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Recent Theoretical Developments on the Formation of Liesegang Patterns

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Abstract

When an electrolyte A diffuses into a gel containing another electrolyte B, the eventual formation of a rhythmic pattern of precipitate by the moving chemical reaction front is known as the Liesegang phenomenon. Although the Liesegang phenomenon has been studied for a century, the mechanisms responsible for these structures are still under discussion. However, recently, important theoretical progresses have been made towards a theoretical understanding of this phenomena. A critical analysis of the present state of the art as well as a discussion of some open problems is presented.

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REFERENCES

  1. R. E. Liesegang, Naturwiss. Wochenschr. 11:353 (1896).

    Google Scholar 

  2. R. E. Liesegang, Photog. Archiv. 21:221 (1896).

    Google Scholar 

  3. H. K. Henisch, Periodic Precipitation (Pergamon Press, 1991).

  4. H. W. Morse and G. W. Pierce, Proc. American Academy of Arts and Sciences 38:625–647 (1903).

    Google Scholar 

  5. K. Jablczynski, Bull. Soc. Chim. France 33:1592 (1923).

    Google Scholar 

  6. M. Droz, J. Magnin, and M. Zrínyi, J. Chem. Phys. 110:9618 (1999).

    Google Scholar 

  7. R. Matalon and A. Packter, J. Colloid Sci. 10:46 (1955).

    Google Scholar 

  8. A. Packter, Kolloid Zeitschrift 142:109 (1955).

    Google Scholar 

  9. T. Antal, M. Droz, J. Magnin, Z. Rácz, and M. Zrinyi, J. Chem. Phys. 109:9479, (1998).

    Google Scholar 

  10. W. Ostwald, Lehrbuch der Allgemeinen Chemie (Engelman edt., Leipzig, 1897).

  11. C. Wagner, J. Colloid Sci. 5:85 (1950).

    Google Scholar 

  12. S. Prager, J. Chem. Phys. 25:279 (1956).

    Google Scholar 

  13. Ya. B. Zeldovitch, G. I. Barrenblatt, and R. L. Salganik, Sov. Phys. Dokl. 6:869 (1962).

    Google Scholar 

  14. D. A. Smith, J. Phys. Chem. 81:3102 (1984).

    Google Scholar 

  15. G. Venzl and J. R. Ross, J. Chem. Phys. 77:1302 (1982); S. C. Muller, S. Kal, and J. R. Ross, J. Phys. Chem. 86:4078 (1982); M. E. LeVan and J. R. Ross, J. Phys. Chem. 91:6300 (1987).

    Google Scholar 

  16. G. T. Dee, Phys. Rev. Lett. 57:275 (1986).

    Google Scholar 

  17. B. Chopard, P. Luthi and M. Droz, Phys. Rev. Lett. 72:1384 (1994); J. Stat. Phys. 76 (1994).

    Google Scholar 

  18. S. Shinohara, J. Phys. Soc. Japan 29:1073 (1970).

    Google Scholar 

  19. T. Antal, M. Droz, J. Magnin, and Z. Räcz, Phys. Rev. Lett. 83:2880 (1999).

    Google Scholar 

  20. J. D. Gunton, M. San Miguel, and P. S. Sahni, The dynamics of first order transitions, in Phase Transition and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, 1983).

  21. J. D. Gunton and M. Droz, Introduction to the Theory of Metastable and Unstable States, Lecture Notes in Physics, Vol. 183 (Springer-Verlag, 1983).

  22. L. Gálfi and Z. Rácz, Phys. Rev. A 38:3151 (1988).

    Google Scholar 

  23. S. Cornell and M. Droz, Phys. Rev. Lett. 70:3824 (1993)

    Google Scholar 

  24. R. J. Glauber, J. Math. Phys. 4:294 (1963).

    Google Scholar 

  25. K. Kawasaki, Phys. Rev. 145:224 (1966).

    Google Scholar 

  26. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49:435 (1977).

    Google Scholar 

  27. H. Larralde, M. Araujo, S. Havlin, and H. E. Stanley, Phys. Rev. A 46:855 (1992).

    Google Scholar 

  28. Z. Rácz in the proceedings of the NATO Advanced Workshop on Statistical Physics Applied to Practical Problems (Budapest, 1999), to be published.

  29. J. S. Kirkaldy, Rep. Prog. Phys. 55:723 (1992).

    Google Scholar 

  30. T. Antal, M. Droz, J. Magnin, A. Pekalski, and Z. Rácz (to appear).

  31. M. A. Einarsrud, F. A. Maao, A. Hansen, M. Kiekedelen, and J. Samseth, Phys. Rev. E 57:6767 (1998).

    Google Scholar 

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Droz, M. Recent Theoretical Developments on the Formation of Liesegang Patterns. Journal of Statistical Physics 101, 509–519 (2000). https://doi.org/10.1023/A:1026489416640

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  • DOI: https://doi.org/10.1023/A:1026489416640

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