MOLECULAR-TRANSPORT IN A 2-DIMENSIONAL LATTICE OF SORPTION SITES

It is known from experimental study of the sorption of some aromatic c ompounds (such as p-xylene) in zeolites with the MFI lattice that the adsorption kinetics in such systems exhibits appreciable deviations fr om the 2nd Fick law. To account for those deviations, whose origin lie s in the crystal bulk, the existence of two phases which are not in lo cal chemical equilibrium is postulated: a mobile phase is assumed to o ccur in the straight zeolite channels whereas an immobile phase is ass umed in the zig-zag channels. A microkinetic model is proposed assumin g localization of the sorbed molecules on two kinds of centres arrange d in a regular two-dimensional lattice, along which migration takes pl ace in agreement with the Langmuir kinetics of exchange of molecules b etween the occupied and unoccupied centres. For an exact description o f the time evolution of the considered physical system the model resul ts in a set of ordinary differential equations which are transformed i nto a system of two partial differential equations providing a spatial ly continuous description of the physical system. This approach enable s the phenomenological kinetic parameters to be interpreted in terms o f the jump frequency of molecules between the various kinds of adsorpt ion centres. For small perturbations in the concentration of the sorbi ng substance the mathematical model is linearized, and the behaviour o f the system is illustrated using the numerical solution of the model equations. In dependence on changes in the model parameters, the trans ition from the case of pure diffusion along a one-dimensional lattice in the mobile phase, with the zig-zag channels inaccessible, via the c ase of a slowly establishing local equilibrium between the two sub-lat tices, to the limiting case of instantaneously establishing local equi librium between the sub-lattices is discussed.