Zeolite diffusion 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. 

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... 

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)... 

---