Quantitation of diffusion in zeolite catalysts
Introduction
Among the multitude of processes intimately correlated with diffusion [1], [2], chemical conversion in solid catalysts [3], [4], [5] is one of the most important examples. This correlation occurs because catalyst performance depends on the rates of both conversion within the catalysts (the “intrinsic” reactivity) and molecular exchange between the catalyst particles and the surroundings. The smaller of these rates dominates the overall process. In other words, irrespective of the intrinsic reactivity, overall conversion cannot proceed faster than allowed by the rate of transport of the molecules involved.
In general, solid catalysts are highly complex systems with correspondingly complex transport properties. Over decades, the experimental techniques for studying these transport phenomena were rather limited [4], [6], [7], [8]. All techniques were essentially based on an analysis of the time dependence of molecular uptake by or release from the catalyst particles, while the direct observation of the transport phenomena in the various catalyst components was beyond the experimental possibilities [9], [10]. This deficiency has become particularly meaningful with zeolite catalysts where the microscopic size of the zeolite crystallites additionally complicates distinction between the different transport phenomena involved.
Thus, the deficiency in the experimental methods for directly observing molecular displacements, fluxes or concentration evolutions within the individual catalyst constituents has prompted many researchers to abandon Fick’s original conception to refer diffusivities to the mutually corresponding concentrations and fluxes. Instead, it has become common practice to deal with “effective” or “net” diffusivities where the supplements refer to either the combined effect of various structural constituents [11] or to the fact that fluxes and concentration gradients do not directly correspond to each other: Whilst the fluxes considered on the left hand side of Fick’s 1st law (Eq. (1) in Section 2.1) are those within the catalyst particles, the right hand side refers to the gas phase concentration necessary for maintaining the intraparticle concentrations at equilibrium, rather than to the actual intraparticle concentrations themselves [12], [13], [14]. Not unexpectedly, such deviations from the original Fickian definition of diffusivities implies the risk of misinterpretations [15]. Examples include the orders-of-magnitude difference between the diffusivities in ZSM-5 type catalysts deduced in [12] via the Thiele concept and the genuine intracrystalline diffusivities, as clarified in [16], [17], or the statement that in the Knudsen regime surface roughness affects transport diffusion and self-diffusion differently [14], which is probably related to the definitions used [18]. In fact, following the basic definition given by Fick’s 1st law (Eq. (1) in Section 2.1), both diffusivities must coincide as required for non-interacting diffusants [9]. At the end of Section 3.2, as a further example, we shall explicitly refer to the ambiguity of the definition of the tortuosity factor if the meaning of the “effective” diffusivity is not clearly specified.
Lothar Riekert was among the first scientists who recognized the particular role of diffusion in zeolite catalysis [19] and who, moreover, emphasised the deficiencies in the classical techniques of diffusion measurement for the assessment of the relevant transport phenomena [20]. The dramatic progress in the development of experimental methods of diffusion measurement [1], [21], [22] over the last decade includes the development of important microscopic measuring techniques, which provide novel access to monitoring molecular transport in zeolite catalysts. Simultaneously with the acquisition of this new type of information, in numerous cases the necessity to refer to “effective” diffusivities (with all their inherent pitfalls) rather than to genuine diffusivities may thus be overcome. In this way, for the first time a sound experimental basis for correlating intrinsic reaction rates with the different rates of molecular propagation in solid catalysts has been established.
With respect to these novel possibilities of quantitation of the transport phenomena inherent to heterogeneous catalysis in the next section the principles of diffusion as described, e.g., in Crank’s classical textbook [23] are revisited and adapted to molecular transport in zeolite catalysts. Subsequently, in Section 3, the experimental options and measuring techniques for monitoring the different transport phenomena processes of molecular transport in zeolite catalysts will be discussed, with particular emphasis on the pulsed field gradient (PFG) NMR technique. Describing its application for identifying and quantitating the rate-controlling step of mass transfer during fluid catalytic cracking, Section 4 concludes the paper by an illustration of the potential of PFG NMR for the elucidation of transport phenomena in heterogeneous catalysis.
Section snippets
Various diffusivities and their significance
In analogy to Ohm’s law of electric current and Fourier’s law of heat conduction, Fick’s 1st law of diffusion relates the particle flux density j to the gradient of particle concentration ∂c/∂x bywith D denoting the diffusion coefficient (or, completely equivalently, the diffusivity) [24]. Eq. (1) signifies that D is not a function of the concentration gradient, while it may clearly depend on the nature of the system and on further experimental parameters such as the concentration of
Macroscopic vs. microscopic techniques
Conventionally, the measurement of molecular diffusion in (zeolite) catalysts has been performed by subjecting the sample under study to a step in the pressure of the surrounding atmosphere and recording the sample response, i.e. in general, by monitoring the time dependence of the thus induced change of the amount adsorbed, e.g., gravimetrically. This procedure, i.e. relating the intrinsic change of the amount adsorbed to a corresponding change in the surrounding atmosphere, has prompted the
Diffusion in FCC catalysts: a case study
Typically, each particle of a formed FCC catalyst possesses a complex system of pores consisting of nanopores located in the zeolite crystallites and of meso- and macropores located in the “matrix” which surrounds the crystals. The assessment of the relevance of intracrystalline diffusion and of diffusion in the meso- and macropores for the overall process is still an open problem, controversially discussed in the literature [87], [88], [89].
In order to illustrate the suggested perspective on
Conclusions
Chemical conversion in zeolite catalysts is a complex process comprising a hierarchy of transport phenomena. Depending on their mutual relation and on their relation to the intrinsic reaction rates, molecular transport may become rate determining for the overall chemical reaction on quite different levels of this hierarchy. The pulsed field gradient technique of NMR (PFG NMR) has been shown to provide quantitative information about these different mechanisms of molecular transport, enabling an
Acknowledgement
With this paper, one of us (J.K.) expresses his particular gratitude to Lothar Riekert, Karlsruhe, for his support and countless, most stimulating discussions about diffusion and catalysis. The “case study” presented in this paper has been performed in the framework of the “TROCAT” project (contract G5RD-CT-2001-00520), funded by the European Community under the “Competitive and Sustainable Growth” Programme. Within this cooperation, we are particularly obliged to Jens Weitkamp and his
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