From atomic scale ordering to mesoscale spatial patterns in surface reactions: A heterogeneous coupled lattice-gas simulation approach

Multiscale Modeling and Simulation

Volumn 4, Issue 2, 2005, Pages 424-446

  Liu, Da Jiang ^a   Evans, J W ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

Kinetic Monte Carlo; Pattern formation; Reaction diffusion; Surface reaction

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; MONTE CARLO METHODS; OXIDATION; PERCOLATION (SOLID STATE); REACTION KINETICS; SUPERLATTICES;

ATOMIC SCALE ORDERING; MESOSCALE SPATIAL PATTERNS; PATTERN FORMATION; SURFACE DIFFUSION;

SURFACE REACTIONS;

EID: 33646203859     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/040606405     Document Type: Article

References (49)

1. A. Brandt, Multiscale scientific computation: Review 2001, in Multiscale and Multiresolution Methods: Theory and Applications, T. J. Barth, T. F. Chan, and R. Haimes, eds., Lect. Notes Comput. Sci. Eng. 20, Springer-Verlag, Heidelberg, 2001, pp. 3-95.
2. A. Bunde and S. Havlin, eds., Fractals and Disordered Systems, Springer-Verlag, Berlin, 1991.
3. P. G. de Gennes, Relation between percolation theory and elasticity of gels, J. Phys. Lett. Paris., 37 (1976), pp. L1-L2.
4. W. E and B. Engquist, The heterogeneous multiscale methods, Comm. Math. Sci., 1 (2003), pp. 87-132.
5. R. G. Edwards, J. Goodman, and A. D. Sokal, Multigrid method for the random-resistor problem, Phys. Rev. Lett., 61 (1988), pp. 1333-1335.
6. T. Engel and G. Ertl, Elementary steps in the catalytic oxidation of carbon monoxide on platinum metals, Adv. Catal., 28 (1979), pp. 1-78.
7. M. H. Ernst, Systematic density expansion of transport properties of random lattices, Physica A, 140 (1986), pp. 390-396.
8. M. H. Ernst, T. M. Nieuwenhuizen, and P. F. J. van Velthoven, Density expansion of transport coefficients on a 2D site-disordered lattice: II, J. Phys. A, 20 (1987), pp. 5335-5350.
9. J. W. Evans, D.-J. Liu, and M. Tammaro, From atomistic lattice-gas models for surface reactions to hydrodynamic reaction-diffusion equations, Chaos, 12 (2002), pp. 131-143.
10. R. Fogelholm, The conductivity of large percolation network samples, J. Phys. C, 13 (1980), pp. L571-L574.
11. D. J. Frank and C. J. Lobb, Highly efficient algorithm for percolative transport studies in two dimensions, Phys. Rev. B, 37 (1988), pp. 302-307.
12. C. W. Gear, I. G. Kevrekidis, and C. Theodoropoulos, "Coarse" integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods, Comp. Chem. Eng., 26 (2002), pp. 941-963.
13. C. W. Gear, J. Li, and I. G. Kevrekidis, The gap-tooth method in particle simulations, Phys. Lett. A, 316 (2003), pp. 190-195.
14. P. Grassberger, Conductivity exponent and backbone dimension in 2-d percolation, Phys. A, 262 (1999), pp. 251-263.
15. R. Imbihl, Oscillatory reactions on single crystal surfaces, Prog. Surf. Sci., 44 (1993), pp. 185-343.
16. R. Imbihl and G. Ertl, Oscillatory kinetics in heterogeneous catalysis, Chem. Rev., 95 (1995), pp. 697-733.
17. E. W. James, D.-J. Liu, and J. W. Evans, Relaxation effects in random sequential adsorption: Application to chemisorption systems, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 165 (2000), pp. 241-254.
18. E. W. James, C. Song, and J. W. Evans, CO-oxidation model with superlattice ordering of adsorbed oxygen. I. Steady-state bifurcations, J. Chem. Phys., 111 (1999), pp. 6579-6589.
19. R. Kapral and K. Showalter, eds., Chemical Waves and Patterns, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995.
20. S. Kirkpatrick, Percolation and conduction, Rev. Modern Phys., 45 (1973), pp. 574-588.
21. K. Krischer, M. Eiswirth, and G. Ertl, Oscillatory CO oxidation on Pt(110): Modeling of temporal self-organization, J. Chem. Phys., 96 (1992), pp. 9161-9172.
22. R. Kutner, Chemical diffusion in the lattice gas of non-interacting particles, Phys. Lett. A, 81 (1981), pp. 239-240.
23. D.-J. Liu and J. W. Evans, Ordering and percolation transitions for hard squares: Equilibrium versus nonequilibrium models for adsorbed layers with c(2x2) superlattice ordering, Phys. Rev. B, 62 (2000), pp. 2134-2145.
24. D.-J. Liu and J. W. Evans, Surface diffusion in mixed overlayers with superlattice ordering: Percolative transport around obstacles and along domain boundaries, J. Chem. Phys., 113 (2000), pp. 10252-10264.
25. D.-J. Liu and J. W. Evans, Symmetry-breaking and percolation transition in a surface reaction model with superlattice ordering, Phys. Rev. Lett., 84 (2000), pp. 955-959.
26. D.-J. Liu and J. W. Evans, From atomic scale reactant ordering to mesoscale reaction front propagation: CO oxidation on Pd(100), Phys. Rev. B, 70 (2004), 193408.
27. D.-J. Liu, N. Pavlenko, and J. W. Evans, Crossover between mean-field and Ising critical behavior in a lattice-gas reaction-diffusion model, J. Statist. Phys., 114 (2004), pp. 101-114.
28. E. Loscar and E. V. Albano, Critical behaviour of irreversible reaction systems, Rep. Progr. Phys., 66 (2003), pp. 1343-1382.
29. C. H. Mak, H. C. Andersen, and S. M. George, Monte Carlo studies of diffusion on inhomogeneous surfaces, J. Chem. Phys., 88 (1988), pp. 4052-4061.
30. A. G. Makeev, D. Maroudas, and I. G. Kevrekidis, "Coarse" stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examples, J. Chem. Phys., 116 (2002), pp. 10083-10091.
31. A. G. Makeev, D. Maroudas, A. Z. Panagiotopoulos, and I. G. Kevrekidis, Coarse bifurcation analysis of kinetic Monte Carlo simulations: A lattice-gas model with lateral interactions, J. Chem. Phys., 117 (2002), pp. 8229-8240.
32. A. S. Mikhailov, Foundations of Synergetics I: Distributed Active Systems, Springer-Verlag, Berlin, 1994.
33. T. M. Nieuwenhuizen, P. F. J. van Velthoven, and M. H. Ernst, Diffusion and long-time tails in a two-dimensional site-percolation model, Phys. Rev. Lett., 57 (1986), pp. 2477-2480.
34. T. M. Nieuwenhuizen, P. F. J. van Velthoven, and M. H. Ernst, Density expansion of transport properties on 2d site-disordered lattices: I. General theory, J. Phys. A, 20 (1987), pp. 4001-4015.
35. L. Onsager, Reciprocal relations in irreversible processes. I., Phys. Rev., 37 (1931), pp. 405-426.
36. L. Onsager, Reciprocal relations in irreversible processes. II., Phys. Rev., 38 (1931), pp. 2265-2279.
37. N. Pavlenko, J. W. Evans, D.-J. Liu, and R. Imbihl, Catalytic CO oxidation on nanoscale Pt factes: Effect of interfacet CO diffusion on bifurcation and fluctuation behavior, Phys. Rev. E, 65 (2002), 016121.
38. N. Pavlenko, R. Imbihl, J. W. Evans, and D.-J. Liu, Critical behavior in an atomistic model for a bistable surface reaction: CO oxidation with rapid CO diffusion, Phys. Rev. E, 68 (2003), 016212.
39. R. Rico-Martínez, C. W. Gear, and I. G. Kevrekidis, Coarse projective kMC integration: Forward/reverse initial and boundary value problems, J. Comput. Phys., 196 (2004), pp. 474-489.
40. V. B. Shenoy, R. Miller, E. B. Tadmor, R. Phillips, and M. Ortiz, Quasicontinuum models of interfacial structure and deformation, Phys. Rev. Lett., 80 (1998), pp. 742-745.
41. M. Tammaro and J. W. Evans, Chemical diffusivity and wave propagation in surface reactions: Lattice-gas model mimicking CO-oxidation with high CO-mobility, J. Chem. Phys., 108 (1998), pp. 762-773.
42. M. Tammaro and J. W. Evans, Hydrodynamic limits for the monomer-dimer surface reaction: Chemical diffusion, wave propagation, and equistability, Phys. Rev. E, 57 (1998), pp. 5087-5094.
43. M. Tammaro, M. Sabella, and J. W. Evans, Hybrid treatment of spatio-temporal behavior in surface reactions with coexisting immobile and highly mobile reactants, J. Chem. Phys., 103 (1995), pp. 10277-10285.
44. S. Völkening and J. Wintterlin, CO oxidation on Pt(111) - scanning tunneling microscopy experiments and Monte Carlo simulations, J. Chem. Phys., 114 (2001), pp. 6382-6395.
45. J. Wintterlin, S. Völkening, T. V. W. Janssens, T. Zambelli, and G. Ertl, Atomic and macroscopic reaction rates of a surface-catalyzed reaction, Science, 278 (1997), pp. 1931-1934.
46. W.-G. Yin and R. Tao, Algorithm for finding two-dimensional site percolation backbones, Phys. B, 279 (2000), pp. 84-86.
47. 2 → 2AB reaction complicated by spatial constraints for adsorption, formation of islands, and steps, Surf. Sci., 412/413 (1998), pp. 527-543.
48. 2 reaction model using a constant-coverage kinetic ensemble, Phys. Rev. A, 46 (1992), pp. 4630-4633.
49. R. M. Ziff, E. Gulari, and Y. Barshad, Kinetic phase transitions in an irreversible surface-reaction model, Phys. Rev. Lett., 56 (1986), pp. 2553-2556.