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Hard versus soft dynamics for adsorption-desorption kinetics: Exact results in one-dimension

S. J. Manzi, V. J. Huespe, R. E. Belardinelli, and V. D. Pereyra

  • Departamento de Física, Instituto de Física Aplicada (INFAP)–CONICET, Universidad Nacional de San Luis, Chacabuco 917, 5700 San Luis, Argentina

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Phys. Rev. E 80, 051112 – Published 12 November, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.051112

Abstract

The adsorption-desorption kinetics is discussed in the framework of the kinetic lattice-gas model. The master equation formalism has been introduced to describe the evolution of the system, where the transition probabilities are written as an expansion of the occupation configurations of all neighboring sites. Since the detailed balance principle determines half of the coefficients that arise from the expansion, it is necessary to introduce ad hoc, a dynamic scheme to get the rest of them. Three schemes of the so-called hard dynamics, in which the probability of transition from single site cannot be factored into a part which depends only on the interaction energy and one that only depends on the field energy, and five schemes of the so-called soft dynamics, in which this factorization is possible, were introduced for this purpose. It is observed that for the hard dynamic schemes, the equilibrium and nonequilibrium observables, such as adsorption isotherms, sticking coefficients, and thermal desorption spectra, have a normal or physical sustainable behavior. While for the soft dynamics schemes, with the exception of the transition state theory, the equilibrium and nonequilibrium observables have several problems. Some of them can be regarded as abnormal behavior.

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References (81)

  1. Frontier in Surface and Interface Science, edited by C. B. Duke and E. W. Plummer (North-Holland, Amsterdam, 2002).
  2. Handbook of Heterogeneous Catalysis, edited by G. Ertl, H. Knozinger, and J. Weitkamp (Wiley, New York, 1997).
  3. A. Cassuto and D. A. King, Surf. Sci. 102, 388 (1981).
  4. A. Córdoba and M. C. Lemos, J. Chem. Phys. 99, 4821 (1993).
  5. J. W. Evans, Rev. Mod. Phys. 65, 1281 (1993) and references therein.
  6. D. Menzel, in Interactions on Metal Surfaces, edited by R. Gomer (Springer-Verlag, Berlín, 1975), p. 102.
  7. Y. K. Tovbin, in Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, Studies in surface science and catalysis, Vol. 104, edited by W. Rudzinski, A. Steele, and G. Zgrablich (Elsevier, New York, 1997) and references therein.
  8. V. P. Zhdanov and B. Kasemo, Chem. Phys. 177, 519 (1993) and references therein.
  9. H. J. Kreuzer and Z. W. Gortel, Physisorption Kinetics (Springer-Verlag, Berlin, 1986).
  10. H. J. Kreuzer and S. H. Payne, Surf. Sci. 198, 235 (1988).
  11. H. J. Kreuzer and S. H. Payne, Surf. Sci. 200, L433 (1988).
  12. S. H. Payne and H. J. Kreuzer, Surf. Sci. 205, 153 (1988).
  13. C. Uebing and V. P. Zhdanov, J. Chem. Phys. 109, 3197 (1998).
  14. V. P. Zhdanov, Elementary Physicochemical Processes on Solid Surfaces (Plenum, New York, 1991).
  15. M. Silverberg and A. Ben-Shaul, Surf. Sci. 214, 17 (1989).
  16. S. J. Lombardo and A. T. Bell, Surf. Sci. Rep. 13, 3 (1991).
  17. H. J. Kreuzer and S. H. Payne, in Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, Studies in Surfaces Science and Catalysis, Vol. 104, edited by W. Rudzinski, W. A. Steele, G. Zgrablich (Elsevier, New York, 1997). p. 153, and references therein.
  18. H. J. Kreuzer, J. Chem. Phys. 104, 9593 (1996).
  19. R. J. Glauber, J. Math. Phys. 4, 294 (1963).
  20. K. Kawasaki, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic Press, New York, 1972), Vol. 2, p. 443.
  21. H. J. Kreuzer and J. Zhang, Appl. Phys. A: Mater. Sci. Process. 51, 183 (1990).
  22. S. H. Payne, H. A. McKay, H. J. Kreuzer, M. Gierer, H. Bludau, H. Over, and G. Ertl, Phys. Rev. B 54, 5073 (1996).
  23. S. H. Payne, G. Ledue, J. C. Michael, and H. J. Kreuzer, Surf. Sci. 512, 151 (2002).
  24. S. H. Payne, H. J. Kreuzer, M. Kinne, R. Denecke, and H.-P. Steinruck, Surf. Sci. 513, 174 (2002).
  25. G. Costanza, S. Manzi, and V. D. Pereyra, Surf. Sci. 524, 89 (2003).
  26. O. Furlong, S. Manzi, G. Costanza, and V. D. Pereyra, Physica A 339, 267 (2004).
  27. G. Costanza, S. Manzi, and V. D. Pereyra, Surf. Sci. 600, 3484 (2006).
  28. S. H. Payne and H. J. Kreuzer, Phys. Rev. B 75, 115403 (2007).
  29. A. Wierzbicki and H. J. Kreuzer, Surf. Sci. 257, 417 (1991).
  30. S. J. Manzi, R. E. Belardinelli, G. Costanza, and V. D. Pereyra, Phys. Rev. E 79, 021103 (2009).
  31. O. Shochet, K. Kassner, E. Ben-Jacob, S. B. Lipson, and H. Müller-Krümbhaar, Physica A 181, 136 (1992) and references therein.
  32. D. P. Landau and K. Binder, Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, 2000).
  33. M. Siegert and M. Plischke, Phys. Rev. E 50, 917 (1994).
  34. Y. Shim and D. P. Landau, Phys. Rev. E 64, 036110 (2001).
  35. P. A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000).
  36. P. A. Rikvold and M. Kolesik, J. Phys. A 35, L117 (2002).
  37. P. A. Rikvold and M. Kolesik, Phys. Rev. E 66, 066116 (2002).
  38. P. A. Rikvold and M. Kolesik, Phys. Rev. E 67, 066113 (2003).
  39. G. M. Buendía, P. A. Rikvold, and M. Kolesik, Phys. Rev. B 73, 045437 (2006); J. Mol. Struct.; THEOCHEM 769, 207 (2006).
  40. J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Model (Cambridge University Press, Cambridge, 1999), Chap. 7.
  41. S. Frank, D. E. Roberts, and P. A. Rikvold, J. Chem. Phys. 122, 064705 (2005).
  42. K. Saito, S. Takesue, and S. Miyashita, Phys. Rev. E 61, 2397 (2000).
  43. K. Park and M. A. Novotny, Comput. Phys. Commun. 147, 737 (2002).
  44. G. M. Buendía, P. A. Rikvold, M. Kolesik, K. Park, and M. A. Novotny, Phys. Rev. B 76, 045422 (2007).
  45. S. Frank and P. A. Rikvold, Surf. Sci. 600, 2470 (2006).
  46. G. M. Buendía, P. A. Rikvold, K. Park, and M. A. Novotny, J. Chem. Phys. 121, 4193 (2004).
  47. K. Park, P. A. Rikvold, G. M. Buendía, and M. A. Novotny, Phys. Rev. Lett. 92, 015701 (2004).
  48. K. A. Fichthorn and W. H. Weinberg, J. Chem. Phys. 95, 1090 (1991).
  49. H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989).
  50. T. Ala-Nissila and S. C. Ying, Prog. Surf. Sci. 39, 227 (1992).
  51. T. Ala-Nissila, R. Ferrando, and S. C. Ying, Adv. Phys. 51, 949 (2002).
  52. T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992).
  53. K. Kawasaki, Phys. Rev. 145, 224 (1966), ; 148, 375 (1966); 150, 285 (1966).
  54. H. J. Kreuzer and S. H. Payne, Computational Methods in Colloid and Interface Science (Dekker, New York, 1999).
  55. S. H. Payne, A. Wierzbicki, and H. J. Kreuzer, Surf. Sci. 291, 242 (1993).
  56. D. ben-Avraham and J. Köhler, Phys. Rev. A 45, 8358 (1992).
  57. J. Evans, D. K. Hoffman, and H. Pak, Surf. Sci. 192, 475 (1987).
  58. S. H. Payne and H. J. Kreuzer, Surf. Sci. 222, 404 (1989).
  59. F. Haake, M. Leeuweinstein, and M. Wilkens, Z. Phys. B 54, 333 (1984); 55, 211 (1984).
  60. J. H. Luscombe, Phys. Rev. B 29, 5128 (1984).
  61. E. Oguz, O. T. Valls, G. F. Mazenko, and J. H. Luscombe, Surf. Sci. 118, 578 (1981).
  62. D. J. W. Geldart, H. J. Kreuzer, and F. S. Rys, Surf. Sci. 176, 284 (1986).
  63. J. A. Boscoboinik, C. Plaisance, M. Neurock, and W. T. Tysoe, Phys. Rev. B 77, 045422 (2008).
  64. V. P. Zhdanov, Surf. Sci. 111, 63 (1981); 111, L662 (1981); 123, 106 (1982); 133, 469 (1983); 157, L384 (1985); 165, L31 (1986); 171, L461 (1986); 209, 523 (1989).
  65. V. P. Zhdanov, Surf. Sci. Rep. 12 185 (1991) and reference therein.
  66. V. D. Pereyra and G. Zgrablich, Langmuir 6, 118 (1990).
  67. V. D. Pereyra, G. Zgrablich, and V. P. Zhdanov, Langmuir 6, 691 (1990).
  68. B. Li, C.-S. Zhang, V. P. Zhdanov, and P. R. Norton, Surf. Sci. 322, 373 (1995).
  69. V. P. Zhdanov and B. Kasemo, Surf. Sci. 412, 527 (1998).
  70. P. Piercy, K. De’Bell, and H. Pfnür, Phys. Rev. B 45, 1869 (1992).
  71. C. Schwennicke and H. Pfnür, Phys. Rev. B 56, 10558 (1997).
  72. V. P. Zhdanov and T. Matsushima, Phys. Rev. Lett. 98, 036101 (2007).
  73. R. Kose, W. A. Brown, and D. A. King, J. Phys. Chem. 103, 8722 (1999).
  74. C. Stampfl, H. J. Kreuzer, S. H. Payne, H. Pfnür, and M. Scheffler, Phys. Rev. Lett. 83, 2993 (1999).
  75. E. Hansen and M. Neurock, Surf. Sci. 441, 410 (1999).
  76. J.-S. McEwen and A. Eichler, J. Chem. Phys. 126, 094701 (2007).
  77. A. P. J. Jansen and W. K. Offermans, J. Comput. Methods Sci. Eng. 2, 351 (2002).
  78. C. G. M. Hermse, F. Frechard, A. P. van Bavel, J. J. Lukkien, J. W. Niemantsverdriet, R. A. van Santen, and A. P. J. Jansen, J. Chem. Phys. 118, 7081 (2003).
  79. R. A. van Santen and J. W. Niemantsverdriet, Chemical Kinetics and Catalysis (Plenum Press, New York, 1995).
  80. J. L. Sales and G. Zgrablich, Phys. Rev. B 35, 9520 (1987); Surf. Sci. 187, 1 (1987).
  81. J. L. Sales, R. O. Uñac, M. V. Gargiulo, V. Bustos, and G. Zgrablich, Langmuir 12, 95 (1996).

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Phys. Rev. E 80, 051112– Published 12 November, 2009
  • Received 15 April 2009

© 2009 American Physical Society

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