Diffusion true intracrystalline

These results demand a reassessment of our basic ideas on sorption kinetics and the role of intracrystalhne diffusion in zeohte-based processes. It seems clear that intracrystalline diffusion can be reliably measured only by microscopic or mesoscopic techniques. In ideal crystals these values should correspond with the values derived from macroscopic measurements of sorption rates, but, since the majority of crystals that have been studied appear to be far from ideal, such a correspondence should not be assumed a priori. Conversely, the role of true intracrystalline diffusion in determining the rates of sorption and catalytic processes may be minimal and we may be forced to conclude that the rates of most large-scale processes are in fact largely influenced or even controlled by surface and internal barriers imre-lated to the ideal zeohte structure. 

When type X is utQized, in any of its ion exchange forms, for dehydration or possibly for sweetening (sulfur removal), there is little likelihood that the intracrystalline diffusion will be the dominant resistance to mass transfer. Large aromatic sulfurs would of course be an exception. When type X is used for adsorption of hydrocarbons or aromatics then it is possible that the micro-pore diffusion might dominate. When type A is used there is always a distinct possibility that intra-crystalline diffusion will be slow and may dominate the mass transfer, even for relatively small molecules. This is especially true when the chosen structure is a K A or type 3A. Selection of other small pore structures, for separations or purification applications can also create situations where the dominant resistance is found in the crystaUites. 

The first hypothesis seems unlikely to be true in view of the rather wide variation in the ratio of carbon dioxide s kinetic diameter to the diameter of the intracrystalline pores (about 0.87, 0.77 and 0.39 for 4A, 5A and 13X, respectively (1J2)). The alternative hypothesis, however, (additional dif-fusional modes through the macropore spaces) could be interpreted in terms of transport along the crystal surfaces comprising the "walls" of the macropore spaces. This surface diffusion would act in an additive manner to the effective Maxwell-Knudsen diffusion coefficient, thus reducing the overall resistance to mass transfer within the macropores. 

Here Ca is the concentration of isotopically labelled species at a point where the concentration of unlabelled species is Ca. La a and La a are the straight and cross phenomenological coefficients of the irreversible thermodynamic formulation of diffusion. The original relation, Equation 1, assumes a zero cross coefficient, which in dense intracrystalline fluids certainly is not likely to be true. 

This is true in particular for diffusion in homogeneous (or quasihomogeneous) systems, comprising the limiting cases of intracrystalline (for R) and long-range (for R) diffusion in assemblages of zeolite crystal-... 

There is no fundamental reason why the corrected diffusivity should be independent of concentration, but experimental evidence shows that for many systems this is approximately true [41-43] (see, for example. Fig. 13). From molecular simulations of intracrystalline diffusion Krishna has identified two limiting cases depending on the degree to which the sorbate molecules are confined strong confinement [Dq a (1 - 0)] and weak confinement [Do constant] [44]. 

Since the heat of adsorption is usually larger than the activation energy of intracrystalline diffusion, the parameter y decreases with an increase in temperature. This means that the micropore diffusion is more important at higher temperatures and the macropore diffusion is more significant at lower temperatures. This is only true for linear isotherm. We will discuss this effect on nonlinear isotherm in the next section. To illustrate the temperature effect on the parameter y for the linear isotherm case, we take the following example ... 

---