68 UNIVERSITÄT OSNABRÜCK, FACHBEREICH PHYSIK O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, P. Hertel, H. Dötsch, A.F. Popkov: Analysis of polarization independent Mach-Zehnder type integrated optical isolator, International Workshop on Optical Waveguide Theory und Numerical Modelling, Hagen, Germany (1998) Besuchte Lehrveranstaltungen Anwendungen <strong>oxidischer</strong> Kristalle (Ringvorlesung für Doktoranden) Seminar des Graduierentenkollegs Kolloquium des SFB 225 Projekte der Magnetooptik (Seminar)
GRADUIERTENKOLLEG MIKROSTRUKTUR OXIDISCHER KRISTALLE 69 Surface Reactions: Monte Carlo Simulations of Systems with Creation, Annihilation and Diffusion of Energetically Interacting Reactants Beginn des Projekts: 01.06.1999 Dipl.-Phys. Guntars Zvejnieks Betreuer: Prof. Dr. G. Borstel Abstract The standard Lotka-type model, which exhibits self-organized concentration oscillations, was introduced for the first time by Mai et al. (J. Phys. A: Math. 30, 4171, 1997) for a simplified description of autocatalytic surface reactions. To study (i) the resonance behavior and to determine (ii) the effect of mobile and energetically interacting reactants on oscillatory properties of the A+B→2B reaction, the corresponding mathematical model is modified here by incorporation of (i) periodic modulation of the only control parameter and (ii) diffusion of reactants (with/without energetic interaction between them), respectively. The mathematical formalism is proposed for determining the dependence of transition rates on the interaction energy (and temperature) for the general mathematical model, and the Lotka-type model in particular. By means of Monte-Carlo computer simulations, we have found that the modulation of the control parameter drives the system through a sequence of frequency locking, quasiperiodic, and resonance behavior. In turn, the diffusion leads to a desynchronization of oscillations and a subsequent decrease of oscillation amplitude. The energetic interaction between reactants has a dual effect depending on the type of mobile reactants. In the limiting case of mobile reactants B the repulsion results in a decrease of amplitudes. However, these amplitudes increase if reactants A are mobile and repulse each other. A simplified interpretation of the obtained results is given. Introduction In the last decade along with studies of dissipative structures in homogeneous catalytic reactions of the Belousov-Zhabotinskii-type, considerable attention was attracted to the heterogeneous catalytic reactions. They reveal a whole spectrum of synergetic effects, e.g., rate oscillations, concentration waves, spirals and chaos [1]. The heterogeneous systems are simpler than the homogeneous ones. Therefore, one can use for their study a number of powerful experimental and theoretical methods, which allow to determine the origin of spatio-temporal structures. In particular, the oscillatory kinetics was observed in heterogeneous catalysis on many metal surfaces as well as on oxide catalysts [1]. The mechanism of oscillations is different for various catalysts [2]. The more so, for the same catalyst the origin of oscillations is different in the high and low gas pressure limits. However, independently on the type of a catalyst, the global synchronization of oscillations is observed [1]. This fact implies the existence of very universal rules in the behavior of oscillatory systems, which exist independently on both type of catalyst and mechanism of a particular catalytic reaction. An important method for treating self-oscillating systems, in particular autocatalytic reactions, is the periodical variation of an external parameter in time and analysis of the system’s response. This has been done experimentally in Ref. [3] for the autocatalytic CO+1/2O2 reaction on Pt(110) surfaces in the low-pressure limit. In this study the external parameter, varied periodically in time, was the partial pressure of O2 gas above the Pt(110) sample. It was shown experimentally that, depending on the modulation frequencies, the self-oscillations in the system exhibit sub- and superharmonic resonance, phase locking, and quasiperiodic behavior. One of the theoretical methods used to attack the problem of catalysis is a Monte-Carlo (MC) computer simulation (see [4], [5] and references therein). Its role considerably increased during the last years due to increase of computational facilities. The idea of the MC method is to define a mathematical model, which accounts for basic experimentally detected reaction steps. The reactants are assumed to be classical particles (usually denoted as A, B, etc.), which can occupy sites on a discrete lattice. This allows easily to describe adsorption, desorption, diffusion and reaction of reactants as one- or two-site processes with the corresponding rates. Extension of the model to time dependent transition rates is straightforward. Both reconstructed and non-reconstructed surfaces can be modeled by assigning different sticking coefficients of reactants to lattice sites. Some models consist of more than ten-step reactions. A detailed mathematical model often complicates an analysis of simulation results and thus prevents from the understanding of basic driving mechanisms, e.g., the origin of synchronization of oscillations.
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