N.V. Peskov

Chaos and synchronisation in heterogeneous catalytic systems: CO oxidation over Pd zeolite catalysts

The influence of experimental parameters on the structure of global reaction rate oscillations and the coupling of local oscillators on a catalyst bed in a continuous stirred tank reactor is studied for the oxidation of CO on zeolite supported palladium catalysts. Global coupling can be achieved via mass transfer through the gas phase or via heat transfer in the case of a support of high heat conductivity. Characteristic differences in the activity of catalysts as well as in the period and the amplitude of the oscillations are related to the size of the palladium clusters and can be simulated by adding the state of the oxidation of the metal surface as a parameter to a common kinetic model. The analysis of observed chaotic behaviour leads to the conclusion that diffusional chaos characteristic of a distributed system is observed on the level of the zeolite crystallite that supports the palladium clusters.

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

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.

Analysis and simulation of the dynamics of a catalyzed model reaction: CO oxidation on zeolite supported palladium

The particle size effect on the oscillatory behavior during CO oxidation over zeolite-supported Pd catalysts is simulated with the help of a deterministic point model and a stochastic mesoscopic model. The point model is developed on the basis of the well-known Sales–Turner–Maple model, which is modified to consider the slow processes of oxidation and reduction of the Pd bulk as well as the effects of the bulk oxidation on the catalyst activity. It is demonstrated that the point model developed can simulate many experimental trends, e.g., the dependence of the catalytic activity and the waveform of the oscillations on the particle size and the pretreatment of the catalyst, as well as the counterclockwise hysteresis, depending on the reaction rate during the cyclic variation of the CO inlet concentration. The higher activity of the smaller particles can be explained by the attainment of a more reduced state of Pd in smaller particles in the course of the reaction. The stochastic model simulates the reaction by a Markovian chain of elementary stages of the reaction. The model variables are the numbers of reagent atoms. Transition probabilities of the stochastic model are chosen in accordance with the rates of the developed point model. It is shown that intrinsic fluctuations and correlations of stochastic variables can significantly change the reaction dynamics on nm-sized particles by extending the oscillatory region in the parameter space.

Identification of the intermittency-I route to chaos in oscillating CO oxidation on zeolite-supported Pd

For the oscillating oxidation of CO on a zeolite-supported palladium catalyst the transition to chaos could be observed in a very narrow region of the CO concentration in the feed. The reaction was carried out under the conditions of a continuous stirred tank reactor. A careful choice of the method for time series analysis led to the unambiguous identification of the intermittency-I route to chaos in the catalytic system despite the rather limited number of data points which can be acquired under normal pressure conditions. The route to chaos could be derived from the variation of the Fourier spectrum and the Poincare section as a function of the CO concentration in the feed. The embedding dimensions for the observed chaotic attractors of dE > or = 10 are much higher than the embedding dimensions obtained during UHV single crystal studies. High embedding dimensions indicate that the dynamic behaviour of the system has to be simulated with a distributed model which describes the collective behaviour of many Pd particles in the zeolite crystallite.

Mathematical model of reaction rate oscillations on a chain of nm-sized catalyst particles

The model of reaction rate oscillations over the surface of nanoparticles embedded into zeolite matrix is numerically investigated. The reaction rate oscillations on each particle are described by a lumped model. The reactions on separate particles interact via the gas diffusion through the pores, which is modeled in the frame of the Maxwell-Stefan approach. The reaction reveals a complex dynamical behavior if a nonhomogeneous distribution of reagent concentrations exists along the chain of particles with a sufficiently large gradient near the ends of the chain.

Nonlinear Phenomena in Heterogeneous Catalysis

The manuscript demonstrates with a few selected examples how the nonlinear phenomena can change the way in which heterogeneous reactions proceed. Firstly it is shown that the kinetic oscillations and synergetic effect can originate due to the diffusion coupling of two different catalysts. Secondly it is demonstrated that due to the nonlinearity of the system and the ability to form spatial structures two catalysts can produce the same catalytic activity as one catalyst.