Theoretical and experimental aspects of surface diffusion in porous catalysts I. Nonreactive conditions

Tsotsis, Theodore T.; Sane, R.C.; Webster, Ian A.; Goddard, J. D.

doi:10.1016/0021-9517(86)90269-1

Cited by 9 publications

(3 citation statements)

References 12 publications

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“…Mobility cannot be rigorously described with existing knowledge about surface chemistry and migration mechanisms, and cannot be independently measured on equivalent at surfaces without signiÿcant concerns about ÿdelity. The length of the surface connecting path is not measurable without an independent assessment of surface mobility; the consequent absence of surface tortuosity measurements impedes our progress in understanding and predicting contributions from surface di usion to overall transport within complex porous structures (Tsotsis, Sane, Webster, & Goddard, 1986). In this study, we have developed relations between void and surface tortuosities for solids with a given void fraction achieved via well-deÿned mechanisms for void formation and destruction (densiÿcation or coarsening).…”

Section: Implications For Description and Understanding Of Pore Strucmentioning

confidence: 98%

Monte-Carlo simulations of surface and gas phase diffusion in complex porous structures

Zalc

Reyes

Iglesia

2003

Chemical Engineering Science

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A new procedure for estimating surface di usivities and tortuosities within realistic models of complex porous structures is reported. Our approach uses Monte-Carlo tracer methods to monitor mean-square displacements for molecules restricted to wander on pore walls within model random mesoporous solids typical of those used as adsorbents, heterogeneous catalysts, and porous membranes. We consider model porous solids formed from initial packings of spheres with unimodal, Gaussian, or bimodal distributions of size; changes in pellet porosity are achieved by increasing microsphere radii and by randomly removing spheres from highly densiÿed packings in order to simulate densiÿcation and coarsening, respectively. Geometric tortuosities for the surface phase reached large values at void fractions near 0.04 and 0.42 for densiÿed solids; the surface tortuosity gave a minimum value of 1.9 at a void fraction of ∼0.26. These high tortuosities correspond to percolation thresholds for the void and solid phases, which in turn re ect packing densities at which each phase becomes discontinuous. Surface tortuosities for coarsened solids at low void fractions were similar to those in densiÿed solids; however, at void fractions above ∼0.3, surface tortuosities of coarsened solids increased only gradually with void fraction, because coarsening retains signiÿcant overlap among spheres at void fractions above those giving disconnected solids in densiÿed structures. Simulations of bulk di usion within voids were used to compare the transport properties and connectivity of the void space with those of surfaces that deÿne this void space. Surface and void tortuosities were similar, except for void fractions near the solid percolation threshold, because unconnected solid particles interrupt surface connectivity but not gas phase di usion paths. Surface and void tortuosities were also similar for channels within linear chains of overlapping hollow spheres as both tortuosities increased with decreasing extent of sphere overlap. These simulations provide a basis for estimates of surface and void tortuosities, which are essential in the interpretation and extrapolation of di usion rates in complex porous media. Surface and void di usivity estimates di ered signiÿcantly from those obtained from lattice and capillary models of complex porous structures. ?

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Section: Implications For Description and Understanding Of Pore Strucmentioning

confidence: 98%

Monte-Carlo simulations of surface and gas phase diffusion in complex porous structures

Zalc

Reyes

Iglesia

2003

Chemical Engineering Science

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“…While A and B are to be thought of as ordinary reaction and product molecules, the symbols with asterisks refer to mobile intermediates, either in bulk or adsorbed on solid surfaces. In the latter case, the aq and w3 reflect physico chemical adsorption-desorption rates (Tsotsis et al 1986(Tsotsis et al , 1988, while the concentrations A*,B*,..., together with the fluxes and the various mathematical operations in (1), ( 2), et seq., are to be interpreted accordingly. Although monomolecular in appearance, the elementary forms (47) and their consequents can readily be applied to more complex stoichiometry on replacing A, B ,..., by appropriate stoichiometric multiples; or they can be reinterpreted in a conceptual way by viewing each symbol as a collection of chemical species.…”

Section: Applications To Reactive Transport Schemamentioning

confidence: 99%

“…From a physical point of view, the most interesting result is, rather, the appearance of concentration-dependent diffusivities in ( 57) and ( 58). These terms, representing facilitated diffusion, due to mobile intermediates or adsorbed species, are also known in other contexts (Goddard 1974;Tsotsis et al 1986Tsotsis et al , 1988 although they may not be fully appreciated in the general literature on transport and reaction. With more complex reaction schema the general analysis of §2 shows that diffusive coupling, as well as variable diffusivities, may also arise in otherwise uncoupled systems.…”

Section: Rapid Activation or Adsorptionmentioning

confidence: 99%

Consequences of the partial-equilibrium approximation for chemical reaction and transport

1990

Proc. R. Soc. Lond. A

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This paper is concerned with the relation between various mathematical methods for formulating the equations of convective diffusion in the presence of infinitely-rapid reaction pathways. The notions of general composition variables, reaction invariance and differential geometry provide useful conceptual tools for comparing various methods. In particular, the method of ‘composite fluxes’ is shown to represent a mixed-coordinate description, with separate composition coordinates for spatial fluxes and concentration fields. While this method avoids a coordinate degeneracy sometimes associated with fast-reaction invariants, it is shown that such degeneracy should never occur in chemical systems having stable equilibria for the fast reactions. An elementary reaction scheme, involving mobile intermediates or adsorbed surface species, is treated to illustrate the coupled and facilitated diffusion effects resulting from the partial-equilibrium approximation. Also, the relation of the latter to the well-known quasi steady-state approximation (QSSA) of chemical kinetics is established. It is shown that, apart from certain exceptional circumstances, the usual ab initio invocation of the QSSA has no unforeseen consequences for diffusive transport. On the other hand, strong spatial fluxes can cause breakdown of such equilibrium approximations, in much the same way as strong unsteadiness is known to do.

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Theoretische Grundlagen

Keil¹

1999

Diffusion Und Chemische Reaktionen in Der Gas/Feststoff-Katalyse

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Theoretical and experimental aspects of surface diffusion in porous catalysts I. Nonreactive conditions

Cited by 9 publications

References 12 publications

Monte-Carlo simulations of surface and gas phase diffusion in complex porous structures

Monte-Carlo simulations of surface and gas phase diffusion in complex porous structures

Consequences of the partial-equilibrium approximation for chemical reaction and transport

Theoretische Grundlagen

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