Theoretical models of the Liesegang phenomena are studied and simple expressions for the spacing coefficients characterizing the patterns are derived. The emphasis is on displaying the explicite dependences on the concentrations of the inner-and the outer-electrolytes. Competing theories (ionproduct supersaturation, nucleation and droplet growth, induced sol-coagulation) are treated with the aim of finding the distinguishing features of the theories. The predictions are compared with experiments and the results suggest that the induced sol-coagulation theory is the best candidate for describing the experimental observations embodied in the Matalon-Packter law.

Spinodal decomposition in the presence of a moving particle source is proposed as a mechanism for the formation of Liesegang bands. This mechanism yields a sequence of band positions xn that obeys the spacing law xn ∼ Q(1 + p) n . The dependence of the parameters p and Q on the initial concentration of the reagents is determined and we find that the functional form of p is in agreement with the experimentally observed Matalon-Packter law.

The so-called width law for Liesegang patterns, which states that the positions xn and widths wn of bands verify the relation xn ∼ w α n for some α > 0, is investigated both experimentally and theoretically. We provide experimental data exhibiting good evidence for values of α close to 1. The value α = 1 is supported by theoretical arguments based on a generic model of reaction-diffusion.

A kinetic Ising model description of Liesegang phenomena is studied using Monte Carlo simulations. The model takes into account thermal fluctuations, contains noise in the chemical reactions, and its control parameters are experimentally accessible. We find that noisy, irregular precipitation takes place in dimension d=2 while, depending on the values of the control parameters, either irregular patterns or precipitation bands satisfying the regular spacing law emerge in d=3.Comment: 7 pages, 8 ps figures, RevTe

The effect of dissociation of the invading electrolyte on the formation of Liesegang bands is investigated. We find, using organic compounds with known dissociation constants, that the spacing coefficient, 1 + p, that characterizes the position of the n-th band as xn ∼ (1 + p) n , decreases with increasing dissociation constant, K d . Theoretical arguments are developed to explain these experimental findings and to calculate explicitly the K d dependence of 1 + p.

Abstract. We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical simulations reveal this solution, which is exact in the limit of perfect traps, to be remarkably robust with respect to a significant lowering of the trapping probability. We demonstrate that for randomly distributed traps, the long-time asymptotics of our result recovers the known stretched exponential decay. We also study an anisotropic three-dimensional version of our model, where for sufficiently large transverse diffusion the system is described by the mean-field kinetics. We discuss possible applications of some of our findings to the decay of excitons in semiconducting organic polymer materials, and emphasize the crucial influence of the spatial trap distribution on the kinetics.

The A + B → C reaction-diffusion process is studied in a system where the reagents are separated by a semipermeable wall. We use reaction-diffusion equations to describe the process and to derive a scaling description for the long-time behavior of the reaction front. Furthermore, we show that a critical localization-delocalization transition takes place as a control parameter which depends on the initial densities and on the diffusion constants is varied. The transition is between a reaction front of finite width that is localized at the wall and a front which is detached and moves away from the wall. At the critical point, the reaction front remains at the wall but its width diverges with time (as t 1/6 in mean-field approximation).

We discuss, at the mean-field level, the asymptotic shape of the reaction fronts in the general nA+mB → C reaction-diffusion processes with initially separated reactants, thus generalizing to arbitrary reaction-order kinetics the work done by Gálfi and Rácz for the case n = m = 1. Consequences for the formation of Liesegang patterns are discussed.