Understanding the Reaction Dynamics on Heterogeneous Catalysts Using a Simple Stochastic Approach

Punia, Bhawakshi; Chaudhury, Srabanti; Kolomeisky, Anatoly B.

doi:10.1021/acs.jpclett.1c03557

Cited by 8 publications

(12 citation statements)

References 27 publications

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“…The reactivity has units of meter per second and ranges from 0 for an inert impermeable target (no reaction) to +∞ for a perfectly reactive target, in which case Dirichlet boundary condition is retrieved. The emergence of Robin boundary condition was further rationalized via various microscopic mechanisms, including stochastic gating or rapid switching between active and passive states in time [11][12][13], homogenization of micro-heterogeneity of reactive patches [14][15][16][17][18][19][20], overcoming energetic or entropic barriers or interactions [21][22][23][24][25]. Probabilistic interpretations of Robin boundary condition via random walks and reflected Brownian motions were discussed [26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

An encounter-based approach for restricted diffusion with a gradient drift

Grebenkov

2022

J. Phys. A: Math. Theor.

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We develop an encounter-based approach for describing restricted diﬀusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis to derive a spectral decomposition for the full propagator, i.e., the joint probability density function for the particle position and its boundary local time. This is the central quantity that determines various characteristics of diﬀusion-inﬂuenced reactions such as conventional propagators, survival probability, ﬁrst-passage time distribution, boundary local time distribution, and reaction rate. As an illustration, we investigate the impact of a constant drift onto the boundary local time for restricted diﬀusion on an interval. More generally, this approach accesses how external forces may inﬂuence the statistics of encounters of a diﬀusing particle with the reactive boundary.

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Section: Introductionmentioning

confidence: 99%

An encounter-based approach for restricted diffusion with a gradient drift

Grebenkov

2022

J. Phys. A: Math. Theor.

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“…The statistical quantities that are obtained reflect the stochasticity of systems and predict the mechanistic details of ongoing chemical reactions. We have also validated our theoretical predictions through computer simulations. ,, …”

Section: Discussionmentioning

confidence: 62%

“…We have also validated our theoretical predictions through computer simulations. 89,91,99 These methods can be easily extended in many directions, as shown in this review, as well as in other cases which we did not discuss here. In the context of protein folding−unfolding studies, starting from the protein activation to the required activity, there can be many intermediate steps.…”

Section: Discussionmentioning

confidence: 92%

“…The molecular details of reactions and the number of active sites influence the higher moments of reaction times . We later extended this theory and developed a simple discrete-state stochastic model of the catalytic chemical reactions on particles with multiple active sites, which can be solved analytically for any number of active sites and all ranges of relevant parameters . The theory provides quantitative bounds for realistic dynamic properties of catalytic processes that can be directly applied to analyze the experimental observations.…”

Section: Mathematical Framework/methods To Derive the Pdfsmentioning

confidence: 99%

“… 98 We later extended this theory and developed a simple discrete-state stochastic model of the catalytic chemical reactions on particles with multiple active sites, which can be solved analytically for any number of active sites and all ranges of relevant parameters. 99 The theory provides quantitative bounds for realistic dynamic properties of catalytic processes that can be directly applied to analyze the experimental observations. Our discrete state approaches where the temporal evolution of the probability density functions is governed by a set of master equations provide a way to quantify the molecular mechanisms of processes at nanocatalysts.…”

Section: Mathematical Framework/methods To Derive the Pdfsmentioning

confidence: 99%

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Theoretical Tools to Quantify Stochastic Fluctuations in Single-Molecule Catalysis by Enzymes and Nanoparticles

2022

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Single-molecule microscopic techniques allow the counting of successive turnover events and the study of the time-dependent fluctuations of the catalytic activities of individual enzymes and different sites on a single heterogeneous nanocatalyst. It is important to establish theoretical methods to obtain the statistical measurements of such stochastic fluctuations that provide insight into the catalytic mechanism. In this review, we discuss a few theoretical frameworks for evaluating the first passage time distribution functions using a self-consistent pathway approach and chemical master equations, to establish a connection with experimental observables. The measurable probability distribution functions and their moments depend on the molecular details of the reaction and provide a way to quantify the molecular mechanisms of the reaction process. The statistical measurements of these fluctuations should provide insight into the enzymatic mechanism.

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Theoretical Understanding of Dynamic Catalysis

Jangid,

Chaudhury,

Kolomeisky

2024

J. Phys. Chem. C

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Dynamic catalysis is a phenomenon in which the catalytic properties of the system change with time. It has been recently proposed as an alternative to the current widely utilized static catalytic approach because of potential significant improvements in catalytic efficiency. Dynamic restructuring of active sites on surfaces has also been observed in some nanocatalysts. However, the microscopic mechanisms of underlying processes remain not well understood. We developed a new stochastic framework that allows us to quantitatively describe dynamic catalysis and compare its properties with the static approach. It is found that fluctuations between different catalytic pathways might lead to enhancements in chemical reaction rates but only for specific ranges of kinetic parameters. Our theoretical method can explain these observations from the microscopic point of view. We show that the temporal efficiency of dynamic catalysis depends only on the rates of chemical reactions and transitions between different catalytic pathways while being independent of the number of active sites. It is also argued that the effects of dynamic catalysis are purely nonequilibrium, and the associated energy dissipation is the source of improvements in catalytic efficiency. In addition, the stochasticity of dynamic catalysis is investigated. The proposed theoretical approach clarifies some important microscopic aspects of catalytic processes.

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Understanding the Reaction Dynamics on Heterogeneous Catalysts Using a Simple Stochastic Approach

Cited by 8 publications

References 27 publications

An encounter-based approach for restricted diffusion with a gradient drift

An encounter-based approach for restricted diffusion with a gradient drift

Theoretical Tools to Quantify Stochastic Fluctuations in Single-Molecule Catalysis by Enzymes and Nanoparticles

Theoretical Understanding of Dynamic Catalysis

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