Local framework structure

Aluminum-27 Double Rotation NMR spectroscopy (DOR) has been used to investigate framework ordering in the aluminophosphate molecular sieves VPI-5, AIPO4-5, and AIPO4-8. Well-resolved peaks in the Al DOR spectra of both hydrated and dehydrated VPI-5 allow isotropic shifts to be conelated with local framework structure. More distorted aluminum environments are reflected by broader lines in Al DOR spectra of AIPO4-5 and AIPO4-8. 

The multiresolution framework allows us to reconsider more constructively some of the features of the structure adaptation algorithm. First, a strictly forward move in the ladder of subspaces [Eq. (8)] is not necessary. Due to localization, the structural correction can be sought in higher spaces before ail functions in the previous space are exhausted. This... 

Section II introduces the formal framework for the definition anc description of process trends at all levels of detail qualitative, order-of magnitude, and analytic. A detour through the basic concepts of scale-spact filtering is necessary in order to see the connection between the concept o process trends and the classical material on signal analysis. Within th( framework of scale-space filtering we can then elucidate the notions o episode, scale, local filtering, structure of scale, distinguishec features, and others. 

To develop the kinetic equations in condensed phases the master equation must be formulated. In Section 3 the master equation is used to generate the kinetic equations for local concentrations and pair correlation functions. The latter set of equations permits consideration of history of formation of the local solid structure as well as its influence on the subsequent elementary stages. The many-body problem and closing procedure for kinetic equations are discussed. The influence of fast and slow stages on a closed system of equations is demonstrated. The multistage character of the kinetic processes in condensed phase creates a problem of self-consistency in describing the dynamics of elementary stages and the equilibrium state of the condensed system. This problem is solved within the framework of a lattice-gas model description of the condensed phases. 

A second, even more speculative point is that the mathematical framework of nonlinear dynamics may provide a basis to begin to bridge the gap between local microstructural features of a fluid flow or transport system and its overall meso- or macroscale behavior. On the one hand, a major failure of researchers and educators alike has been the inability to translate increasingly sophisticated fundamental studies to the larger-scale transport systems of traditional interest to chemical engineers. On the other hand, a basic result from theoretical studies of nonlinear dynamical systems is that there is often an intimate relationship between local solution structure and global behavior. Unfortunately, I am presently unable to improve upon the necessarily vague notion of a connection between these two apparently disparate statements. 

There are at least three types of cluster expansions, perhaps the most conventional simply being based on an ordinary MO-based SCF solution, on a full space entailing both covalent and ionic structures. Though the wave-function has delocalized orbitals, the expansion is profitably made in a localized framework, at least if treating one of the VB models or one of the Hubbard/PPP models near the VB limit -and really such is the point of the so-called Gutzwiller Ansatz [52], The problem of matrix element evaluation for extended systems turns out to be somewhat challenging with many different ideas for their treatment [53], and a neat systematic approach is via Cizek s [54] coupled-cluster technique, which now has been quite successfully used making use [55] of the localized representation for the excitations. 

XPS-NMR Comparisons. While the physics associated with NMR and XPS measurements are very different, both techniques are sensitive to changes in the local environment and electronic structure of the individual atomic species. The observation of a correlation between bulk T-atom environments probed by NMR and surface T-atom environments probed by XPS would indicate that XPS truly provides information about the framework structure and not just a defective region at the surface of the crystals. 

There a been a number of interesting applications of the framework developed in the studies of the simple ions were MD simulations of the quadrupolar relaxation has been performed on counterions in heterogeneous systems. Studies of a droplet of aqueous Na embedded in a membrane of carboxyl groups [54], showed that the EFG was strongly effected by the local solvent structure and that continuum models are not sufficient to describe the quadrupolar relaxation. The Stemheimer approximation was employed, which had been shown to be a good approximation for the Na ion. Again, the division into molecular contributions could be employed to rationalize the complex behavior in the EFG tensor. Similar conclusions has been drawn from MD simulation studies of ions solvating DNA... 

The deeper oxidation of ethylbenzene over TS-2 can be explained with the slower diffusion of 1-phenylethanol and aeetophenone formed in the zeolite pores where they could undergo additional oxidation to aeetophenone or other products, respectively. Another possible reason could be some differences in the local geometry of the titanium sites due to the different framework structure of the two titanium silicalites. 

A structure similar to that of LaY zeolites has been suggested for CeY zeolites (3,7). However, structural x-ray studies of CeX zeolites have shown (9) that the presence of trivalent and especially tetravalent- cerium results in a considerable distortion of the 6-membered ring. Such a distortion could explain the lower hydrothermal stability and stronger dealumination of CeY zeolites vs LaY zeolites. Indeed, the loss in crystallinity and surface area observed for steamed CeY zeolites as compared to corresponding LaY zeolites (Table I) is indicative of significant structural collapse. Furthermore, the paramagnetism of trivalent cerium ions and the local framework distortions, caused primarily by tetravalent cerium ions, will result in a deterioration of spectral resolution. 

PLATE VIII Top left - framework structure of ETS-IO right - local structure around framework Ti in ETS-10, as determined from EXAFS and computer modelling bottom left - comparison between experimental and simulated EXAFS data for ETS-10. 

All of the atoms making up the zeolite lattice [those enumerated in the bracketed part of Eq. (1) j have NMR-active isotopes and thus can be investigated by solid-state NMR. The important nuclei and their natural abundances are Si (4.7%), Al (100%), and O (0.04%). Because of the low natural abundance of O, isotopic enrichment is usually necessary. The 100% abundant P nucleus is also present in the aluminophosphate systems discussed above. In addition, H (100%) may be present in any of these framework structures in OH groups at defect sites. We will discuss the information regarding zeolite structure available through study of these nuclei and the interactions of their spins with local electric and magnetic fields. 

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