-neighbors; superimposed on this is a second weaker constraint that the Al-Al are avoided to be the next-nearest neighbor.
Based on the distribution Model-Ⅱ, the relative populations of type Al（m-Al） （m=0-3） were calculated as well. Because both calculated Si（n-Al） and Al（m-Al） were obtained from the same Monte Carlo sample space, their correlation was then established on reasonable theoretical foundation. The former, Si（n-Al）, can be checked by ²⁹Si MAS NMR observation experimentally, the latter, Al（m-Al）, is connected with the catalytic properties of the parent mordenites.