Adsorption and diffusion in a square lattice gas with strong attraction between particles: The real-space renormalization group approach

Abstract

A two-dimensional lattice gas with an attractive nearest neighbor (NN) pairwise lateral interaction on a lattice of square symmetry and its equivalent two-dimensional Ising spin model have been investigated by using the real-space renormalization group (RSRG) approach with blocks of different sizes and symmetries. We have calculated (a) adsorption isotherms for different temperatures and (b) the spontaneous magnetization for the Ising spin ferromagnet. The RSRG data are compared with the well-known exact expression. The coincidence between the exact and RSRG data is rather good. It is shown that the precision of the RSRG method strongly depends not only on the number of sites in the block but also on its symmetry.

In addition, we have calculated the coverage dependences of the pair correlation function for nearest neighbor adparticles, the isothermal susceptibility and the chemical adparticle diffusion coefficient at different temperatures. Furthermore, we have calculated the critical behavior of the mean square adparticle density fluctuations and of the chemical diffusion coefficient. The critical exponent is close to the value obtained by other methods. The RSRG data have been compared with results from Monte Carlo simulations. The coincidence is very good and, therefore, we conclude that the RSRG method can be applied at least for the systems discussed here to investigate the thermodynamic and kinetic properties of interacting adsorbates.

References

1. R. Gomer, Rep. Prog. Phys., 1990, 53, 917.
2. C. Uebing and R. Gomer, J. Chem. Phys., 1991, 95, 7626; 1991, 95, 7636; 1991, 95, 7641; 1991, 95, 7648.
3. A. V. Myshlyavtsev, A. A. Stepanov, C. Uebing and V. P. Zhdanov, Phys. Rev. B, 1995, 52, 5977.
4. A. A. Tarasenko, L. Jastrabik and C. Uebing, Phys. Rev. Sect. B, 1998, 57, 10166.
5. M. Bowker and D. A. King, Surf. Sci., 1978, 71, 583.
6. D. A. Reed and G. Ehrlich, Surf. Sci., 1981, 105, 603.
7. D. A. Reed and G. Ehrlich, Surf. Sci., 1981, 102, 588.
8. A. A. Chumak and A. A. Tarasenko, Surf. Sci., 1980, 91, 694.
9. V. P. Zhdanov, Elementary Physicochemical Processes on Solid Surfaces, Plenum, New York, 1991.
10. L. Onsager, Phys. Rev., 1944, 65, 117.
11. H. A. Kramers and G. H. Wannier, Phys. Rev., 1941, 60, 252.
12. Th. Niemeyer and J. M. J. van Leeuwen, Physica., 1974, 71, 17.
13. M. Nauenberg and B. Nienhuis, Phys. Rev. Lett., 1974, 33, 1598.
14. B. Nienhuis and M. Nauenberg, Phys. Rev. Lett., 1975, 35, 477.
15. The interested reader is referred to ref. 16 for a detailed description of the RSRG method and to ref. 17 and 18 for applications of the RSRG method to lattice gas models.
16. Th. Niemeyer and J. M. J. van Leeuwen, in Phase Transitions and Critical Phenomena, ed. C. Domb and M. S. Green, vol. 6, ch. 7, Academic Press, London, 1976.
17. K. R. Sabbaswamy and G. D. Mahan, Phys. Rev. Lett., 1976, 37, 642.
18. G. D. Mahan and F. H. Claro, Phys. Rev. Sect. B, 1997, 16, 1168.
19. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, Oxford, 1971.
20. B. Nienhuis and M. Nauenberg, Phys. Rev. B, 1975, 11, 4152.
21. M. Schick, J. S. Walker and M. Wortis, Phys. Lett. A, 1976, 58, 479.
22. M. Schick, J. S. Walker and M. Wortis, Phys. Rev. B, 1977, 16, 2205.
23. K. W. Kehr, R. Kutner and K. Binder, Phys. Rev. Sect. B, 1981, 23, 4931.
24. R. Kutner, K. Binder and K. W. Kehr, Phys. Rev. Sect. B, 1982, 26, 2967.
25. A. Sadiq and K. Binder, Surf. Sci., 1983, 128, 350; 1984, 145, 350.
26. K. Kehr and K. Binder, in Applications of the Monte Carlo Method in Statistical Physics, ed. K. Binder, vol. 36 of Topics in Current Physics, Springer-Verlag, Berlin, 1987, p. 181.
27. C. N. Yang, Phys. Rev., 1952, 85, 808.
28. G. S. Rushbrooke, J. Chem. Phys., 1963, 39, 842.
29. B. Widom, J. Chem. Phys., 1965, 43, 3892, 3898.