Abstract
We introduce a new method to analyze the coexistence region of the constant rate ensemble ZGB discontinuous transition. The method clearly delineates the spinodal and coexistence points in the constant rate ZGB model. Increase in system size reduces the gap between the spinodal and coexistence points. Next we quantify the effect of metastability by introducing a droplet/nucleus of CO occupied sites in the initial system. In systems with initial nucleus of increasing size the distance between the spinodal and the coexistence point decreases, until for a large enough droplet spanning the initial system, the spinodal and the coexistence points become indistinguishable.
References
Ziff, R.M., Gulari, E., Barshad, Y.: Kinetic phase transitions in an irreversible surface-reaction model. Phys. Rev. Lett. 56, 2553–2556 (1986)
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)
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)
Jensen, I., Fogedby, H.C.: Kinetic phase transitions in a surface-reaction model with diffusion: computer simulations and mean field theory. Phys. Rev. A 42, 1969–1975 (1990)
Buendía, G.M., Machado, E., Rikvold, P.A.: Response of a model of CO oxidation with CO desorption and diffusion to a periodic external CO pressure. J. Mol. Struct., Theochem 769, 189–192 (2006)
Albano, E.V.: A dimer-monomer catalyzed reaction process with surface reconstruction coupled to reactant coverages. Langmuir 13, 4013–4017 (1997)
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)
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)
Sinha, I., Mukherjee, A.K.: Ziff-Gulari-Barshad model with CO desorption under oscillating reactant pressure. Physica A 389, 3128–3133 (2010)
Sreekumar, P., Jayaraman, V.K., Kulkarni, B.D.: Monte Carlo and cellular automata modeling of CO oxidation on a catalytic surface including the Eley-Rideal step and CO diffusion. Ind. Eng. Chem. Res. 37, 2188–2192 (1998)
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)
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)
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)
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 (1989)
Meakin, P., Scalapino, D.J.: Simple models for heterogeneous catalysis: phase transition-like behavior in nonequilibrium systems. J. Chem. Phys. 87, 731 (1987)
Yaldram, K., Sadiq, A.: Time evolution of a catalytic surface reaction: oxidation of carbon monoxide. J. Phys. A 22, L925 (1989)
Ziff, R.M., Brosilow, B.J.: Investigation of the first-order phase transition in the A-B2 reaction model using a constant-coverage kinetic ensemble. Phys. Rev. A 46, 4630–4635 (1992)
Loscar, E.S., Albano, E.V.: Hysteretic effects in the first-order irreversible phase transition of the ZGB model. Comput. Phys. Commun. 180, 488 (2009)
Loscar, E.S., Albano, E.V.: Numerical study of the evaporation/condensation phase transition of droplets for an irreversible reaction model. Europhys. Lett. 85, 30004 (2009)
Adams, D.A., Ziff, R.M., Sander, L.M.: Computation of nucleation at a nonequilibrium first-order phase transition using a rare-event algorithm. J. Chem. Phys. 133, 174107 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sinha, I., Mukherjee, A.K. Effect of Droplet Size on the First Order Ziff-Gulari-Barshad (ZGB) Phase Transition. J Stat Phys 147, 707–715 (2012). https://doi.org/10.1007/s10955-012-0508-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-012-0508-8