Abstract
Using kinetic Monte Carlo simulations, we study the effect of oscillatory kinetics due to surface reconstructions on Ziff-Gulari-Barshad (ZGB) model discontinuous phase transition. To investigate the transition, we do extensive finite size scaling analysis. It is found that the discontinuous transition still exists. On inclusion of desorption in the model, the order-parameter probability distribution broadens but remains bimodal. That is, the first-order phase transition becomes weaker with increase in desorption rate.
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Christmann, K.: Introduction to Surface Physical Chemistry. Steinkopff Verlag, Darmstadt (1991)
Zhdanov, V.P., Kazemo, B.: Kinetic phase transitions in simple reactions on solid surfaces. Surf. Sci. Rep. 20, 113–189 (1994)
Hinrichsen, H.: Nonequilibrium critical phenomena and phase transitions into absorbing states. Adv. Phys. 49, 815–958 (2000)
Odor, G.: Universality classes in nonequilibrium lattice systems. Rev. Mod. Phys. 76, 663–724 (2004)
Ziff, R.M., Gulari, E., Barshad, Y.: Kinetic phase transitions in an irreversible surface-reaction model. Phys. Rev. Lett. 56, 2553–2556 (1986)
Marro, J., Dickman, R.: Nonequilibrium Phase Transitions in Lattice Models. Cambridge University Press, Cambridge (1999)
Evans, J.W., Ray, T.R.: Interface propagation and nucleation phenomena for discontinuous poisoning transitions in surface-reaction models. Phys. Rev. E 50, 4302–4314 (1994)
Goodman, R.H., Graff, D.S., Sander, L.M., Leroux-Hugon, P., Clément, E.: Trigger waves in a model for catalysis. Phys. Rev. E 52, 5904–5909 (1995)
Evans, J.W., Miesch, M.S.: Characterizing kinetics near a first-order catalytic-poisoning transition. Phys. Rev. Lett. 66, 833–836 (1991)
Loscar, E., Albano, E.V.: Critical behaviour of irreversible reaction systems. Rep. Prog. Phys. 66, 1343–1382 (2003)
Machado, E., Buendía, G.M., Rikvold, P.A.: Decay of metastable phases in a model for the catalytic oxidation of CO. Phys. Rev. E 71, 031603 (2005)
Liu, Da-Jiang, Evans, J.W.: Atomistic and multiscale modeling of CO-oxidation on Pd(100) and Rh(100): from nanoscale fluctuations to mesoscale reaction fronts. Surf. Sci. 603, 1706–1716 (2009)
Schlögl, F.: Chemical reaction models for non-equilibrium phase transitions. Z. Phys. 253, 147–161 (1972)
Grassberger, P.: On phase transitions in Schlögl’s second model. Physica B, Condens. Matter 47, 365–374 (1982)
Guo, X., Liu, Da-Jiang, Evans, J.W.: Schloegl’s second model for autocatalysis with particle diffusion: lattice-gas realization exhibiting generic two-phase coexistence. J. Chem. Phys. 130, 074106 (2009)
Engel, T., Ertl, G.: Elementary steps in the catalytic oxidation of carbon monoxide on platinum metals. Adv. Catal. 28, 1–78 (1979)
Meakin, P.: Simple models for heterogeneous catalysis with a poisoning transition. J. Chem. Phys. 93, 2903–2910 (1990)
Tambe, S.S., Jayaraman, V.K., Kulkarni, B.D.: Cellular automata modelling of a surface catalytic reaction with Eley-Rideal step: the case of CO oxidation. Chem. Phys. Lett. 225, 303–308 (1994)
Mukherjee, A.K., Sinha, I.: Effect of the Eley-Rideal step on catalytic oxidation of CO under periodic external pressure. Appl. Surf. Sci. 255, 6168–6172 (2009)
Ehsasi, M., Matloch, M., Frank, O., Block, J.H., Christmann, K., Rys, F.S., Hirschwald, W.: Steady and nonsteady rates of reaction in a heterogeneously catalyzed reaction: oxidation of CO on platinum, experiments and simulations. J. Chem. Phys. 91, 4949–4960 (1989)
Tome, T., Dickman, R.: Ziff-Gulari-Barshad model with CO desorption: an Ising-like nonequilibrium critical point. Phys. Rev. E 47, 948–952 (1993)
Buendía, G.M., Machado, E., Rikvold, P.A.: Effect of CO desorption and coadsorption with O on the phase diagram of a Ziff-Gulari-Barshad model for the catalytic oxidation of CO. J. Chem. Phys. 131, 184704 (2009)
Sinha, I., Mukherjee, A.K.: Ziff-Gulari-Barshad model with CO desorption under oscillating reactant pressure. Physica A 389, 3128–3133 (2010)
Machado, E., Buendía, G.M., Rikvold, P.A., Ziff, R.M.: Response of a catalytic reaction to periodic variation of the CO pressure: increased CO2 production and dynamic phase transition. Phys. Rev. E 71, 016120 (2005)
Imbihl, R., Ertl, G.: Oscillatory kinetics in heterogeneous catalysis. Chem. Rev. 95, 697–733 (1995)
Sales, B.C., Turner, J.E., Maple, M.B.: Oscillatory oxidation of CO over Pt, Pd and Ir catalysts: theory. Surf. Sci. 114, 381–394 (1982)
Noussiou, V.K., Provata, A.: Kinetic Monte Carlo simulations of the oscillatory CO oxidation at high pressures: the surface oxide model. Chem. Phys. 348, 11–20 (2008)
Graham, M.D., Bar, M., Kevrekidis, I.G., Asakura, K., Lauterbach, J., Rotermund, H.H., Ertl, G.: Catalysis on microstructured surfaces: pattern formation during CO oxidation in complex Pt domains. Phys. Rev. E 52, 76–93 (1995)
Wolff, J., Papathanasiou, A.G., Rotermund, H.H., Ertl, G., Katsoulakis, M.A., Li, X., Kevrekidis, I.G.: Wave initiation through spatiotemporally controllable perturbations. Phys. Rev. Lett. 90, 148301-4 (2003)
Dickman, R.: Kinetic phase transitions in a surface-reaction model: mean-field theory. Phys. Rev. A 34, 4246–4250 (1986)
Albano, E.V.: A dimer–monomer catalyzed reaction process with surface reconstruction coupled to reactant coverages. Langmuir 13, 4013–4017 (1997)
Albano, E.V.: On the influence of reactant’s induced surface transformations in the behavior of a heterogeneously catalyzed dimer–monomer reaction model. J. Chem. Phys. 109, 7498–7505 (1998)
Eiswirth, M., Möller, P., Wetzl, K., Imbihl, R., Ertl, G.: Mechanisms of spatial self-organization in isothermal kinetic oscillations during the catalytic CO oxidation on Pt single crystal surfaces. J. Chem. Phys. 90, 510–521 (1989)
Imbihl, R., Cox, M.P., Ertl, G.: Kinetic oscillations in the catalytic CO oxidation on Pt(100): experiments. J. Chem. Phys. 84, 3519–3534 (1986)
Kortluke, O., Kuzovkov, V.N., von Niessen, W.: Simulation of kinetic oscillations in surface reactions on reconstructing surfaces. J. Chem. Phys. 110, 11523–11533 (1999)
Provata, A., Noussiou, V.K.: Spatiotemporal oscillations and clustering in the Ziff-Gulari-Barshad model with surface reconstruction. Phys. Rev. E 72, 066108-14 (2005)
Albano, E.V.: Critical and oscillatory behavior of a dimer-monomer catalyzed reaction process. Phys. Rev. E 57, 6840–6843 (1998)
Landau, D.P., Binder, K.: A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press, Cambridge (2000)
Borgs, C., Kotecký, R.: A rigorous theory of finite-size scaling at first-order phase transitions. J. Stat. Phys. 61, 79–119 (1990)
Binder, K., Landau, D.P.: Finite-size scaling at first-order phase transitions. Phys. Rev. B 30, 1477–1485 (1984)
Challa, M.S., Landau, D.P., Binder, K.: Finite-size effects at temperature-driven first-order transitions. Phys. Rev. B 34, 1841–1852 (1986)
Fisher, M.E., Berker, A.N.: Scaling for first-order phase transitions in thermodynamic and finite systems. Phys. Rev. B 26, 2507–2513 (1982)
Ngo, V.T., Hoang, D.T., Diep, H.T.: Flat energy-histogram simulation of the phase transition in an Ising fully frustrated lattice. J. Phys., Condens. Matter 23, 226002-7 (2011)
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Sinha, I., Mukherjee, A.K. First-Order Phase Transition in a Modified Ziff-Gulari-Barshad Model with Self-oscillating Reactant Coverages. J Stat Phys 146, 669–686 (2012). https://doi.org/10.1007/s10955-011-0414-5
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DOI: https://doi.org/10.1007/s10955-011-0414-5