Langevin and Fokker-Planck Analyses of Inhibited Molecular Passing Processes Controlling Transport and Reactivity in Nanoporous Materials

Wang, Chi-Jen; Ackerman, David M.; Slowing, Igor I.; Evans, James W.

doi:10.1103/physrevlett.113.038301

Cited by 6 publications

(58 citation statements)

References 24 publications

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“…Ref. 34). Next, we provide a more comprehensive picture of the variation of P(d) versus d by combining the simulation results for ∆t = 0.01 with analytic insights into behavior for d close to d c and for large d.…”

Section: B Passing Propensity: Simulations and Analytic Considerationsmentioning

confidence: 99%

“…This analysis will be augmented exploiting analytic results motivated by the equivalent Fokker-Planck formulation for this diffusive passing problem and associated first-passage problems. 34 We also utilize analytic results which provide insight into the form of P(d) for both large and small d where Langevin simulation is inefficient. For example, for small d, these analytic results reveal a non-trivial scaling of the form 34 P ∼ A(dd c ) σ for d just above the critical value, d c , of the pore diameter for the onset of SFD due to steric blocking.…”

Section: Introductionmentioning

confidence: 99%

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Pore diameter dependence of catalytic activity: p-nitrobenzaldehyde conversion to an aldol product in amine-functionalized mesoporous silica

Garcia

Slowing

Evans

2018

The Journal of Chemical Physics

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The reaction yield for conversion of p-nitrobenzaldehyde (PNB) to an aldol product in amine-functionalized mesoporous silica nanoparticles (MSN) exhibits a 20-fold enhancement for a modest increase in pore diameter, d. This enhanced catalytic activity is shown to reflect a strong increase in the "passing propensity," P, of reactant and product species inside the pores. We find that P ≈ 0, corresponding to single-file diffusion, applies for the smallest d which still significantly exceeds the linear dimensions of PNB and the aldol product. However, in this regime of narrow pores, these elongated species must align with each other and with the pore axis in order to pass. Thus, P reflects both translational and rotational diffusion. Langevin simulation accounting for these features is used to determine P versus d. The results are also augmented by analytic theory for small and large d where simulation is inefficient. The connection with the catalytic activity and yield is achieved by the incorporation of results for P into a multi-scale modeling framework. Specifically, we apply a spatially coarse-grained (CG) stochastic model for the overall catalytic reaction-diffusion process in MSN. Pores are treated as linear arrays of cells from the ends of which species adsorb and desorb, and between which species hop and exchange, with the exchange rate reflecting P. CG model predictions including yield are assessed by Kinetic Monte Carlo simulation.

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Section: B Passing Propensity: Simulations and Analytic Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pore diameter dependence of catalytic activity: p-nitrobenzaldehyde conversion to an aldol product in amine-functionalized mesoporous silica

Garcia

Slowing

Evans

2018

The Journal of Chemical Physics

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“…In fact, Γ ⊥ (2) will exhibit a power-law relationship with Γ (1) , expressed as Γ ⊥ (2)~( Γ (1) ) 2 3 ⁄ . Such a wrong dependence of Γ ⊥ (2) on Γ (1) given by the assumption ( ⊥ = * ) is shown in Fig. 5(b), as a comparison of the correct dependence in Fig.…”

Section: Introductionmentioning

confidence: 96%

“…Based on the concept of λ , we define an effective Saffman length * for a particle monolayer near a water-oil interface, expressed as * ≡ Γ (1) 6 ⁄ . The effective Saffman length is the ratio of the friction coefficient Γ (1) of the particles in the monolayer to the traditional friction coefficient 6 of the particles in a bulk liquid. In the present system, the effective coefficient * is written as * = Γ (1)…”

Section: Introductionmentioning

confidence: 99%

Relationship between characteristic lengths and effective Saffman length in colloidal monolayers near a water–oil interface*

Zhang

Chen

2019

Chinese Phys. B

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The hydrodynamic interactions (HIs) in colloidal monolayers are strongly influenced by the boundary conditions and can be directly described in terms of the cross-correlated diffusion of the colloid particles. In this work, we experimentally 2 measured the cross-correlated diffusion in colloidal monolayers near a water-oil interface. The characteristic lengths of the system were obtained by introducing an effective Saffman length. The characteristic lengths of a particle monolayer near a water-oil interface were found to be anisotropic in the longitudinal and transverse directions. From these characteristic lengths, the master curves of cross-correlated diffusion are obtained, which universally describe the HIs near a liquid-liquid interface.

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“…Direct molecular or Langevin dynamics simulation [26][27][28] is not viable to describe the overall reactiondiffusion process on the appropriate time scale (i.e., reactants entering, diffusing within, reacting, and products diffusing within and being extruded from the pore, with dynamics generally mediated by the presence of a solvent). Thus, instead spatially discrete coarse-grained stochastic modeling is typically implemented [3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Catalytic conversion reactions in nanoporous systems with concentration-dependent selectivity: Statistical mechanical modeling

et al. 2016

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Statistical mechanical modeling is developed to describe a catalytic conversion reaction A → B c or B t with concentration-dependent selectivity of the products, B c or B t , where reaction occurs inside catalytic particles traversed by narrow linear nanopores. The associated restricted diffusive transport, which in the extreme case is described by single-file diffusion, naturally induces strong concentration gradients. Furthermore, by comparing kinetic Monte Carlo simulation results with analytic treatments, selectivity is shown to be impacted by strong spatial correlations induced by restricted diffusivity in the presence of reaction and also by a subtle clustering of reactants, A.

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Langevin and Fokker-Planck Analyses of Inhibited Molecular Passing Processes Controlling Transport and Reactivity in Nanoporous Materials

Cited by 6 publications

References 24 publications

Pore diameter dependence of catalytic activity: p-nitrobenzaldehyde conversion to an aldol product in amine-functionalized mesoporous silica

Pore diameter dependence of catalytic activity: p-nitrobenzaldehyde conversion to an aldol product in amine-functionalized mesoporous silica

Relationship between characteristic lengths and effective Saffman length in colloidal monolayers near a water–oil interface*

Catalytic conversion reactions in nanoporous systems with concentration-dependent selectivity: Statistical mechanical modeling

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