Liesegang Phenomenon Research Articles

Liesegang patterns: Estimation of diffusion coefficient and a plausible justification for colloid explanation

The Liesegang phenomenon is interpreted as a moving boundary problem. The existing time law, spacing law, and width law are revisited and reformulated on the basis of the new scenario. A better understanding of the basic facts associated with pattern formation is made possible with the new concept. The phenomenon is explained on the basis of colloidal kinetics. Diffusion coefficients of the outer electrolyte in the gel for various experiments in the literature are calculated. The diffusion coefficients so calculated range from 1.792–5.996×10–10 m2 s–1. It is suggested that such values confirm the fast colloidal dynamics during the process of periodic precipitation pattern formation.

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.

Recent Theoretical Developments on the Formation of Liesegang Patterns

When an electrolyte A diffuses into a gel containing another electrolyte B, the eventual formation of a rhythmic pattern of precipitate by the moving chemical reaction front is known as the Liesegang phenomenon. Although the Liesegang phenomenon has been studied for a century, the mechanisms responsible for these structures are still under discussion. However, recently, important theoretical progresses have been made towards a theoretical understanding of this phenomena. A critical analysis of the present state of the art as well as a discussion of some open problems is presented.

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.

Salt crystallization in porous construction materials. II. Mass transport and crystallization processes

In order to study the processes of salt weathering of monumental stones, several samples were partially immersed in sodium, potassium and magnesium sulphate solutions which ascended through their capillary network and, eventually, crystallized. This procedure pretends to simulate the conditions in which foundations and lower walls of building structures are, within the zone of capillary rise of saline groundwater. Mass transport and the rhythmic nature of crystallization fronts inside samples reminds the Liesegang phenomenon, so they have been considered as a form of dissipative structures. The saline deposits developed on the surface of the samples were efflorescences (mirabilite and epsomite), subefflorescences (picromerite, aphthitalite and arcanite) and crusts (aphthitalite and arcanite). The most devastating effects resulted from massive crystallization inside the samples or from surface peeling due to the development of subefflorescences or crusts.

Solid State Reactions in the Ag-Ti-Si System - Periodice Layer Formation

The isothermal cross-section through the ternary phase diagram Ag—Ti—Si at 1123 K was determined by means of multiphase diffusion couples. No ternary phases are pres ent on this Ag—Ti—Si isotherm. A thermodynamic assessment of this system was performed using the data from the binary systems. The formation of a periodic structure consisting of alternating layers of titanium-silicides and silver was observed in sandwich diffusion couples Ag/Ti-foil/Si after annealing between 1023 K and 1123 K. It was attributed to the internal reaction between titanium and silicon within the Ag-layer formed in situ during the solid state interaction, This pro cess, periodic in space and time, resembles the well-known Liesegang phenomenon.

Computer simulation of regular Liesegang structures

A heterogeneous chemical pattern formation, the so-called Liesegang phenomenon, was studied by means of computer simulation. A one dimensional algorithm based on Ostwald’s supersaturation theory was developed and used for determining the effect of different initial conditions on the final structure. Four ‘‘reduced’’ parameters have been introduced that unambiguously determine the spacing coefficient of the final structure. The relationship between the initial concentration of the outer electrolyte and the spacing coefficient that was suggested by Matalon and Packter has been found to be valid only for high outer electrolyte concentrations.

Two dimensional chemical pattern formation in gels. Experiments and computer simulation

Precipitate forming chemical reactions have been studied in chemically cross-linked poly(vinyl-alcohol) gel layers and in thin silica films. One of the reactive components was incorporated into the gel, the other was allowed to diffuse into the film. This reaction-diffusion process resulted in patterns that were different in some respects from that of the regular Liesegang phenomena often occurring in such systems. Instead of stripes, tree-like precipitate structures have developed. Digital image analysis provided evidence that the tree-like structures involve a periodicity of the Liesegang type. Occurrence of this periodicity was found not only parallel but also perpendicular to the direction of the diffusion. Computer simulations were carried out in order to find possible mechanisms for these variants of the Liesegang phenomenon and to establish the influence of various factors on the chemical pattern formation involved in the model.

Parabolic periodic solutions of precipitation-modified ternary diffusion equations

Closed-form generalizations of Zener's binary solutions to the diffusion equations in one and two semi-inifite dimensions are found for the case where unstable dilute precipitation accompanies directed ternary diffusion. It has been argued elsewhere that instabilities caused by fine precipitates, subject to local conservation of the independent diffusion species and capillarity in a semi-infinite ternary medium, are evidenced by the appearance of a negative determinant of the effective diffusion matrix and a negative eigenvalue as in spinodal decomposition. In the unstable directed-diffusion planar case the eigenfunction corresponding to the negative coefficient is a spatially periodic Kummerian function of the parabolic coordinate [Formula: see text]. In the important asymptotic limit λ → ∞ this solution implies the exact Jablczynski-scaling relation for the time-independent position of the periodic precipitate bands, which is a well-known characteristic of the Liesegang phenomenon. This contrasts with the Belousov–Zhabotinskii instability where travelling waves are the norm. The cylindrical case exhibits an analogous character but is much richer in pattern, including rings, spirals of multifold character, and broken rings, all of which are observed. A free-boundary degeneracy as in the Saffman–Taylor problem is identified.

An experimental study of the Liesegang phenomenon and crystal growth in silica gels

About 100 diffusion experiments were carried out in separate test tubes; the growth of the resulting crystals and precipitates was extremely interesting to watch and often very colorful and spectacular.

X-ray photoelectron spectroscopy and Rutherford backscattering spectrometry study of anion incorporation in anodically grown films

Anodic oxide films on titanium and zirconium were grown in the presence of sodium tungstate. The surface and bulk characteristics of these films have been analyzed by X-ray photoelectron spectroscopy (XPS) and Rutherford backscattering spectrometry (RBS) as a function of terminal voltage and temperature. XPS results show a close association between the sodium and tungsten incorporated from the forming solution at the film surface. The RBS data reveal the existence of the tungsten species in a layered structure. These layers are distributed at regularly spaced intervals beneath the surface. The results are discussed in terms of a periodic precipitation reaction, also known as the Liesegang phenomenon.

Transmission-line modelling of the Liesegang phenomenon

This paper presents details of the application of the transmission-line matrix (TLM) method to an analysis of the Liesegang phenomenon. The technique does not suffer from some of the mathematical problems which have been encountered with other formulations. The spacing and time relationships are in good agreement with published experimental data.

The precipitation of sparingly‐soluble alkaline‐earth metal phosphates in gelatine gels by diffusion of anion (i). the precipitation of calcium hydrogen phosphate dihydrate and basic calcium phosphates

AbstractThe precipitation of different calcium phosphates in gelatine gels was studied by diffusion of disodium hydrogen phosphate solutions into ten percent gels containing calcium cation at liquid gel pHs from 6 to 11. At pHs 6.0 to 7.5, calcium hydrogen phosphate dihydrate (CaHPO4 · 2 H2O) was deposited as a continuous precipitate and then as rings of precipitate (the Liesegang phenomenon): their spacing coefficients varied with the reciprocal initial anion concentrations according to the Packter‐Matalon relation.At liquid gel pHs 8.0, 8.5, tretacalcium phosphate (Ca4H(PO4)3) was deposited as a continuous precipitate.At liquid gel pHs from 8.5 to 11, hydroxyapatite (Ca10(PO4)6(OH)2, Ca/P ratios = 1.50 to 1.67) was deposited as a continuous precipitate.The mechanisms of precipitation of the different calcium phosphates (in gelatine gels) is briefly discussed.

Periodic corrosion phenomena in bronze antiquities

AbstractInvestigations into the structure of some ancient bronze artifacts revealed periodic corrosion product formation. Examination by reflected polarized light microscopy suggested that information concerning the banding observable in these objects could be used to support the hypothesis that Liesegang phenomena were responsible for the periodicity of corrosion product formation. Some analytical data for the bronze fragments were obtained by electron probe microanalysis, using both spot analyses and elemental line scan traverse across the polished sections of the fragments under study.

Periodic precipitation of lanthanum molybdate crystals in silica gel

Formation of Liesegang rings on the growth of La2(MoO4)3·XH2O in silica gel by single diffusion technique is discussed. The nature of the periodic precipitation is found to depend on the concentration of inner and outer electrolytes, gel medium and its pH. The ‘time law’, ‘spacing law’ and ‘the law relating diffusion depth and width’ are found obeyed in this system. The one-dimensional Liesegang phenomena is thus investigated quantitatively making use of the simple laws of diffusion.

Revert and direct Liesegang phenomenon of silver iodide: Factors influencing the transition point

The experimental conditions for obtaining the revert type followed by the direct Liesegang rings of silver iodide in agar gel columns have been reported. The existing theories of Ostwald, Mathur, Shinohara, and Ross have been critically reviewed. A new theory based on the DLVO theory of stability of colloids has been proposed to explain the mechanism of revert and direct Liesegang phenomenon and the transition of revert to direct type. This theory takes into account the surface potential, the zeta potential, the zero point of charge and the reversal of charge of the sol particles. The factors influencing the transition point have been reported. The concentration and pH of the gel have a pronounced effect on the transition of revert to direct. The influence of different additives has been discussed. All the observations have been explained on the basis of the proposed theory.

Periodic precipitation of barium molybdate in silica gel

AbstractThe mechanism of formation of the rhythmic pattern of precipitate of barium molybdate in one‐dimensional Liesegang phenomena is investigated quantitatively. They rhythmicity is found to be influenced by the molarity of inner and outer electrolytes and pH of the gel medium. The ‘time‐law’, ‘spacing‐law’ and ‘Δx‐law’ are verified.

Solute reaction mediated precipitate patterns in cross gradient free systems

Recent studies on the spontaneous formation of undulatory patterns of precipitate concentration, such as Liesegang and related phenomena, have shown that these effects can be explained on the basis of a competitive particle growth mechanism as underlies Ostwald ripening. However these effects require an overall gradient or boundary perturbation to induce regular patterning on a scale greater than the interparticle spacing to override the single crystal-so called “greedy giant” instability. Here we show that by allowing for precipitate particle mediated reactions involving the solute species (from which the precipitate is constructed) a fastest growing mode of wave vectorkd, 0<kd<∞, exists and thus pattern formation can occur completely autonomously at a well defined wave length without the need of cross gradients. These processes may be much more widely realized in physical and biological self organization processes than the familiar reaction diffusion (Turing) model due to the rather nonspecific nature of the present phenomenon.

Periodic Formation of FeSi Bands in Diffusion Couples Fe(15 wt.% Si) - Zn

During the reaction in Fe(15 wt.% Si)-Zn diffusion couples at temperatures between 623 and 723 K thin regularly spaced parallel bands containing very small FeSi precipitates are observed throughout the 6 and ~ reaction layers. The periodic nature of this effect is strongly reminiscent of the well-known Liesegang phenomenon. A detailed analysis of our results with respect to the principles underlying the Liesegang mechanism, however, shows that such a mechanism cannot explain the observed phenomenon in our case. A more probable explanation is found in the action of shear and tenSile stresses in the diffusion couple which lead to a periodic release ofthe continuously formed FeSi precipitates from the Fe(15 wt.% Si) substrate. Preliminary results obtained with substrates of varying thicknesses are strongly in favour of the latter explanation.

Anomalous stratification of copper carbonate in agar Gel

AbstractDuring the periodic precipitation of copper carbonate in agar gel it is observed that the spacing law of Jablczynski is not obeyed if the rings have to occupy all the positions of the series. Instead, if it is assumed that there may be discontinuities in the observed pattern which indicate that the rings of corresponding orders might not have been formed, the geometric law is faithfully obeyed. These discontinuities disappear if thiourea is added as an impurity along with the inner electrolyte. For different pH values of gel the pattern splits up into a number of groups, each exhihibits a revert type Liesegang phenomenon in which the last group contains revert followed by direct ring. The Liesegang phenomenon of this system has been explained on the basis of coagulation theory.