Morphological Characteristics of Liesegang Rings and Their Simulations

Journal of Physical Chemistry A

Volumn 103, Issue 39, 1999, Pages 7811-7820

  Krug, Hans Jürgen ^a   Brandtstädter, Hermann ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000495208     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp991092l     Document Type: Article

References (70)

1. Ord, W. M. On the Influence of Colloids upon Crystalline Form and Cohesion; E. Stanford: London, 1879.
2. Liesegang, R. Ed. Chemische Fernwirkung. Lieseg. photograph. Arch. 1896, 37 (800), 305-309, continued in (801), 331-336. A-Linien Lieseg. photograph. Arch. 1896, 37 (801), 321-326. Über einige Eigen-schaften von Gallerten Naturwiss. Wochenschr. 1896, 11, 353. The genesis of his early works on ring formation is described in Liesegang's autobiography "Und doch!" in: Krug, H.-J.; Pohlmann, L., Eds. Evolution und Irreversibilität; Duncker & Humblot: Berlin, 1997; pp 215-296.
3. Liesegang, R. Ed. Chemische Fernwirkung. Lieseg. photograph. Arch. 1896, 37 (800), 305-309, continued in (801), 331-336. A-Linien Lieseg. photograph. Arch. 1896, 37 (801), 321-326. Über einige Eigen-schaften von Gallerten Naturwiss. Wochenschr. 1896, 11, 353. The genesis of his early works on ring formation is described in Liesegang's autobiography "Und doch!" in: Krug, H.-J.; Pohlmann, L., Eds. Evolution und Irreversibilität; Duncker & Humblot: Berlin, 1997; pp 215-296.
4. Liesegang, R. Ed. Chemische Fernwirkung. Lieseg. photograph. Arch. 1896, 37 (800), 305-309, continued in (801), 331-336. A-Linien Lieseg. photograph. Arch. 1896, 37 (801), 321-326. Über einige Eigen-schaften von Gallerten Naturwiss. Wochenschr. 1896, 11, 353. The genesis of his early works on ring formation is described in Liesegang's autobiography "Und doch!" in: Krug, H.-J.; Pohlmann, L., Eds. Evolution und Irreversibilität; Duncker & Humblot: Berlin, 1997; pp 215-296.
5. Liesegang, R. Ed. Chemische Fernwirkung. Lieseg. photograph. Arch. 1896, 37 (800), 305-309, continued in (801), 331-336. A-Linien Lieseg. photograph. Arch. 1896, 37 (801), 321-326. Über einige Eigen-schaften von Gallerten Naturwiss. Wochenschr. 1896, 11, 353. The genesis of his early works on ring formation is described in Liesegang's autobiography "Und doch!" in: Krug, H.-J.; Pohlmann, L., Eds. Evolution und Irreversibilität; Duncker & Humblot: Berlin, 1997; pp 215-296.
6. Liesegang, R. Ed. Geologische Diffusionen; Th. Steinkopf: Dresden and Leipzig, 1913.
7. Liesegang, R. Ed. Die Achate; Th. Steinkopf: Dresden and Leipzig, 1915.
8. Ortoleva, P. Geochemical Self-Organization; Oxford University Press: Oxford, New York, 1994.
9. Leduc, S. Das Leben in seinem physikalisch-chemischen Zusammenhang; L. Hofstetter: Halle, 1912.
10. Küster, E. Über Zonenbildung in kolloidalen Medien; G. Fischer: Jena, 1913, 1931.
11. Hedges, E. S.; Myers, J. E. The Problem of Physicochemical Periodicity; Longmans Green: London, 1926.
12. Hedges, E. S. Liesegang Rings and Other Periodic Structures; Chapman and Hall: London, 1932.
13. Henisch, H. K. Crystals in Gels and Liesegang Rings; Cambridge University Press: Cambridge, 1988.
14. Henisch, H. K. Periodic Precipitation; Pergamon Press: Oxford, 1991.
15. Stern, K, H. Bibliography of Liesegang Rings, 2nd ed.; U.S. Government Printing Office: Washington D.C., 1967.
16. Kuhnert, L.; Niedersen, U. Selbstorganisation chemischer Strukturen. = Ostwalds Klassiker der exakten Wissenschaften, Geest & Portig: Leipzig, 1987; Vol. 272.
17. Spotz, E. L.; Hirschfelder, J. O. Liesegang ring formation arising from diffusion of ammonia and hydrogen chlorine gases through air. J. Chem. Phys. 1951, 19, 1215.
18. Senf, L. Rhythmic precipitation (Liesegang rings) in gases. Z. Phys. Chem. (Leipzig) 1989, 270, 1020-1022.
19. Flicker, M.; Ross, J. Mechanism of chemical instability for periodic precipitation. J. Chem. Phys. 1974, 60, 3458-3456.
20. McBirney, A. R.; Noyes, R. M. Crystallization and layering of the Skaergaard intrusion. J. Petrol. 1973, 20, 487-554.
21. Ostwald, W.; A-Linien von R. E. Liesegang (review) Z. Phys. Chem. (Leipzig) 1897, 23, 356; Lehrbuch der allgemeinen Chemie, 2. Aufl., II, 2.: Verwandtschaftslehre; Engelmann: Leipzig, 1899; p 779.
22. Ostwald, W.; A-Linien von R. E. Liesegang (review) Z. Phys. Chem. (Leipzig) 1897, 23, 356; Lehrbuch der allgemeinen Chemie, 2. Aufl., II, 2.: Verwandtschaftslehre; Engelmann: Leipzig, 1899; p 779.
23. Ostwald, W.; A-Linien von R. E. Liesegang (review) Z. Phys. Chem. (Leipzig) 1897, 23, 356; Lehrbuch der allgemeinen Chemie, 2. Aufl., II, 2.: Verwandtschaftslehre; Engelmann: Leipzig, 1899; p 779.
24. Prager, S. Periodic precipitation J. Chem. Phys. 1956, 25, 279-283.
25. Dee, J. T. Patterns produced by precipitation at a moving reaction front. Phys. Rev. Lett. 1986, 57, 275-278; The patterns produced at a moving reaction front. Physica D 1986, 23, 340-344.
26. Dee, J. T. Patterns produced by precipitation at a moving reaction front. Phys. Rev. Lett. 1986, 57, 275-278; The patterns produced at a moving reaction front. Physica D 1986, 23, 340-344.
27. Le Van, M. E.; Ross, J. Measurements and a hypothesis on periodic precipitation processes. J. Phys. Chem. 1987, 91, 6300-6308.
28. Dhar, N. R.; Chatterji, A. C. Theorien der Liesegangringbildung, Kolloid.-Z. 1925, 37, 2-9, 89-97.
29. Büki, A.; Kárpáti-Smidróczki, E.; Zrínyi, M. Experimental and theoretial investigation of static and dynamic chemical pattern formations in gels. Prog. Colloid. Polym. Sci. 1996, 102, 110-117.
30. Ostwald, Wo. Zur Theorie der Liesegang'sehen Ringe. Kolloid-Z. 1925, (Suppl. to Vol. 36, R. Zsigmondy Festschrift), 380-390.
31. Chopard, B.; Luthi, P.; Droz, M. Reaction-diffusion cellular automaton model for the formation of Liesegang patterns. Phys. Rev. Lett. 1994, 72, 1384-1387.
32. Feinn, D.; Ortoleva, P.; Scalf, W.; Schmidt, S.; Wolff, M. Spontaneous pattern formation in precipitating systems. J. Chem. Phys. 1978, 69, 27-39.
33. Müller, S. C.; Venzl, G. Pattern formation in precipitation processes. In Modelling of Patterns in Space and Time, Lecture Notes Biomath.; Jäger, W., Murray, J. D., Eds.; Springer: Berlin, Heidelberg, New York, Tokyo, 1984; Vol. 55, pp 254-278.
34. Kai, Sh. Gradient-free structures in Liesegang phenomena. In Spatio-Temporal Patterns in Nonequilibrium Complex Systems; Cladis, P. E., Palffy-Muhoray, P., Eds.; Nato Adv. Res. Workshop 1993; Addison-Wesley: Reading, MA, 1995; pp 445-468.
35. Ortoleva, P. Solute reaction mediated precipitate patterns in cross gradient free systems. Z. Phys. B: Condens. Matter, 1982, 49, 149-156.
36. Feeney, R.; Schmidt, S. L.; Strickholm, P.; Chadam, J.; Ortoleva, P. Periodic precipitation and coarsening waves: Applications of the competitive particle growth model. J. Chem. Phys. 1983, 78, 1293-1311.
37. Sultan, R.; Ortoleva, P. Periodic and aperiodic macroscopic patterning in two precipitate post-nucleation systems. Physica D 1993, 63, 202-212.
38. Lifshitz, I. M.; Slyozov, V. V. The kinetics of precipitation from supersaturated solutions. J. Phys. Chem. Solids 1961, 19, 35-50.
39. Ortoleva, P. From nonlinear waves to spiral and speckle patterns. Physica D 1984, 12, 305-320.
40. Krug, H.-J.; Jacob, K. H. Genese und Fragmentierung rhythmischer Bänderungen durch Selbstorganisation. Z. Dtsch. Geol. Ges. 1993, 144, 451-460.
41. Krug, H.-J.; Jacob, K. H.; Dietrich, S. The formation and fragmentation of periodic bands through precipitation and Ostwald ripening. In Kruhl, J. H., Ed.; Fractals and Dynamic Systems in Geoscience; Springer: Berlin, Heidelberg, New York, 1994; pp 269-282.
42. Polezhaev, A. A.; Müller, S. C. Complexity of precipitation patterns: Comparison of simulation with experiment. Chaos 1994, 4, 631-636.
43. Krug, H.-J.; Brandtstädter, H.; Jacob, K. H. Morphological instabilities in pattern formation by precipitation and crystallization processes. Geol. Rundsch. 1996, 85, 19-28.
44. Liesegang, R. Ed. Zur Übersättigungstheorie einiger scheinbar rhythmischer Reaktionen. Z. Phys. Chem. (Leipzig) 1911, 75, 371-373.
45. Liesegang, R. Ed. Über die Reifung von Silberhalogenidemulsionen. Z. Phys. Chem. (Leipzig) 1911, 75, 374-377.
46. Küster, E. Über die morphologischen Charaktere der Liesegang'schen Ringe. Kolloid-Z. 1916, 18, 107-116.
47. Liesegang, R. Ed. Silberchromatringe und -Spiralen. Z. Phys. Chem. (Leipzig) 1914, 88, 1-12.
48. Liesegang, R. Ed. Pseudoklase. Neues Jahrb. für Min. Geol. Pal. 1914, 39 (Suppl. Vol., Max Bauer Festschrift), 268-276.
49. Kuo, Ch. Sh.; López Cabarcos, E.; Bansil, R. Two-dimensional pattern formation in reaction-diffusion systems. Influence of the geometry. Physica A 1997, 239, 120-128.
50. Büki, A.; Kárpáti-Smidróczki, E.; Zrínyi, M. Two-dimansional chemical pattern formation in gels. Experiments and computer simulation. Physica A 1995, 220, 357-375.
51. Kárpáti-Smidróczki, E.; Büki, A.; Zrínyi, M. Pattern-forming precipitation in gels due to coupling of chemical reactions with diffusion. Colloid. Polym. Sci. 1995, 273, 857-565.
52. Rothmund, V. Löslichkeit und Löslichkeitsbeeinflussung. = Handbuch der Angewandten Physikalischen Chemie in Einzeldarstellungen. (Hrsg. G. Bredig) Vol. 7, Joh. Ambr. Barth: Leipzig 1907; pp 5-14.
53. Liesegang, R. Ed. Chemische Reaktionen in Gallerten; Th. Steinkopff: Leipzig, 1924; p 67.
54. Liesegang, R. Ed. Spiralenbildung bei Niederschlägen in Gallerten. Kolloid-Z. 1939, 87, 57-58.
55. Tillmans, J.; Heublein, O. Neues von den Liesegangschen Ringen. Umschau (Frankfurt a. M.) 1914, 19, 930-933.
56. Hatschek, E. Der Einfluss des Lichtes auf Bleichromat-Schichtungen. Kolloid-Z. 1925, 37, 297-298.
57. Müller, S. C.; Kai, S.; Ross, J. Curiosities in periodic precipitation patterns. Science 1982, 216, 635-637.
58. Chernavskii, D. S.; Polezhaev, A. A.; Müller, S. C. A model of pattern formation by precipitation. Physica D 1991, 54, 160-170.
59. Hatschek, E. Silberchromatschichtungen in Kieselsäuregel. Kolloid-Z. 1926, 38, 151-154.
60. Kai, S.; Müller, S. C.; Ross, J. Measurements of temporal and spatial sequences of events in periodic precipitation processes. J. Chem. Phys. 1982, 76, 1392-1406.
61. Lexa, D.; Holba, V. Periodic precipitation of silver chromate/ dichromate in gelatin. Colloid Polym. Sci. 1993, 271, 884-890.
62. Venzl, G.; Ross, J. Nucleation and colloidal growth in concentration gradients (Liesegang rings). J. Chem. Phys. 1982, 77, 1302-1307.
63. Büki, A.; Kárpáti-Smidróczki, E.; Zrínyi, M. Computer simulation of regular Liesegang structures. J. Chem. Phys. 1995, 103, 10387-10392.
64. López Cabarcos, E.; Kuo, Ch. Sh.; Scala, A.; Bansil, R. Crossover between spatially confined precipitation and periodic pattern formation in reaction diffusion systems. Phys. Rev. Lett. 1996, 77, 2834-2837.
65. Kuo, Ch. Sh.; López Cabarcos, E.; Scala, A.; Bansil, R. Kinetics of spatially confined precipitation and periodic pattern formation. Physica A 1997, 239, 390-403.
66. Gmelin. Handbuch der anorganischen Chemie. Silber. Teil B 4; Springer: Berlin, Heidelberg, New York, 1974; pp 294, 297, 301.
67. -2 in section 4.
68. Jablczynski, K. Bull. Soc. Chim. 1923, 33, 1592.
69. This is a valid assumption for heterogeneous precipitation in grained media where n is identical with the particle number density of the grains. See: Sultan, R.; Ortoleva, P.; De Pasquale, F.; Tartaglia, P. Bifurcation of the Ostwald-Liesegang supersaturation-nucleation-depletion cycle. Earth-Sci. Rev. 1990, 29, 163-173.
70. Zsigmondy, R. Kolloidchemie, 3. Aufl.; Otto Spamer: Leipzig, 1920; p 95.