Influence of isotherm inflection on diffusion in silicalite

Krishna, Rajamani; Vlugt, Thijs J. H.; Smit, Berend

doi:10.1016/s0009-2509(98)00538-7

Cited by 100 publications

(87 citation statements)

References 21 publications

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“…Then, species concentrations per unit length become functions of a continuous variable K (x = na) ≈ a −1 K n , where we leave implicit the tdependence. To develop h-RDE, one needs an appropriate description of collective or chemical diffusion in this multispecies lattice-gas system 4,5,16,17,26 incorporating the singlefile nature of diffusion.…”

Section: Hydrodynamic Regime and Reaction-diffusion Equationsmentioning

confidence: 99%

“…A similar expression applies for the flux, J B , of B. The four diffusion coefficients, D K,K , with K, K = A or B, can be conveniently collected into a 2 × 2 diffusion tensor D. Onsager's theory 16,17,26 further shows that this tensor involves both a thermodynamic "inverse compressibility" factor and a kinetic "conductivity" factor.…”

Section: Hydrodynamic Regime and Reaction-diffusion Equationsmentioning

confidence: 99%

“…Again X m = 1/a is the maximum concentration per unit length. This previously utilized result 16,17,28 can be obtained from Onsager theory accounting for the known thermodynamics of a noninteracting lattice-gas, but also incorporating a crude approximation for species conductivity. 27 However, it is instructive to note that an alternative simple kinetic derivation of the MF result (9) is also possible 14,29 : one simply applies the MF factorization to J A n>n+1 and J B n>n+1 in Eqs.…”

Section: B Mean-field Diffusion Fluxesmentioning

confidence: 99%

“…where F(y) = erfc(y/2), (16) and where erfc is the complementary error function. 34 Thus, concentration profiles collapse onto a single curve for increasing t after rescaling the n-axis by (W diff t) 1/2 .…”

Section: B Transient Behaviormentioning

confidence: 99%

“…It has been recognized that Onsager's classic theory of transport can be applied to assess chemical diffusion fluxes in multispecies systems with and without single-file constraints. 16,17 Also, some of the above studies of single-file conversion reactions have described the corresponding discrete RDE, but only based on approximate mean-field treatments. 9,14 However, what has not been exploited is the existence of exact results for diffusion fluxes in multispecies lattice-gas models with site exclusion and species-independent hop rates and interactions.…”

Section: Introductionmentioning

confidence: 99%

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Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: Hydrodynamic versus stochastic behavior

Ackerman

Wang

Wendel

et al. 2011

The Journal of Chemical Physics

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We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity. Keywordscatalytic conversion, catalytic sites, continuum hydrodynamics, conversion reactions, discrete lattices, hydrodynamic treatment, kinetic Monte Carlo simulation, master equations, reaction diffusion, scaling behavior, single file diffusion, spatiotemporal behaviors, fluid dynamics Disciplines Mathematics | Physical Chemistry | Physics CommentsThe following article appeared in Journal of Chemical Physics 134,11 (2011) We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions a...

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