Intracrystalline molecular propagation

Figure 2 summarizes the three main parameters of molecular transport accessible by PEG NMR and illustrates the conditions under which they may be obtained. Sections 3 and 4 provide examples of the message provided by the study of long-range diffusion (Dh ) and intercrystalHne exchange rates (Tjjjtra )- Since the scientific interest in molecular propagation is primarily focussed on intracrystalline diffusion, the main part of this contribution (Sect. 5) will be devoted to the measurement of Dintra. 

Deviations from normal diffusion, i.e. from molecular propagation within a quasi-homogeneous, essentially infinitely extended medium, may be taken into account by introducing an effective diffusivity Dgff. It is defined in the same way as the self-diffusivity, i.e. via Eqs. 6 and 7, however, without the requirement of the validity of Pick s laws 1 and 2. Therefore, Dgff may become a function of the (observation) time. In the considered case of zeolitic diffusion and for intracrystalline diffusion paths being sufficiently small in comparison with the crystallite radii, the effective diffusivity may be shown to be represented by a power series [106-108], leading to... 

The quantitative information provided by PPG NMR about the existence of additional transport resistances on the external surface of the zeolite crystallites (surface barriers) results from a comparison of the values for the intracrystalline mean life time determined directly (viz. Tintra) by an analysis of the time dependence of the spin-echo attenuation (and, hence, of the propagator), and determined indirectly (viz. tP ) from the intracrystalline diffusivity on the assumption that molecular exchange between different crystallites is controlled by intracrystalhne diffusion. On the additional assumption that the shape of the crystallites may be approximated by spheres with a mean square radius (R ) one has in the latter case [87,103]... 

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