Theory of diffusion-controlled reactions on spherical surfaces and its application to reactions on micellar surfaces

Sano, Hisatake; Tachiya, M.

doi:10.1063/1.442360

Cited by 108 publications

(116 citation statements)

References 18 publications

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“…Detailed formulation is based on the reactiondiffusion equation for the pair survival probability with an appropriate restricted diffusion operator [370]. It can be integrated numerically [368], but a more convenient and computationally superior way is to expand the solution into a discrete set of eigenfunctions of the diffusion operator, as we did in Section III.B.…”

Section: Microheterogeneous Environmentsmentioning

confidence: 99%

Solvent Effects in Nonadiabatic Electron‐Transfer Reactions: Theoretical Aspects

Barzykin

Frantsuzov

Seki

et al. 2002

Advances in Chemical Physics

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138

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Section: Microheterogeneous Environmentsmentioning

confidence: 99%

Solvent Effects in Nonadiabatic Electron‐Transfer Reactions: Theoretical Aspects

Barzykin

Frantsuzov

Seki

et al. 2002

Advances in Chemical Physics

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120

138

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“…Besides, interfacial reactions, for which molecules react on target sites located on the surface of a confining domain [8], play an important role in situations as various as heterogeneous catalysis [9], reactions in porous media, or biochemical reactions on DNA [10] and in vesicular systems [11][12][13]. The trajectories involved in such reactions, combining bulk and surface-mediated diffusion phases, can now be observed at the single molecule scale [14].…”

Section: Introductionmentioning

confidence: 99%

Interfacial territory covered by surface-mediated diffusion

2012

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We consider a minimal model of heterogeneous catalysis in which a molecule performs surface-mediated diffusion inside a confining domain whose boundary contains catalytic sites. We explicitly take into account the combination of surface and bulk diffusion, and we obtain exact results for the mean and variance of the territory covered on the boundary by the particle before its exit in the case of a two-dimensional spherical domain. Depending on the relative positions of the entrance and exit points, very different behaviors with respect to the mean adsorption time of the molecule on the surface are found. We also determine both exact lower and upper bounds and an approximate expression of the probability of reacting with catalytic sites before exiting the domain. These results provide a quantitative measure of the efficiency of an idealized catalyst.

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“…42 However, if the initial population is not in equilibrium, the mean reaction time approach may lead to inadequate description of the kinetics. The effect of the nonequilibrium initial condition on the rate of the electron transfer reactions has been clearly pointed out by Tachiya and Murata.…”

Section: Nonequilibrium Initial Conditionmentioning

confidence: 99%

Diffusion-assisted long-range reactions in confined systems: Projection operator approach

Seki

Barzykin

Tachiya

1999

The Journal of Chemical Physics

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Articles you may be interested inAn accurate expression for the rates of diffusion-influenced bimolecular reactions with long-range reactivity J. Chem. Phys. 138, 164123 (2013); 10.1063/1.4802584Diffusion-assisted long-range reaction between the ends of a polymer: Effective sink approximation Long time behavior of reversible diffusion-influenced reaction perturbed by photolysis: Brownian dynamics simulationThe diffusion-assisted long-range reversible reaction equation is solved for the pair survival probability using a projection operator method in terms of the diffusion propagator in the absence of reaction. For a localized ͑delta function͒ reaction sink, the well-known analytical solution is immediately reproduced from the operator expression. It is emphasized that the mean reaction time approach, often used to approximate the overall reaction rate, is not adequate for a nonequilibrium initial condition. The general operator solution for a delocalized sink is shown to reduce to a closed matrix form, provided the propagator has a discrete spectrum of eigenmodes. The matrix solution is exact and applies for an arbitrary functional form and strength of the reaction sink. Although matrices of infinite dimensions are involved, they can be truncated at a certain finite dimension to attain any prescribed precision. Convergence of the truncated matrix solution is fast and often only a few of the lowest eigenmodes are sufficient to obtain quantitatively reasonable results. Several long-range reaction models are analyzed in detail revealing the breakdown of the widely used closure approximation obtained as a first-order Padé approximation of the operator solution.

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Theory of diffusion-controlled reactions on spherical surfaces and its application to reactions on micellar surfaces

Cited by 108 publications

References 18 publications

Solvent Effects in Nonadiabatic Electron‐Transfer Reactions: Theoretical Aspects

Solvent Effects in Nonadiabatic Electron‐Transfer Reactions: Theoretical Aspects

Interfacial territory covered by surface-mediated diffusion

Diffusion-assisted long-range reactions in confined systems: Projection operator approach

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