Topology Fourier analysis

The electron crystallography method (21) has been used to characterize three-dimensional structures of siliceous mesoporous catalyst materials, and the three-dimensional structural solutions of MCM-48 (mentioned above) and of SBA-1, -6, and -16. The method gives a unique structural solution through the Fourier sum of the three-dimensional structure factors, both amplitude and phases, obtained from Fourier analysis of a set of HRTEM images. The topological nature of the siliceous walls that define the pore structure of MCM-48 is shown in Fig. 28. 

The topological analysis of the total density, developed by Bader and coworkers, leads to a scheme of natural partitioning into atomic basins which each obey the virial theorem. The sum of the energies of the individual atoms defined in this way equals the total energy of the system. While the Bader partitioning was initially developed for the analysis of theoretical densities, it is equally applicable to model densities based on the experimental data. The density obtained from the Fourier transform of the structure factors is generally not suitable for this purpose, because of experimental noise, truncation effects, and thermal smearing. 

We have investigated the photooxidation of toluene in several different zeolite hosts (BaX, BaY, CaY, BaZSM-5, and NaZSM-5) using in-situ Fourier Transform Infrared (FT-IR) spectroscopy and ex-situ Gas Chromatography (GC) to analyze product formation and product yields. This combined approach allows for a more detailed analysis of the product distribution. The product selectivity in these reactions appears to be governed by the presence of a small number of acid sites rather than by the framework composition or topology of the zeolite host. 

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