Liesegang phenomenon

Periodic reactions of this kind have been mentioned before, for example, the Liese-gang type phenomena during internal oxidation. They take place in a solvent crystal by the interplay between transport in combination with supersaturation and nuclea-tion. The transport of two components, A and B, from different surfaces into the crystal eventually leads to the nucleation of a stable compound in the bulk after sufficient supersaturation. The collapse of this supersaturation subsequent to nucleation and the repeated build-up of a new supersaturation at the advancing reaction front is the characteristic feature of the Liesegang phenomenon. Its formal treatment is quite complicated, even under rather simplifying assumptions [C. Wagner (1950)]. Other non-monotonous reactions occur in driven systems, and some were mentioned in Section 10.4.2, where we discussed interface motion during phase transformations. 

Related phenomena are voltage oscillations at Ag/AgI contact observed in Ref.275 periodic bands in precipitation reactions (Liesegang phenomenon)177 or oscillations involving proton conductors.276... 

Kabalnov, A. and Weers, J., Kinetics of mass transfer in micellar systems surfactant adsorption, solubilization kinetics, and ripening, Langmuir, 12, 3442, 1996. Kanniah, N., Gnanam, F.D., and Ramasamy, F, Revert and direct Liesegang phenomenon of silver iodide Factors influencing the transition point, J. Colloid Interface Set, 94, 412, 1983. 

Klueh, R.L. and Mullins, W.W., Periodic precipitation (Liesegang phenomenon) in solid silver II. Modification of Wagner s mathematical analysis, Acto Met, 17,69,1969. Knapp, R. and Aris, R., On the equations for the movement and deformation of a reaction front. Arch. Rat Mech. Anal, 44, 165, 1972. 

The Liesegang phenomenon [521], which is a striking nonequilibrimn effect (not only) in laboratory chemistry, describes the formation of periodic precipitation bands of internal reaction products the effect can involve periodicity in time and space and depends on the interference of diffusion, supersaturation, nucleation and growth. The collapse and reformation of supersatnration is of importance, in the sense of an overshoot of a partial process. 

Periodic precipitation phenomena, commonly called Liesegang rings, have been studied for a long time. According to recent experimental results (Kai et al., 1982 Muller et al., 1982) patterned precipitation is a postnucleation phenomenon which occurs after a continuous distribution of colloid has been established. The phenomenon can be described at least formally by an instability mechanism based on the autocatalytic growth of colloid particles with diffusion (Ross, 1985). 

The model is essentially that of Ostwald which emphasized a cycle of supersaturation, nucleation and depletion of co-precipi-tates to explain Liesegang bands [9] However this theory, especially as formulated mathematically by Prager [10] emphasizes the presence of a gap between bands. This occurs in the model presented here as a special limit of parameter values but is not required. The model presented here as well as teh Ostwald-Prager theory are designed with phenomenon (i) in mind. They clearly cannot explain the other phenomena, however. 

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