Advertisement

Liesegang Rings, Spirals and Helices

  • Sabine DietrichEmail author
Chapter
Part of the The Frontiers Collection book series (FRONTCOLL)

Abstract

The periodic precipitation process known as Liesegang ring formation has been investigated during the past 120 years and is one of the most recognized spatial and temporal heterogeneous structures in physical chemistry. If a soluble electrolyte is placed in contact with a second electrolyte in a gelatinous mass and, on interdiffusion, both react to form a poorly soluble salt, rhythmically arranged, separate precipitation develops parallel to the diffusion front. The beauty of this precipitation aside, research into Liesegang rings was mainly stimulated by the obvious parallels to processes in technology, geological structures and patterns in plant and animal life. Structural researchers increasingly consider the Liesegang experiments and their multifaceted manifestations as a basic phenomenon and a model case for a number of structuring processes in inorganic, organic and living nature. A continuous, end-to-end theory that takes the large number of interacting individual factors into account, thus enabling a full description of the complex reaction-diffusion mechanism, is still lacking. This is why attempts to extend the described phenomena of precipitate reactions in gelatinous masses to other structure formation processes are still tentative. This article provides an introduction.

Notes

Acknowledgements

I am thankful for fruitful discussions on Liesegang systems with Prof. Dr.-Ing. K.-H. Jacob. Ph.D. and my then colleagues Dr. H.-J. Krug and H. Brandtstädter. Figures from references are reproduced with the kind permission of the respective owners of the publishing rights. I would like to thank D. McCartney for her translation and revision of this text. I would also like to express my gratitude to Dr. K. Tsuji and Prof. Dr. S.C. Müller for their inspiring initiative to publish this book as well for the fruitful discusstions on spiraling Liesegang systems.

References

  1. 1.
    F.F. Runge, (1855). Der Bildungstrieb der Stoffe: veranschaulicht in selbständig gewachsenen Bildern (Selbstverlag oranienburg)Google Scholar
  2. 2.
    W.M. Ord, On the Influence of Colloids Upon Crystalline Form and Cohesion (E. Stanford, London, 1879)Google Scholar
  3. 3.
    R.E. Liesegang, A-Linien, Liesegangs photographisches Archiv 800, 305–309, 331–336, and 801, 321–326 (1896)Google Scholar
  4. 4.
    W. Ostwald, A-Linien von R.E. Liesegang (review). Z. Phys. Chem. 23, 356 (1897)Google Scholar
  5. 5.
    W. Ostwald, Zur Theorie der Liesegang’schen Ringe, Kolloid Z. Suppl. to 36, 380–390 (1925)Google Scholar
  6. 6.
    N.R. Dhar, A.C. Chatterji, Theorien der Liesegangringbildung. Kolloid Z. 37, 2–9, 89–97 (1925)Google Scholar
  7. 7.
    C. Wagner, Mathematical analysis of the formation of periodic presipitations. J. Colloid Sci. 1, 85–97 (1950)CrossRefGoogle Scholar
  8. 8.
    B. Keller, S.I. Rubinow, Recurrent precipitation and Liesegang rings. J. Chem. Phys. 74, 5000–5007 (1981)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    J.T. Dee, Patterns produced by precipitation at a moving reaction front. Phys. Rev. Lett. 57, 275–278 (1986)ADSCrossRefGoogle Scholar
  10. 10.
    P. Ortoleva, Solute reaction mediated precipitate patterns in cross gradient free systems. Z. Phys. B 49, 149–156 (1982)ADSCrossRefGoogle Scholar
  11. 11.
    S.C. Müller, S. Kai, J. Ross, Curiosities in periodic precipitation patterns. Science 216, 635–637 (1982)ADSCrossRefGoogle Scholar
  12. 12.
    S.C. Müller, J. Ross, Spatial structure formation in precipitation reactions. J. Phys. Chem. A 107, 7997–8008 (2003)CrossRefGoogle Scholar
  13. 13.
    D.S. Chernavskii, A.A. Polezhaev, S.C. Müller, A model of pattern formation by precipitation. Phys. D 54, 160–170 (1991)CrossRefzbMATHGoogle Scholar
  14. 14.
    H.-J. Krug, H. Brandtstädter, Morphological characteristics of Liesegang rings and their simulations. J. Phys. Chem. A 103, 7811–7820 (1999)CrossRefGoogle Scholar
  15. 15.
    E.S. Hedges, Liesegang Rings and Other Periodic Structures (Chapman and Hall, London, 1932)Google Scholar
  16. 16.
    V. Rothmund, Löslichkeit und Löslichkeitsbeeinflussung, in Handbuch der Angewandten Physikalischen Chemie in Einzeldarstellungen, vol. 7, ed. by G. Bredig (Johann Ambrosius Barth, Leipzig, 1907), pp. 5–14Google Scholar
  17. 17.
    R.E. Liesegang, Silberchromatringe und -spiralen. Z. Phys. Chem. 88, 1–12 (1914)CrossRefGoogle Scholar
  18. 18.
    R.E. Liesegang, Chemische Reaktionen in Gallerten (Theodor Steinkopf, Dresden, 1924), p. 90Google Scholar
  19. 19.
    R.E. Liesegang, Spiralenbildung bei chemischen Niederschlägen. Naturwissenschaften 28, 645–646 (1930)ADSCrossRefGoogle Scholar
  20. 20.
    R.E. Liesegang, Spiralenbildung bei Niederschlägen in Gallerten. Kolloid Z. 87, 57–58 (1939)CrossRefGoogle Scholar
  21. 21.
    E. Hatschek, A series of abnormal Liesegang stratifications. Biochem. J. 14, 419–421 (1920)CrossRefGoogle Scholar
  22. 22.
    E. Hatschek, Anomalous stratifications produced by the action of light. R. Soc. Proc. A 99, 496–502 and plate 8 (1921)Google Scholar
  23. 23.
    S. Kai, S.C. Müller, Spatial and temporal macroscopic structures in chemical reaction systems - precipitation patterns and interfacial motion. Sci. Form 1, 9–39 (1985)Google Scholar
  24. 24.
    H.-J. Krug, K.-H. Jacob, S. Dietrich, The formation and fragmentation of periodic bands through precipitation and Ostwald ripening, in Fractals and Dynamic Systems in Geoscience, ed. by H.-J. Kruhl (Springer, Berlin, 1994), pp. 269–282Google Scholar
  25. 25.
    S. Dietrich, K.-H. Jacob, Understanding earth: the self-organization concept and its geological significance; on the example of Liesegang-structures and electric fields, in Complexity and Synergetics, ed. by S.C. Müller, P.J. Plath, G. Radons, A. Fuchs (Springer, Cham, 2018), pp. 101–115CrossRefGoogle Scholar
  26. 26.
    S. Thomas, G. Varhhese, D. Bárdfalvy, I. Lagazi, Z. Rácz, Helicoidal precipitation patterns in silica and agarose gels. Chem. Phys. Lett. 599, 159–162 (2014)ADSCrossRefGoogle Scholar
  27. 27.
    R. Toth, R.M. Walliser, I. Lagzi, F. Bouoire, M. Düggelin, A. Braun, C.E. Housecroft, E.C. Constable, Probing the mystery of Liesegang band formation: revealing the origin of self-organized dual-frequency micro and nanoparticle arrays. Soft Matter 12, 8367–8374 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    S. Thomas, I. Lagzi, F. Molnár Jr., Z. Rácz, Probability of the emergence of helical precipitation patterns in the wake of reaction-diffusion fronts. Phys. Rev. Lett. 110, 078303 (2013)ADSCrossRefGoogle Scholar
  29. 29.
    B. Chopard, P. Lüthi, M. Droz, Reaction-diffusion cellular automata model for the formation of Liesegang patterns. Phys. Rev. Lett. 72, 1384–1387 (1994)ADSCrossRefGoogle Scholar
  30. 30.
    A.A. Polezhaev, S.C. Müller, Complexity of precipitation patterns: comparison of simulation with experiment. Chaos 4, 634 (1994)ADSCrossRefGoogle Scholar
  31. 31.
    J. Mares, J. Stávek, J. Šesták, Quantum aspects of self-organized periodic chemical reactions. J. Chem. Phys. 21, 1499–1503 (2004)ADSCrossRefGoogle Scholar
  32. 32.
    S. Thomas, F. Moinár, Z. Rácz, I. Lagzi, Matalon-Packter law for stretched helicoids formed in precipitation processes. Chem. Phys. Lett. 577, 38–41 (2013)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Earth SciencesTechnical University BerlinBerlinGermany

Personalised recommendations