Outer Electrolyte Research Articles

Taming ring morphology in 2D Co(OH)2 Liesegang patterns

We present here novel expermients on the formation of Liesegang rings in 2D. We consider the system of propagating Co(OH)2 bands studied extensively in 1D, from the viewpoint of a large number of considerations. In this paper, we focus on morphological aspects and, in the first part, we seek to steer the appearance of the pattern to achieve a pre-determined morphology. We aim at attaining three main features: minimizing the re-dissolution of Co(OH)2 at the back of the propagating pattern, clearing the fuzzy precipitate region lagging behind, and increasing the ring spacing. We vary three experimental parameters to achieve that threefold purpose: 1. decreasing the concentration of the diffusing (outer) electrolyte (NH4OH), 2. applying a constant electric field radially across the circular pattern, and, 3. increasing the gel concentration to a moderately high value. The best pattern was obtained under the conditions: 9% gelatin, [NH4OH]0 = 1.33 M, and applied potential V = 4.0 V, for a 0.100 M CoCl2 taken as constant throughout the whole set of experiments performed. The observations are discussed in relation to the effects that cause them, and the known properties of Liesegang patterns. In the second part of the study, we monitor distortions of the ring pattern from circular symmetry, by applying a constant linear electric field across the circular medium. Elliptical distortions are obtained, which become notably important as the applied potential increases through 1.75 V. The variation of the ring curvature with applied potential is quantified and discussed.

Simulation of Liesegang Patterns: Effect of Reversible Complex Formation of Precipitate

Formation of 1D Liesegang patterns was studied numerically by assuming precipitation and reversible complex formation. The Ostwald's supersaturation model reported by Büki, Kárpáti-Smidróczki, and Zrínyi (BKZ model) was developed and extended further. The position of the first and last bands measured from the junction point of the inner and outer electrolytes is linearly proportional to the square root of its formation time for the different initial concentrations of inner electrolyte (βo). The propagation of patterns along the diffusion column is slower at higher βo. The correlation between the distance of the first and last bands measured from the beginning of the diffusion column is strictly linear. The variation of the total number of bands with βo has a maximum. The presented model reproduces the moving precipitate zones and nonlinear oscillation of the total number of bands in time due to the complex formation of the precipitate.

Front Propagation in Patterned Precipitation. 2. Electric Effects in Precipitation−Dissolution Patterning Schemes

In this paper, we continue the simulation of periodic precipitation systems with redissolution using the model of Muller and Polezhaev (MP). In the first paper of this sequence (J. Phys. Chem. A 2001, 105, 8053), we proposed a reaction scheme involving precipitation and redissolution to which the MP model was adapted. Maps of Liesegang bands and diffusion profiles were calculated at different concentrations of the inner and outer electrolytes. In this paper, we extend the study to the investigation of the effect of an applied constant electric field on the front propagation. Two reaction schemes, representative of the Co(OH)2 and Cr(OH)3 precipitation/redissolution systems, are studied. In the former scheme, the band stratum propagates faster, and the spacing between the bands increases with increasing field strength, exactly reproducing the experimental behavior. In the latter, treated under conditions yielding a single propagating band, two opposing trends are observed: at high field, the propagation i...

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.

Propagating fronts in 2D Cr(OH) 3 precipitate systems in gelled media

Diffusion fronts propagate as two co-precipitate ions inter-diffuse in a gel medium. Liesegang bands of precipitate form periodically behind the diffusion front of an outer electrolyte. The precipitation of Cr(OH) 3 from NaOH diffusing into a Cr 3+ gel matrix is known to yield a single band that propagates in a one-dimensional (1D) tube — Cr(OH) 3 dissolves in excess OH − forming Cr(OH) 4 −. We perform similar experiments on the Cr(OH) 3 system in two dimensions (2D), wherein we obtain a perfectly circular Cr(OH) 3 ring that grows larger and thicker as time advances. Using a specially designed Petri dish, ring propagation is monitored both in the absence and the presence of a constant electric field. The field is applied along a radial direction, and the front velocities with the field on are compared with the field-free case. When the field is applied against the direction of front propagation (“negative” field), wave saturation is obtained, characterized by a slight increase in the velocity of propagation with field strength, until it reaches a constant value as the field strength is further increased. In a positive field situation, the wave velocity increases with field strength and exhibits some other interesting features: (1) wave stopping indicated by a freeze in the ring position at a certain characteristic time; (2) annihilation of the ring formation above a critical value of the field strength. Electrical effects in 2D are also studied when electrodes with different potentials are planted at various locations in the electrolyte periphery. Interesting patterning structures including the distortion of the circular symmetry and the birth of multiple rings are reported.

Front Propagation in Patterned Precipitation. 1. Simulation of a Migrating Co(OH)2 Liesegang Pattern

The model of Müller and Polezhaev for periodic precipitation is applied to a salt system that can dissolve in excess diffusing electrolyte due to complex formation. A typical example is the Co(OH)2 Liesegang pattern from Co2+ and NH4OH, which propagates due to band formation ahead and band dissolution at the tail of the stratum (Co(OH)2 dissolves in excess ammonium hydroxide forming Co(NH3)62+). Diffusion profiles are constructed by plotting the computed distance of the last band (dlb) and that of the first band (dfb) versus time. The propagation is investigated under two main conditions: at fixed concentration of the inner electrolyte (X0) while varying that of the outer electrolyte (Y0), and the reverse (i.e., at fixed Y0 while varying X0). While in the first case, the propagation is faster at higher Y0, the opposite trend is obtained when X0 is varied, exactly reproducing the experimental observations in the literature on Co(OH)2. A correlation close to linear is found between the dissolution and precipitation events. The advancing banded patterns are also displayed in a special map representation combining the diffusion profiles with the band contours. A special criterion is developed, delineating the situations where either a single pulse or a stratum of bands propagates.

Justification for the colloid explanation of Liesegang ring formation

The persuasive evidence for the role of colloid in the formation of Liesegang rings is nullified by the low diffusion constants (less than 2 × 10−11 m2 s−1) of sol particles; however, those values were obtained for sols suspended in otherwise homogeneous solutions. The essential randomness of Brownian motion in such situations is absent in Liesegang experiments, where the large excess of outer electrolyte diffusing into the gel creates a bias in molecular bombardment resulting in sol particles moving a given distance in fewer steps, hence in a shorter time. From Einstein's equation (D=x2/2t) values for D of 2–4 × 10−10 m2 s−1 have been calculated for Liesegang experiments in the literature. It is suggested that such values could well pertain to sol particles diffusing in the heterogeneous conditions existing in those experiments.

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.

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.

Pattern forming precipitation in gels due to coupling of chemical reactions with diffusion

Precipitate-forming chemical reactions have been studied in chemically cross-linked poly(vinyl alcohol) gel medium. One of the reactive components was incorporated into the gel, the other was allowed to diffuse into it. Depending on the experimental conditions the reaction-diffusion process often results in patterns of different type. Experiments performed in tubes and in thin layers were carried out in order to investigate the effects of various factors (cross-linking density, swelling degree as well as the concentrations of the outer and inner electrolytes) on the morphologies of the precipitate patterns. It was found that precipitation occurs not only in the Liesegang bands, but also between bands. Beside Liesegang-type structures, tree-like patterns have been observed, showing a characteristic periodicity in the density profile obtained by digitalized image analyses.

Electrochemical Characteristic of Collodion Membrane Containing Perfluorodecanoic Acid as Ion Exchange Site

Collodion based membranes containing perfluorodecanoic acid (PFDA) were made by cast method. In the membrane - aqueous electrolyte system, the membrane potential, streaming potential, and membrane conductance were measured and the ion exchange characteristic of the collodion membrane was examined. The cation transport numbers evaluated from the membrane potential indicated to be close to unity, and it suggested that the membranes behave as cation exchange membranes. The membrane conductances was analyzed by Donnan's membrane equilibrium and the effective concentration of ion exchange sites, X was estimated. As a result, the membrane conductance turned out to be strongly controlled by not only outer electrolyte concentration but also by the effective concentration of ion exchange site. The electroosmotic coefficient obtained from the streaming potential indicated the characteristic dependence on the effective concentration of ion exchange site, X and the correlation with water transport was discussed.

Chemical pattern formation in gels

AbstractPrecipitate forming chemical reactions have been studied in chemically crosslinked poly(vinyl alcohol) gel medium. One of the reactive components was incorporated into the gel, the other was allowed to diffuse into the swollen network. This reaction‐diffusion process often results in pattern formation which can occur intermittently in terms of time and space or both. Experiments were carried out in order to investigate the effect of various factors (crosslinking density, swelling degree as well as the concentrations of the outer and inner electrolyte). The following precipitates were intensively studied: Mg(OH)2, Cr(OH)3, PbCl2. Three basically different morphologies (Liesegang band formation, moving bands and tree‐like structure) have been observed and investigated. One‐ and twodimensional computer simulations were carried out in order to establish the influence of various factors on the precipitation.

Transport number of an ion across an amphoteric ion-exchange membrane in CaCl 2NaCl system

In an amphoteric membrane-mixed electrolyte system, the ionic concentration within the membrane and the membrane conductance were measured. The additivity concept proposed in our previous paper [J. Membrane Sci, 48 (1990) 25] was applied to the present mixed electrolyte system and each ion transport number in the mixed system was estimated. The transport number of Ca 2+, t Ca, was larger than t Na in the whole range concentration and decreased with increasing concentration of the outer electrolyte solution. Additionally, to ascertain whether the predicted values are reasonable, electrodialysis in the mixed electrolyte system was carried out under the same experimental conditions. The transport numbers estimated in the mixed electrolyte system were approximately in good agreement with the values obtained from the electrodialysis experiments. Furthermore, the transport numbers for two different ionic states in the membrane were evaluated and the concentration dependence of the total transport number, t M, was discussed on the basis of the results.

Growth of Praseodymium Barium Molybdate Single Crystals in Silica Gels

Growth of single crystals of Pr 2 Ba 21 Mo 28 O 108 . Kinetic studies on the growth of octahedral bipyramidal crystals by single diffusion techniques have been carried out under different parameters viz. concentration of outer electrolyte, pH of gel medium. The crystals are characterized by x-ray diffraction

Relation between transport number and concentration of Donnan salt in membranes

In this study the relation between the transport number of counterion and the concentration of Donnan salt was investigated to elucidate the decrease of the transport number in higher concentrations of electrolyte solution equilibrated with the membrane. In the experiment three different types of membranes were examined, and the membrane potential and membrane conductance were measured. In addition, the ionic concentration within the membrane was determined to estimate the transport number due to Donnan salt, t D. The t D was given as a function of Donnan salt concentration, and the mean mobilities of ions which exist as Donnan salts within the membrane were estimated. The values of Ū D also depended upon the valences of counterions and types of membranes. As a result, it was pointed out that the transport numbers of Donnan salts in cases of higher concentration ranges of outer electrolyte solutions were apparently close to those in the aqueous solution, and the decrease of transport numbers evaluated from membrane potential were attributed to the low values of t D.

Effect of Cationic Charge in Electrolyte-Amphoteric Ion-Exchange Membrane System

Abstract In order to clarify the membrane phenomena in an amphoteric membrane, four different experiments were carried out in a simple electrolyte-amphoteric membrane system. The ion transport numbers obtained from the membrane potential and electrodialysis were approximately in agreement with each other. It was indicated that the transport numbers strongly depended on the ionic valence in electrolyte solution. The membrane permeability coefficient representing the dynamic behavior of ion within membrane was evaluated in terms of membrane potential, transport number, and membrane conductance. In addition, the ionic concentrations within membrane equilibrated with outer electrolyte solution were measured to obtain the mobilities within membrane. The membrane phenomena were discussed on basis of the present experimental results.

Periodic crystallization of barium oxalate in silica hydrogel

The experimental conditions for obtaining periodic crystallization of barium oxalate in silica hydrogel are investigated. The Liesegang rings formed by the reaction of oxalic acid and barium chloride are studied. The dependence of velocity constant and the spacing coefficient on pH, concentrations of inner and outer electrolytes and temperature have also been studied and a possible mechanism for the behaviour is suggested. The deviations from Isemura’s general observations are interpreted by considering the microcrystals constituting the rings and the irreversibility of inner and outer electrolytes.

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.

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.

Estimation of diffusion coefficient of Ba++ ions in silica gel from periodic precipitation of BaMoO4

Formation of Liesegang rings on the growth of BaMoO4 crystals in silica gel by single diffusion is discussed. The rhythmic precipitation is found to be influenced profoundly by (a) the molarity of inner and outerelectrolytes (b) the age of gel and (c) the pH of the gel medium. The ‘time law’, ‘spacing law’ and the law relating diffusion depth and width are verified. A method to estimate the diffusion coefficient of the outer electrolyte in the gel medium is developed and calculated for Ba++ions.