Liesegang patterns : Studies on the width law

The so-called "width law" for Liesegang patterns, which states that the positions x_n and widths w_n of bands verify the relation x_n \sim w_n^{\alpha} for some \alpha>0, is investigated both experimentally and theoretically. We provide experimental data exhibiting good evidence for values of \alpha close to 1. The value \alpha=1 is supported by theoretical arguments based on a generic model of reaction-diffusion.Comment: 7 pages, RevTeX, two columns, 5 figure

Formation of Liesegang patterns: Simulations using a kinetic Ising model

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

Derivation of the Matalon-Packter law for Liesegang patterns

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 explicit dependences on the concentrations of the inner- and the outer-electrolytes. Competing theories (ion-product 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.Comment: 9 pages, 7 figures, RevTe

Formation of Liesegang Patterns

It has been recently shown that precipitation bands characteristic of Liesegang patterns emerge from spinodal decomposition of reaction products in the wake of moving reaction fronts. This mechanism explains the geometric sequence of band positions x_n ~ Q(1+p)^n and, furthermore, it yields a spacing coefficient, p, that is in agreement with the experimentally observed Matalon-Packter law. Here I examine the assumptions underlying this theory and discuss the choice of input parameters that leads to experimentally observable patterns. I also show that the so called width law relating the position and the width of the bands w_n ~ x_n follows naturally from this theory.Comment: Talk presented at NATO Advanced Workshop on Statistical Physics Applied to Practical Problems (Budapest, May 1999); to appear in Physica A. 6 pages, 1 jpeg and 3 ps figure

Liesegang patterns: Effect of dissociation of the invading electrolyte

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 x_n ~ (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.Comment: RevTex, 8 pages, 3 eps figure

Band Formation during Gaseous Diffusion in Aerogels

We study experimentally how gaseous HCl and NH_3 diffuse from opposite sides of and react in silica aerogel rods with porosity of 92 % and average pore size of about 50 nm. The reaction leads to solid NH_4Cl, which is deposited in thin sheet-like structures. We present a numerical study of the phenomenon. Due to the difference in boundary conditions between this system and those usually studied, we find the sheet-like structures in the aerogel to differ significantly from older studies. The influence of random nucleation centers and inhomogeneities in the aerogel is studied numerically.Comment: 7 pages RevTex and 8 figures. Figs. 4-8 in Postscript, Figs. 1-3 on request from author

Formation of Liesegang patterns: A spinodal decomposition scenario

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 x_n that obeys the spacing law x_n~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.Comment: RevTex, 4 pages, 4 eps figure

Life and Liesegang: Outcrop-Scale Microbially Induced Diagenetic Structures and Geochemical Self-Organization Phenomena Produced by Oxidation of Reduced Iron

The Kanab Wonderstone is sandstone (Shinarump Member, Chinle Formation) that is cemented and stained with iron oxide. The iron-oxide cementation and staining in these rocks have been considered examples of the Liesegang phenomenon, but we will show that they comprise a microbially induced structure. The spacing of bands of iron-oxide stain follow the Jablczynski spacing law (wherein the spacing between bands of iron-oxide stain increases as one traverses a series of bands) characteristic of Liesegang. Bands of iron-oxide cement exhibit more variable spacing and exhibit a weak but significant correlation between band thickness and distance between bands of cement. The pore-filling cement contains morphotypes that are similar in size and habit to those exhibited by microaerophilic iron-oxidizing bacteria. Other disseminated iron-oxide mineralization occurs as rhombohedra interpreted to be pseudomorphs after siderite. We interpret the cement to be produced by microbially mediated oxidation of siderite (a typical early diagenetic mineral in fluvial sandstones). Iron-oxidizing bacteria colonized the redox interface between siderite-cemented sand and porous sandstone. Microbes oxidized aqueous Fe(II), generating acid that caused siderite dissolution. The iron-oxide cement is the microbial product of a geochemical drive for organization; whereas the iron-oxide stain is true Liesegang. Together, they comprise a distinctive microbially induced structure with high preservation potential. Key Words: Biosignatures—Iron oxides—Diagenesis—Iron-oxidizing bacteria—Shinarump