Modeling tracer counter-permeation through anisotropic zeolite membranes: from mean field theory to single-file diffusion

Nelson, Peter H.; Auerbach, Scott M.

doi:10.1016/s1385-8947(99)00052-2

Cited by 49 publications

(75 citation statements)

References 37 publications

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“…An analogous expression applies for J B . Here, it suffices to consider the local steady state regime with uniform total concentration, X = X in = X in (F) , corresponding to a counter-diffusion mode 19 where ∂A/∂x = −∂B/∂x. Then, (11) and the analogous expression for J B simply reduce to 13,19 J A = −D tr ∂A/∂x and J B = −D tr ∂B/∂x.…”

Section: Generalized Hydrodynamic Reaction-diffusion Equationsmentioning

confidence: 99%

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Controlling reactivity of nanoporous catalyst materials by tuning reaction product-pore interior interactions: Statistical mechanical modeling

Wang¹,

Ackerman²,

Lin³

et al. 2013

The Journal of Chemical Physics

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Statistical mechanical modeling is performed of a catalytic conversion reaction within a functionalized nanoporous material to assess the effect of varying the reaction product-pore interior interaction from attractive to repulsive. A strong enhancement in reactivity is observed not just due to the shift in reaction equilibrium towards completion but also due to enhanced transport within the pore resulting from reduced loading. The latter effect is strongest for highly restricted transport (single-file diffusion), and applies even for irreversible reactions. The analysis is performed utilizing a generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport. Statistical mechanical modeling is performed of a catalytic conversion reaction within a functionalized nanoporous material to assess the effect of varying the reaction product-pore interior interaction from attractive to repulsive. A strong enhancement in reactivity is observed not just due to the shift in reaction equilibrium towards completion but also due to enhanced transport within the pore resulting from reduced loading. The latter effect is strongest for highly restricted transport (single-file diffusion), and applies even for irreversible reactions. The analysis is performed utilizing a generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport.

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Section: Generalized Hydrodynamic Reaction-diffusion Equationsmentioning

confidence: 99%

“…See Ref. 19 for an alternative formulation. Thus, it is immediately clear that F tr (x) → 1, as X → 0 (as required).…”

Section: Generalized Hydrodynamic Reaction-diffusion Equationsmentioning

confidence: 99%

Controlling reactivity of nanoporous catalyst materials by tuning reaction product-pore interior interactions: Statistical mechanical modeling

Wang¹,

Ackerman²,

Lin³

et al. 2013

The Journal of Chemical Physics

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“…It provides a simple explanation for the experimentally observed flux ratio of radioactive tracer-labeled K + permeation 23 (that occurs within the counter-permeation eigenmode of tracer-labeled binary permeation 24,25 ). It was based on the hypothesis that ions move through ion channels in a single file via a one-step mechanism.…”

Section: A Knock-on Modelmentioning

confidence: 99%

“…29 Thus, while the knock-on model accounts for singlefile permeation, it produces a net flux (in the copermeation eigenmode) that is unaffected by the single-file nature of its permeation, analogously with other simple single-file permeation models. 24,25 The knock-on model is thus the simplest single-file permeation model. The symmetric knock-on model has just one adjustable parameter k a , which can be directly related to the "permeability" of the channel.…”

Section: A Knock-on Modelmentioning

confidence: 99%

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A permeation theory for single-file ion channels: One- and two-step models

Nelson

2011

The Journal of Chemical Physics

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How many steps are required to model permeation through ion channels? This question is investigated by comparing one-and two-step models of permeation with experiment and MD simulation for the first time. In recent MD simulations, the observed permeation mechanism was identified as resembling a Hodgkin and Keynes knock-on mechanism with one voltage-dependent rate-determining step [Jensen et al., PNAS 107, 5833 (2010)]. These previously published simulation data are fitted to a one-step knock-on model that successfully explains the highly non-Ohmic current-voltage curve observed in the simulation. However, these predictions (and the simulations upon which they are based) are not representative of real channel behavior, which is typically Ohmic at low voltages. A two-step association/dissociation (A/D) model is then compared with experiment for the first time. This two-parameter model is shown to be remarkably consistent with previously published permeation experiments through the MaxiK potassium channel over a wide range of concentrations and positive voltages. The A/D model also provides a first-order explanation of permeation through the Shaker potassium channel, but it does not explain the asymmetry observed experimentally. To address this, a new asymmetric variant of the A/D model is developed using the present theoretical framework. It includes a third parameter that represents the value of the "permeation coordinate" (fractional electric potential energy) corresponding to the triply occupied state n of the channel. This asymmetric A/D model is fitted to published permeation data through the Shaker potassium channel at physiological concentrations, and it successfully predicts qualitative changes in the negative current-voltage data (including a transition to super-Ohmic behavior) based solely on a fit to positive-voltage data (that appear linear). The A/D model appears to be qualitatively consistent with a large group of published MD simulations, but no quantitative comparison has yet been made. The A/D model makes a network of predictions for how the elementary steps and the channel occupancy vary with both concentration and voltage. In addition, the proposed theoretical framework suggests a new way of plotting the energetics of the simulated system using a one-dimensional permeation coordinate that uses electric potential energy as a metric for the net fractional progress through the permeation mechanism. This approach has the potential to provide a quantitative connection between atomistic simulations and permeation experiments for the first time.

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Mathematical Modelling Based on Transport Phenomena

Dobre

Marcano

2007

Chemical Engineering

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Modeling tracer counter-permeation through anisotropic zeolite membranes: from mean field theory to single-file diffusion

Cited by 49 publications

References 37 publications

Controlling reactivity of nanoporous catalyst materials by tuning reaction product-pore interior interactions: Statistical mechanical modeling

Controlling reactivity of nanoporous catalyst materials by tuning reaction product-pore interior interactions: Statistical mechanical modeling

A permeation theory for single-file ion channels: One- and two-step models

Mathematical Modelling Based on Transport Phenomena

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