Zeolites transition state theory

The results of experimental studies of the sorption and diffusion of light hydrocarbons and some other simple nonpolar molecules in type-A zeolites are summarized and compared with reported data for similar molecules in H-chabazite. Henry s law constants and equilibrium isotherms for both zeolites are interpreted in terms of a simple theoretical model. Zeolitic diffusivitiesy measured over small differential concentration steps, show a pronounced increase with sorbate concentration. This effect can be accounted for by the nonlinearity of the isotherms and the intrinsic mobilities are essentially independent of concentration. Activation energies for diffusion, calculated from the temperature dependence of the intrinsic mobilitieSy show a clear correlation with critical diameter. For the simpler moleculeSy transition state theory gives a quantitative prediction of the experimental diffusivity. 

The delocalized state can be considered to be a transition state, and transition state theory [105], a well-known methodology for the calculation of the kinetics of events, [12,88,106-108] can be applied. In the present model description of diffusion in a zeolite, the transition state methodology for the calculation of the self-diffusion coefficient of molecules in zeolites with linear channels and different dimensionalities of the channel system is applied [88], The transition state, defined by the delocalized state of movement of molecules adsorbed in zeolites, is established during the solution of the equation of motion of molecules whose adsorption is described by a model Hamiltonian, which describes the zeolite as a three-dimensional array of N identical cells, each containing N0 identical sites [104], This result is very interesting, since adsorption and diffusion states in zeolites have been noticed [88],... 

Transition state theory can also be employed to calculate diffusion coefficients in hopping processes. Adsorbates prefer to reside at particular places in a zeolite and because an energy barrier is present between them, they do not transfer easily from one site to another. The possible adsorption sites are located via a Monte Carlo method, and the transition state via migration path analyses. A rate constant can be associated with jumps from site i to siteA surface can be defined that separates sites i and and contains the top of the energy... 

F. Jousse and S. M. Auerbach, /. Chem. Phys., 107, 9629 (1997). Activated Diffusion of Benzene in NaY Zeolite Rate Constants from Transition State Theory with Dynamical Corrections. 

Moreover, it is noted that this method can be applied to studies of slow diffusion, inaccessible in MD simulations. The approach seems very flexible in that it is applicable to a wide range of pore structures and fluids, provided the free-energy barriers are sufficiently high for transition state theory to be valid. The method therefore will fail at sufficiently high temperatures. Studies on diffusion of methane, ethane, and propane in LTL- and LTA-type zeolites were considered. 

Membranes with ordered structures such as zeolites or nanotubes have considerable potential as gas separation membranes [46-48], In addition to having thermal and chemical stability, the porosity of these structures is ordered, and therefore there is usually more control over the separation properties. The pores within these structures are such that gas transport can not be completely explained by the transition state theory. This is because, in nanotubes for example, there is only one transition, from outside of the tube to inside of the tube. Two alternative models are outlined here, the parallel transport model and the resistance in series transport model, which are illustrated in Figure 5.5, and they are explained in detail by the work of Gilron and Softer [27]. 

The models developed here account for unmeasurable intermediates such as adsorbed ions or free radicals. Microkinetic analysis, pioneered by Dumesic and cowokers"", is an example of this approach. It quantifies catalytic reactions in terms of the kinetics of elementary surface reactions. This is done by estimating the gas-phase rate constants from transition state theory and adjusting these constants for surface reactions. For instance, isobutane cracking over zeolite Y-based FCC catalysts has 21 reversible steps defined by 60 kinetic parameters." The rate constants are estimated from transition state theory... 

As examined in the next chapter, transition-state theory is applicable when the rate-limiting step of a molecular process is controlled by a slow passage over a barrier. Not only reactions but also some diffusion processes are characterized by equilibration of a molecule on a surface site, in a cavity of a zeolite, and by movement of a molecule over a barrier (Figure 4.17). For diffusion, the relation between distance of motion and time is given by... 

Catalyst Design Electrostatic Potentials Chemical Applications Transition State Theory Zeolites Applications of Computational Methods. 

There are four widely accepted theories of shape selectivity reactant shape selectivity (RSS), product shape selectivity (PSS), transition state selectivity (TSS) (Figure 12.2), and concentration effect all of them are based on the hypothesis that the reactions occur within the zeolite micropores only. As indicated earlier, this hypothesis is often verified, the external surface area of the commonly used zeolites being much lower (one to two orders of magnitude) than their internal surface area. ... 

A new transition-state-searching algorithm was used to determine the mechanism for methanol condensation to form dimethyl ether within the microporous environment of the zeolite, chabazite, using periodic boundary conditions and density functional theory. An acid site in the zeolite produces MeOH2+ for nucleophilic attack by a second adsorbed MeOH molecule. 

The transport process within the zeolite pore system involves the passage of sorbate molecules through the windows between adjacent cavities. For molecules with critical diameters similar to the free aperture of the window ( 4.2 A for type A zeolites), an activated diffusion process is to be expected, and a molecule at the center of the window may be identified as the transition state. For the A-type lattice the following expression for the limiting diffusivity may be derived from absolute rate theory (14)... 

The theory and implementation of a novel computational method capable of looking at large transition-state shape-selective systems is outlined. It is then applied to the alkylation reaction of toluene in the gas phase as well as in zeolites MFI, MOR and BEA. Alkylating agents from the series methyl, ethyl, /50-propyl and /er/-butyl are employed to investigate the size and shape effects of the confinement. 

Solvation behavior can be effectively predicted using electronic structure methods coupled with solvation methods, for example, the combination of continuum solvation methods such as COSMO with DFT as implemented in DMoF of Accelrys Materials Studio. An attractive alternative is statistical-mechanical 3D-RISM-KH molecular theory of solvation that predicts, from the first principles, the solvation structure and thermodynamics of solvated macromolecules with full molecular detail at the level of molecular simulation. In particular, this is illustrated here on the adsorption of bitumen fragments on zeolite nanoparticles. Furthermore, we have shown that the self-consistent field combinations of the KS-DFT and the OFE method with 3D-RISM-KH can predict electronic and solvation structure, and properties of various macromolecules in solution in a wide range of solvent composition and thermodynamic conditions. This includes the electronic structure, geometry optimization, reaction modeling with transition states, spectroscopic properties, adsorption strength and arrangement, supramolecular self-assembly,"and other effects for macromolecular systems in pure solvents, solvent mixtures, electrolyte solutions, " ionic liquids, and simple and complex solvents confined in nanoporous materials. Currently, the self-consistent field KS-DFT/3D-RISM-KH multiscale method is available only in the ADF software. 

CONTENTS Introduction, Thom H. Dunning, Jr. Electronic Structure Theory and Atomistic Computer Simulations of Materials, Richard P. Messmer, General Electric Corporate Research and Development and the University of Pennsylvania. Calculation of the Electronic Structure of Transition Metals in Ionic Crystals, Nicholas W. Winter, Livermore National Laboratory, David K. Temple, University of California, Victor Luana, Universidad de Oviedo and Russell M. Pitzer, The Ohio State University. Ab Initio Studies of Molecular Models of Zeolitic Catalysts, Joachim Sauer, Central Institute of Physical Chemistry, Germany. Ab Inito Methods in Geochemistry and Mineralogy, Anthony C. Hess, Battelle, Pacific Northwest Laboratories and Paul F. McMillan, Arizona State University. 

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