Catalytic surfaces, spatiotemporal patterns

Oscillations connected with adsorbate-induced surface restructuring were studied also in [29]. The model used was aimed at mimicking oscillations in NO reduction by H2 on a mesoscopic Pt particle containing two catalytically active (100) areas connected by an inactive (111) area that only adsorbed NO reversibly. NO diffusion on and between facets was much faster than other steps. The results obtained show that the coupling of the catalytically active sublattices may synchronize nearly harmonic oscillations observed on these sublattices and also may result in the appearance of aperiodic partially synchronized oscillations. The spatiotemporal patterns corresponding to these regimes are nontrivial. In particular, the model predicts that, due to phase separation, the reaction may be accompanied by the formation of narrow NO-covered zones on the (100) sublattices near the (lOO)-(lll) boundaries. These zones partly prevent NO supply from the (111) sublattice to the (100) sublattices. 

Rate oscillations, spatiotemporal patterns and chaos, e.g. dissipative structures were also observed in heterogeneous catalytic reactions. If compared with pattern formation in homogeneous systems, the surface studies introduced new aspects, like anisotropic diffusion, and the possibility of global synchronization via the gas phase. Application of field electron and field ion microscopy to the study of oscillatory surface reactions provided the capability of obtaining images with near-atomic resolution. The most extensively studied reaction is CO oxidation, which is catalyzed by group VIII noble metals. 

Mathematical model of three-way catalytic converter (TWC) has been developed. It includes mass balances in the bulk gas, mass transfer to the porous catalyst, diffusion in the porous structure and simultaneous reactions described by a complex microkinetic scheme of 31 reaction steps for 8 gas components (CO, O2, C2H4, C2H2, NO, NO2, N2O and CO2) and a number of surface reaction intermediates. Enthalpy balances for the gas and solid phase are also included. The method of lines has been used for the transformation of a set of partial differential equations (PDEs) to a large and stiff system of ordinary differential equations (ODEs . Multiple steady and oscillatory states (simple and doubly-periodic) and complex spatiotemporal patterns have been found for a certain range of operation parameters. The methodology of studies of such systems with complex dynamic patterns is briefly introduced and the undesired behaviour of the used integrator is discussed. 

The examples shown in this chapter are only a small part of the rich variety of behavior encountered in far-from-equilibrium chemical systems. Here our objective is only to show a few examples an extensive description would form a book in itself At the end of the chapter there is a list of monographs and conference proceedings that give a detailed descriptions of oscillations, propagating waves, Turing structures, pattern formation on catalytic surfaces, multistability and chaos (both temporal and spatiotemporal). Dissipative structures have also been found in other fields such as hydrodynamics and optics. 

We begin this chapter with a discussion of the automaton and present the details of the model construction in Section 2. A number of different systems has been studied using this method in order to investigate fluctuation effects on chemical wave propagation and domain growth in bistable chemical systems [6], excitable media and Turing pattern formation [3,4,7], surface catalytic oxidation processes [8], as well as oscillations and chaos [9]. Our discussions will be confined to the Willamowski-Rossler [10] reaction which displays chemical oscillations and chaos as well as a variety of spatiotemporal patterns. This reaction scheme is sufficiently rich to illustrate many of the internal noise effects we wish to present the references quoted above can be consulted for additional examples. Section 3 applies the general considerations of Section 2 to the Willamowski-Rossler reaction. Sections 4 and 5 describe a variety of aspects of the effects of fluctuations on pattern formation and reaction processes. Section 6 contains the conclusions of the study. 

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