Elementary Steps of Diffusion

NMR spectroscopy shares its ability to provide information about the elementary steps of diffusion and the resulting concentration profiles with other spectroscopic techniques like IR [45,46], neutron [47-49] and dielectric [50, 51] spectroscopy. With respect to its ability to follow molecular diffusion paths between himdreds of nanometers up to hundreds of micrometers, however, it is unique. Measurements of this type are based on the apphcation of an inhomogeneous magnetic field. In the technique, being so far the most... 

The elementary steps of diffusion are only possible because of the existence of lattice defects. A single-phase polycrystalline material consists of crystallites containing point defects, dislocations, and low-angle grain boundaries. Between the crystallites there are high-angle grain... 

Molecular-level studies of mechanisms of proton and water transport in PEMs require quantum mechanical calculations these mechanisms determine the conductance of water-filled nanosized pathways in PEMs. Also at molecular to nanoscopic scale, elementary steps of molecular adsorption, surface diffusion, charge transfer, recombination, and desorption proceed on the surfaces of nanoscale catalyst particles these fundamental processes control the electrocatalytic activity of the accessible catalyst surface. Studies of stable conformations of supported nanoparticles as well as of the processes on their surface require density functional theory (DFT) calculations, molecular... 

The third and last part of the book (Chapters 12-16) deals with zeolite catalysis. Chapter 12 gives an overview of the various reactions which have been catalyzed by zeolites, serving to set the reader up for in-depth discussions on individual topics in Chapters 13-16. The main focus is on reactions of hydrocarbons catalyzed by zeolites, with some sections on oxidation catalysis. The literature review is drawn from both the patent and open literature and is presented primarily in table format. Brief notes about commonly used zeolites are provided prior to each table for each reaction type. Zeolite catalysis mechanisms are postulated in Chapter 13. The discussion includes the governing principles of performance parameters like adsorption, diffusion, acidity and how these parameters fundamentally influence zeolite catalysis. Brief descriptions of the elementary steps of hydrocarbon conversion over zeolites are also given. The intent is not to have an extensive review of the field of zeolite catalysis, but to select a sufficiently large subset of published literature through which key points can be made about reaction mechanisms and zeolitic requirements. 

For an aqueous suspension of crystals to grow, the solute must (a) make its way to the surface by diffusion, (b) undergo desolvation, and (c) insert itself into the lattice structure. The first step involves establishment of a stationary diffusional concentration field around each particle. The elementary step for diffusion has an activation energy (AG ), and a molecule or ion changes its position with a frequency of (kBT/h)exp[-AGl,/kBT]. Einstein s treatment of Brownian motion indicates that a displacement of A will occur within a time t if A equals the square root of 2Dt. Thus, the rate constant for change of position equal to one ionic diameter d will be... 

The process of molecular diffusion may be viewed conceptionally as a sequence of jumps with statistically varying jump lengths and residence times. Information about the mean jump length /(P and the mean residence time t, which might be of particular interest for a deeper understanding of the elementary steps of catalysis, may be provided by spectroscopic methods, in particular by quasielastic neutron scattering (see next Section) and nuclear magnetic resonance (NMR). 

It has been demonstrated that the combined application of various NMR techniques for observing molecular rotations and migrations on different time scales can contribute to a deeper understanding of the elementary steps of molecular diffusion in zeolite catalysts. The NMR results (self-diffusion coefficients, anisotropic diffiisivities, jump lengths, and residence times) can be correlated with corresponding neutron scattering data and sorption kinetics as well as molecular dynamics calculations, thus giving a comprehensive picture of molecular motions in porous solids. 

The most complete mathematical model of a nonuniform adsorbed layer is the distributed model, which takes into account interactions of adsorbed species, their mobility, and a possibility of phase transitions under the action of adsorbed species. The layer of adsorbed species corresponds to the two-dimensional model of the lattice gas, which is a characteristic model of statistical mechanics. Currently, it is widely used in the modeling of elementary processes on the catalyst surface. The energies of the lateral interaction between species localized in different lattice cells are the main parameters of the model. In the case of the chemisorption of simple species, each species occupies one unit cell. The catalytic process consists of a set of elementary steps of adsorption, desorption, and diffusion and an elementary act of reaction, which occurs on some set of cells (nodes) of the lattice. 

The interatomic and intennolecular interactions of adsorbed species and their state on the catalyst surface are the basis of all elementary steps of the catalytic process. The importance and reliability of the modeled results depend on the correct choice of the potential of the interatomic interaction. The question about the type and nature of interatomic forces between adsorbed species is the focus. Interatomic forces are diverse and usually anisotropic. Adsorbed species do not form structures at low coverage. When the number of adsorbed species and the rate of their surface diffusion increase, the probabilities of their interaction and formation of surface polyatomic structures increases. These structures can be rather stable and they form islands of adsorbed species. 

The elementary steps of the silver halide photographic process are discussed in reference [127]. The surface diffusion rates of silver atoms on a single silver crystal surface were found to increase by orders of magnitude in the presence of chemisorbed sulfur. Could sulfur-induced sensitization of the photographic process be related to this observation ... 

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