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72 Fig. 3. The amplitude (squares) and frequency (circles) dependence on the jump rate νJ of (i) reactants A, J=A (filled interior) and (ii) reactants B, J=B (open interior). Parameter ζ =0.065. UNIVERSITÄT OSNABRÜCK, FACHBEREICH PHYSIK effective in destroying the oscillatory behavior, because reactants A form clusters and only a portion of reactants at cluster surfaces can diffuse, whereas most of inner reactants A are screened. In contrast, clusters of reactants B are more loose due to reactant B annihilation reaction. Thus, reactants B turn out to be more mobile, which results in more pronounced mobility effects. (iv) Lastly, the nontrivial case occurs if only reactants A are mobile and we consider the energetic interaction only between AA, see Fig. 4. Since the Lotka-type model is asymmetric with respect to A and B reactants, this behavior differs from the case of interacting and mobile reactants B. Now, if we consider an attraction between reactants AA (e AA 0), the critical concentration of reactants A should be larger, in order to create a percolating cluster of A’s. Reactants A, which sit on the surfaces of clusters, repel from reactants A in their NN positions. Thus, a loose structure is formed, which can accumulate additional reactants A. This process is more time-consuming which is well seen from a decrease of the frequency for e AA >0, see Fig. 4. Fig. 4. The amplitude (squares) and frequency (circles) dependence on the dimensionless energetic interaction eAA between similar reactants AA. The jump rate νA=0.14 s -1 , ζ =0.065 and eAB=eBB=0. To understand the impact of modulation and diffusion on temporal structures, we have used here a Lotka-type mathematical model. It allows us to obtain a pictorial view of the basic driving processes. More detailed models could better reproduce experimentally observed structures. However, the understanding of the mechanisms of these phenomena in this case is often problematic or even impossible. Therefore, models like the Lotka-type are of great importance, since they allow to study and understand individual processes, e.g, parameter modulation, diffusion or energetic interaction, independently of other factors. Literatur [1] R. Imbihl and G. Ertl, Chem. Rev. 95, 697 (1995). [2] M. M. Slin’ko and N. I. Jaeger, Studies in Surface Science and Catalysis, Oscillating Heterogeneous Catalytic Systems (Elsevier, Amsterdam, 1994), Vol. 86. [3] M. Eiswirth and G. Ertl, Phys. Rev. Lett. 60, 1526 (1988). [4] E. V. Albano, Heterog. Chem. Rev. 3, 389 (1996). [5] E. V. Albano, Surface Science, Computational Methods in Surface and Colloid Science (Marcel Dekker, Inc.: New York, 2000), Vol. 89, p. 387. [6] J. Mai, V. N. Kuzovkov, and W. von Niessen, J. Phys. A: Math. Gen. 30, 4171 (1997). [7] J.-P. Hovi, A. P. J. Jansen, and R. M. Nieminen, Phys. Rev. E 55, 4170 (1997). [8] A. P. J. Jansen, J. Mol. Catal. A: Chem. 119, 125 (1997). [9] R. M. Nieminen and A. P. J. Jansen, Appl. Catal. A: Gen. 160, 99 (1997). [10] E. A. Kotomin and V. N. Kuzovkov, Modern Aspects of Diffusion-Controlled Reactions: Cooperative Phenomena in Bimolecular Processes (Elsevier, North Holland, Amsterdam, 1996), Vol. 34. [11] M. Silverberg and A. Ben-Shaul, J. Chem. Phys. 87, 3178 (1987). [12] J. Mai and W. von Niessen, J. Chem. Phys. 93, 3685 (1990). [13] I. Jensen and H. C. Fogedby, Phys. Rev. A 42, 1969 (1990). [14] M. Tammaro, M. Sabella, and J. W. Evans, J. Chem. Phys. 103, 10277 (1995). [15] R. J. Gelten et al., J. Chem. Phys. 108, 5921 (1998). [16] H.-P. Kaukonen and R. M. Nieminen, J. Chem. Phys. 91, 4380 (1989). [17] V. P. Zhdanov, Phys. Rev. E 59, 6292 (1999). [18] G. Zvejnieks and V. N. Kuzovkov, Phys. Rev. E 61, 4593 (2000). [19] V. Kashcheyevs (private communication).
GRADUIERTENKOLLEG MIKROSTRUKTUR OXIDISCHER KRISTALLE 73 Eigene Publikationen G. Zvejnieks and V. N. Kuzovkov: Monte Carlo simulations of the periodically forced autocatalytic A+B→2B reaction, Phys. Rev. E 61, 4593 (2000). G. Zvejnieks and V. N. Kuzovkov: Monte-Carlo simulations for Lotka-type model with reactant surface diffusion and interactions (in preparation). Besuchte Lehrveranstaltungen Ringvorlesung des Graduiertenkollegs Seminar des Kollegs Kolloquium des SFB 225 Additional Lectures: Prof. E. A. Kotomin, Computational Methods and Modeling of Advanced Materials, 2000. Prof. E. A. Kotomin, Computational Methods and Modeling of Advanced Materials II, 2000/2001. Konferenzbesuche, Forschungsaufenthalte, auswärtige Vorträge Talk in the III Physic Seminar in honor of F. Pianca, December 2000, Institute of Chemical Physics, University of Latvia (Riga, Latvia): Monte-Carlo simulations of the periodically forced autocatalytic A+B→2B reaction, 29.12.1999 Talk in the 16th Scientific Meeting, The Institute of Solid State Physics, University of Latvia: Monte-Carlo simulations of the periodically forced autocatalytic A+B→2B reaction, Feb. 2000 Talk in the Seminar of the Graduiertenkolleg: Monte-Carlo simulations of the periodically-forced autocatalytic A+B→2B reaction, University of Osnabrück, May, 2000 Talk in the International Workshop on "Microstructure of Oxide Materials": Monte-Carlo simulations of Lotkatype autocatalytic surface reactions, Osnabrück, June 13-15, 2000
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