Stochastic model of reaction rate oscillations in the CO oxidation on nm-sized palladium particles

Abstract

A mesoscopic stochastic model of the catalytic reaction 2CO+O2→2CO2 on the surface of a metal particle is considered. The model is a Markovian chain of elementary reaction steps, which mimics the catalytic oxidation of CO on a nm-sized Pd particle. The model takes into account the effect of the particle size on the reaction rate and the role of temporal fluctuations of the concentrations of the reactants. The main goal of the paper is the comparison of the dynamics produced by the stochastic model and the deterministic model obtained via averaging of the master equation, while the catalyst particle size is reduced. Intrinsic fluctuations during the reaction are shown to change the reaction kinetics drastically for small metal particles with only several hundreds of surface atoms.

On the study of nonlinear dynamics of complex chemical reaction systems

“…In the study of spatio-temporal self-organization in catalytic oxidation of hydrogen on Pt(111), Ertl et al also suggested that a mesoscopic stochastic model should be used to quantitatively explain the experimental observations [45] . In the study of catalytic oxidation of CO on nanoparticles, Peskov et al pointed out that the difference between the oscillations observed on 4-nm and 10-nm particles was a consequence of the internal noise [46,47] .…”

Colored noise-enhanced intrinsic stochastic oscillations in CO oxidation on nanometer-sized Pd particles

“…The model studied here was developed by Peskov and co-workers [24] to describe the temporal dynamics of catalytic oxidation of CO on nm-sized Pd particles. The reaction was assumed to proceed following Langmuir-Hinshelwood (LH) mechanism, including the adsorptions of CO and oxygen, the desorption of CO, the reaction of adsorbed CO and adsorbed oxygen, the diffusion of adsorbed oxygen on the surface into the subsurface, and the diffusion of the subsurface oxygen back to the surface.…”

“…Under this condition, the "jump" Markov process governed by the master equation can be approximated by the "continuous" Markov process governed by the CLE. For the present system involving several hundred to several thousand reactant molecules (absorption centers) on the particle surface [24] , the CLE is valid for the study of the system's kinetics. In the past several years, the CLE has already been used successfully to study the effect of IN in not-too-small chemical systems [10,12,13,[27][28][29][30][31][32][35][36][37][38] .…”

“…In recent ten years, more and more studies have been dedicated to the roles of internal noise (IN) in mesoscopic biological [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and chemical systems [22][23][24][25][26][27][28] . It is known that both EN and IN are unavoidable in small-size systems, where EN originates from the random variation of externally set control parameters, while IN comes from the random fluctuations of the stochastic chemical reaction events for the low reacting molecules in a finite-size chemical system [18][19][20][21] .…”

Ground-state diagrams for lattice-gas models of catalytic CO oxidation

“…CO 2 formation through catalytic oxidation of CO is one of the prototypical surface reactions that has been extensively studied in recent years [1][2][3][4][5][6][7][8][9][10]. Much of the today's insight into heterogeneous catalysis arises from this model system.…”