Theoretical Investigations of the Dynamics of Chemical Reactions on Nanocatalysts with Multiple Active Sites

Abstract

Recent synthetic advances led to the development of new catalytic particles with well-defined atomic structures and multiple active sites, which are called nanocatalysts. Experimental studies of processes at nanocatalysts uncovered a variety of surprising effects, but the molecular mechanisms of these phenomena remain not well understood. We propose a theoretical method to investigate the dynamics of chemical reactions on catalytic particles with multiple active sites. It is based on a discrete-state stochastic description that allows us to explicitly evaluate dynamic properties of the system. It is found that for independently occurring chemical reactions, the mean turnover times are inversely proportional to the number of active sites, showing no stochastic effects. However, the molecular details of reactions and the number of active sites influence the higher moments of reaction times. Our theoretical method provides a way to quantify the molecular mechanisms of processes at nanocatalysts.

Escape kinetics of self-propelled particles from a circular cavity

“…The thermal noise-induced escape rate of passive particles from energetic traps is well commemorated as Kramers' problem [23]. Furthermore, this rate theory had been extended to the external noise-driven nonequilibrium system [23][24][25][26][27][28][29]. Because of its success in explaining experimental findings, the Kramers' rate theory attracted wide attention over the years.…”

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

“…Using this discrete-state stochastic approach, it was explicitly shown that the mean reaction times are inversely proportional to the number of active sites irrespective of the details of underlying chemical reactions . It was also found that the higher moments of reaction times are affected by the details of the chemical reactions at each active site.…”

“…A more advanced theoretical method based on first-passage analysis of chemical dynamics, , which could partially take into account the number of active sites and the related stochastic effects, was proposed later. , But this method was also too simplified in many aspects because it did not consider the details of the underlying chemical reactions or the number of intermediates for the chemical processes at each active site. Recently, we developed a new general theoretical framework for investigating the dynamics of chemical reactions with intermediate states on catalytic particles with multiple active sites . It utilized a discrete-state chemical kinetic approach that takes into account the stochasticity of individual chemical reactions at each catalytic site on a single NP. , The main idea of this method is to follow the dynamics of only those active sites that are just one step before making the final product.…”

“…Recently, we developed a new general theoretical framework for investigating the dynamics of chemical reactions with intermediate states on catalytic particles with multiple active sites . It utilized a discrete-state chemical kinetic approach that takes into account the stochasticity of individual chemical reactions at each catalytic site on a single NP. , The main idea of this method is to follow the dynamics of only those active sites that are just one step before making the final product. This allows better connection with experimental observations and it also significantly decreases the complexity of mathematical calculations of dynamic properties because the originally very complicated multistate system can now be described as a much simpler one-dimensional sequence of effective chemical kinetic “states.”…”

“…For this purpose, one can define a function F n ( t ) as a probability density function to complete the catalytic cycle at time t starting at the state n at time t = 0. The temporal evolution of these first-passage probability densities is governed by a set of backward master equations , where F P ( t ) is for the product state with F P ( t ) = δ­( t ). This physically means that if the system starts in this state, the process is immediately accomplished …”