Formation Of Liesegang Patterns Research Articles

Study on Carbonation of Porcine Blood Hydrogel in the Composite Mortar of Ancient Chinese Architectural Painting.

In the ancient Chinese recipe for composite mortar used in the construction of ground layers for architectural painting, the mixture of porcine blood and lime water is one of the constituent materials. Herein, according to the traditional recipe, the interaction between porcine blood and lime water was systematically and deeply investigated. The experimental investigation demonstrated that porcine blood mixed with lime water at the ratio found in the recipe can form a hydrogel with a hydrophobic surface. During air-drying, the lime water in porcine blood hydrogel can react with CO2 to form calcium carbonate. The crystal morphology of the formed calcium carbonate depends on the surrounding micro-environment of calcium ions in the porcine blood hydrogel. The formed morphology of calcium carbonate includes small calcite crystallites, small graininess calcite crystals with round features, calcite aggregates with layered ladder-like structures, and amorphous calcium carbonate (ACC). Interestingly, the calcium carbonate formed in the inner part of the porcine blood hydrogel exhibits lamellar distribution due to a Liesegang pattern formation. Based on the findings that the porcine blood hydrogel has surface hydrophobicity and brittleness, it can be predicted that in the preparation process of composite mortar for ancient building color painting base course, porcine blood used in the form of a hydrogel is not only easier to be dispersed in hydrophobic tung oil than in liquid porcine blood but also the affinity between porcine blood gel and tung oil is enhanced. As constituent material dispersed in the composite mortar, the layered distribution of calcium carbonate in the porcine blood hydrogel may presumably be beneficial to reduce the internal stress of the composite mortar material.

How the Addition of Chitosan Affects the Transport and Rheological Properties of Agarose Hydrogels

Agarose hydrogels enriched by chitosan were studied from a point of view diffusion and the immobilization of metal ions. Copper was used as a model metal with a high affinity to chitosan. The influence of interactions between copper and chitosan on transport properties was investigated. Effective diffusion coefficients were determined and compared with values obtained from pure agarose hydrogel. Their values increased with the amount of chitosan added to agarose hydrogel and the lowest addition caused the decrease in diffusivity in comparison with hydrogel without chitosan. Liesegang patterns were observed in the hydrogels with higher contents of chitosan. The patterns were more distinct if the chitosan content increased. The formation of Liesegang patterns caused a local decrease in the concentration of copper ions and concentration profiles were affected by this phenomenon. Thus, the values of effective diffusion coefficient covered the influences of pore structure of hydrogels and the interactions between chitosan and metal ions, including precipitation on observed Liesegang rings. From the point of view of rheology, the addition of chitosan resulted in changes in storage and loss moduli, which can show on a "more liquid" character of enriched hydrogels. It can contribute to the increase in the effective diffusion coefficients for hydrogels with higher content of chitosan.

Non-monotonous enzyme-assisted self-assembly profiles resulting from reaction-diffusion processes in host gels

Reaction–diffusion (RD) processes are responsible for surface and in-depth micropatterning in inanimate and living matter. Here we show that enzyme-assisted self-assembly (EASA) of peptides is a valuable tool to functionnalize host gels. By using a phosphatase distributed in a host hydrogel, the diffusion of phosphorylated peptides from a liquid/host gel interface leads to the spontaneous formation of a pattern of dephosphorylated peptide self-assembly presenting at least two self-assembly maxima. Variation of enzyme and peptide concentrations change the pattern characteristics. When a peptide drop is deposited on a phosphatase functionalized gel, a self-assembly pattern is also formed both along the gel-solution interface and perpendicular to the interface. This self-assembly pattern induces a local change of the gel mechanical properties measured by nanoindentation. Its appearance relies on the formation of self-assembled structures by nucleation and growth processes which are static in the hydrogel. This process presents great similarities with the Liesegang pattern formation and must be taken into account for the functionalization of hydrogels by EASA. A mechanism based on RD is proposed leading to an effective mathematical model accounting for the pattern formation. This work highlights EASA as a tool to design organic Liesegang-like microstructured materials with potential applications in biomaterials and artificial living systems design.

Model of layered pattern formation in binary igneous systems

Centimeter to meter-scale repetitive patterns in composition and texture are sometimes observed in igneous systems. Examples are found in layered intrusions and multi-shelled orbicular granites. These patterns may result from the action of nonlinear self-organization processes in which the interplay between crystallization dynamics, diffusion and thermal conduction causes mineral and crystal size segregations. These mechanisms are analogous to the ones underlying the formation of Liesegang bands and lead to comparable features, such as a geometric progression of the band positions and the presence of doublets. We present here a comprehensive one-dimensional numerical model of Liesegang pattern formation process from binary eutectic melts in igneous systems. The model incorporates nucleation, growth and Ostwald ripening and is applied to both the layered intrusion and the orbicular granite configuration with appropriate simple geometries and cooling boundary conditions. The emergence of cyclic layering is described in terms of two key parameters that control the pattern formation: the scaled latent heat of crystallization (Stefan number) and the ratio of the thermal diffusivity to a characteristic diffusion coefficient (Lewis number). It is found that, in intrusions, a banding pattern compatible with the Liesegang spacing law is generated when the Stefan number is large and the Lewis number small, in agreement with previous studies. For orbicular granites with low Lewis number, we show that the band thickness and the crystal size increase with distance from the rim to the core, in agreement with the observations of Zhang and Lee (2020). This suggests that the pattern progresses inwards from the outer boundary, rather than from a colder core, thus supporting the conceptual model reported in Zhang and Lee (2020). Moreover, the results for both geometries indicate that ripening plays an important role in the formation of realistic patterns.

Mechanical Control of Periodic Precipitation in Stretchable Gels to Retrieve Information on Elastic Deformation and for the Complex Patterning of Matter.

Material design using nonequilibrium systems provides straightforward access to complexity levels that are possible through dynamic processes. Pattern formation through nonequilibrium processes and reaction-diffusion can be used to achieve this goal. Liesegang patterns (LPs) are a kind of periodic precipitation patterns formed through reaction-diffusion. So far, it has been shown that the periodic band structure of LPs and the geometry of the pattern can be controlled by experimental conditions and external fields (e.g., electrical or magnetic). However, there are no examples of these systems being used to retrieve information about the changes in the environment as they form, and there are no studies making use of these patterns for complex material preparation. This work shows the formation of LPs by a diffusion-precipitation reaction in a stretchable hydrogel and the control of the obtained patterns by the unprecedented and uncommon method of mechanical input. Additionally, how to use this protocol and how deviations from "LP behavior" of the patterns can be used to "write and store" information about the time, duration, extent, and direction of gel deformation are presented. Finally, an example of using complex patterning to deposit polypyrrole by using precipitation patterns is shown as a template.

Interplay between Spinodal Decomposition and Gelation and Their Role in Two- and Three-Dimensional Pattern Formation at the Gelatin Gel Surface

Understanding the mechanisms underlying the spontaneous formation of Liesegang patterns based on the prenucleation and postnucleation models is of critical importance for understanding pattern formation in nature. In contrast to the rapid experimental and theoretical advances in understanding within the framework of the prenucleation model, discussion of the postnucleation model is mostly limited to numerical analysis. To construct a standard model for a chemical experiment discussed in terms of the postnucleation model, we have investigated the pattern formation mechanism in a mixed system containing gelatin, starch, and sugar. Fluorescence and differential interference contrast microscopy revealed a process of two-dimensional spinodal decomposition into gelatin-rich and gelatin-poor phases. Since the gelation temperature of the gelatin-rich phase was higher, spatially periodic gelation proceeded selectively in the gelatin-rich phase. As both two-dimensional spinodal decomposition and three-dimensional g...

Hybrid Materials with Controlled Precipitation Pattern of Nanoparticles

Hybrid materials with ordered patterns are important to control their functionality. Such ordered structure can be spontaneously formed in nature by self-organization under far from equilibrium, where energies or substances within the system is always dissipated (dS / dt ≠ 0). Although formation mechanism of self-organized patterns in nature are complex and hard to control, development of various materials that mimic self-organization in nature (e.g. bio-mimetics and bio-inspired) have been developed remarkably in recent years. Formation of various patterned structures with useful function by self-organization lead to further development of material chemistry based on mimic of these structures. In the present study, we focused on Liesegang pattern found by R. E. Liesegang in 1896. Liesegang pattern has gained a lot of interests due to several features; simple procedure of the pattern formation, diversity of the pattern morphology and no selection of materials. In fact, Liesegang pattern can be formed by contact between a gel containing an inner electrolyte and an aqueous solution containing an outer electrolyte. Thus, the formed patters consisted of precipitates which is a reaction product between inner and outer electrolytes, has spatial periodicity with geometric series formulated by spacing law (xn +1/xn = 1+p), where xn +1, xn , and p are the position of two consecutive (n+1st and n th) bands measured from the junction point of the electrolytes and spacing coefficient, respectively. Therefore, Liesegang pattern can be applied for patterning technologies because periodic patterns are easily formed. However, control of the periodicity in Liesegang pattern has not been achieved for a long time. Therefore, it is necessary to control periodicity to apply patterning technologies in micro-nanotechnologies. For this purpose, we examined the influence of experimental parameters on the geometry of pattern formation. We focused on the nucleation rate as one of the parameter, whose effect on the pattern formation has not been clarified yet. In this study, we applied the strategy of surface chemistry to control the nucleation rate. Liesegang pattern formation was discussed based on the nucleation and growth model, where the particle is produced through the production of nuclei (solid state) by nucleation of a certain precursors (molecular state) and the growth of nuclei. To occur the nucleation process, it is necessary to bring the energy state in this system unstable to exceed the energy barrier (ΔG). To achieve this process, the concentration of the precursor should exceed the nucleation threshold (C*). Therefore, ΔG governs the nucleation rate and can be considered C* in the model. can be reduced by the coordination of an appropriate ligand for the decrease of surface free energy. Cysteine was used as the ligand for Agn nuclei and/or Ag nanoparticles in the present system to reduce their surface free energy and thus ΔG. In the system without cysteine, the periodic concentric ring pattern (Liesegang pattern) with the interring distance of about 100−200 μm was formed (Figure 1a), where the interring distance increased further away from the edge of agarose stamp. On the other hand, in the system with cysteine, the periodic concentric ring pattern (Liesegang pattern) with the interring spacing of below 100 μm was formed (Figure 1b), meaning that the ring periodicity was almost half that of the pattern formed without cysteine. Thus, the addition of cysteine that is corresponding to the decrease of induced the Liesegang pattern with the finer periodic structures. To prove this relationship between the decrease ofΔG and the finer structures, we used reaction-diffusion simulation with lowered C*. As a result, Liesegang pattern became finer with the lowering C*. Furthermore, to demonstrate the effect of the lowering and C* on a miniaturization of Liesegang pattern in more detail, we compared the spacing coefficient as a measure of the periodicity of patterns. As a result, both lowering and C* gave smaller spacing coefficient (i.e., finer periodic patterns) (Figure 2). Therefore, it was suggested that the lowering induced the lowering C*. Then, the smaller spacing coefficient at lowered C* was discussed in terms of a slower rate of Ostwald ripening. Similar control of C* through surface chemistry can be applied to various precipitation systems to control the periodicity in these systems. In his study, we propose that the approach based on the surface chemistry enable us to control the periodicity of Liesegang patterns by the controlling C*. Figure 1

On the dynamics of Liesegang-type pattern formation in a gaseous system.

Liesegang pattern formations are widely spread in nature. In spite of a comparably simple experimental setup under laboratory conditions, a variety of spatio-temporal structures may arise. Presumably because of easier control of the experimental conditions, Liesegang pattern formation was mainly studied in gel systems during more than a century. Here we consider pattern formation in a gas phase, where beautiful but highly complex reaction-diffusion-convection dynamics are uncovered by means of a specific laser technique. A quantitative analysis reveals that two different, apparently independent processes, both highly correlated and synchronized across the extension of the reaction cloud, act on different time scales. Each of them imprints a different structure of salt precipitation at the tube walls.

Controlling and Engineering Precipitation Patterns

Controlling and engineering chemical structures are the most important scientific challenges in material science. Precipitation patterns from ions or nanoparticles are promising candidates for designing bulk structure for catalysis, energy production, storage, and electronics. There are only a few procedures and techniques to control precipitation (Liesegang) patterns in gel media (e.g., using an electric field, varying the initial concentration of the electrolytes). However, those methods provide just a limited degree of freedom. Here, we provide a robust and transparent way to control and engineer Liesegang patterns by varying gel concentration and inducing impurity by addition of gelatin to agarose gel. Using this experimental method, different precipitation structures can be obtained with different width and spatial distribution of the formed bands. A new variant of a sol-coagulation model was developed to describe and understand the effect of the gel concentration and impurities on Liesegang pattern formation.

Precipitation patterns formed by self-organizing processes in porous media

ABSTRACT We compare laboratory and field examples of self-organized mineral precipitates in porous media. Laboratorytests of silver chromate precipitation in glass beads and glass bead⁄gel mixtures produce structures such as peri-odic banding and mm-size spherules. These are morphologically similar to the varied forms of iron oxide precipi-tates in the Jurassic Navajo Sandstone, Utah USA, that preserve records of former fluid redox boundaries in aporous and permeable sandstone. Experimental studies of periodic precipitates in porous media can providevaluable insight for understanding the diagenetic history of similar precipitates in natural environments.Key words: concretions, Liesegang bands, self-organizationReceived 23 April 2010; accepted 10 December 2010Corresponding author: L. M. Barge, Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109, USA.Email: Laura.M.Barge@jpl.nasa.gov. Tel: +18183938209. Fax: +18183934445.Geofluids (2011) 11, 124–133 INTRODUCTION In this study, we examine precipitates that form viaself-organizing processes in porous and permeable media.Self-organizing patterns in diffusion-controlled chemicalsystems have been studied for over a century, since the dis-covery by R. E. Liesegang in 1896 that the interactionbetween inter-diffusing silver and chromate ions in a gela-tin gel can produce periodically spaced bands of precipitate(Liesegang 1896). These patterns, termed ‘Liesegangbands’, have since been produced using various combina-tions of reactants (Henisch 2005, and references therein)and in many different types of gels, and the pattern mor-phology can vary widely depending on initial experimentalconditions. Liesegang bands are typically described as ‘peri-odic patterns’, and we will retain this description, althoughthe spacing of bands may not be strictly periodic in thespatial sense.The formation of Liesegang patterns has been attributedto various mechanisms including supersaturation–nucle-ation–depletion processes (in which the first band depletesthe immediate area of the least abundant reactant, resultingin the second band being deposited some distance fromthe first (Ostwald 1897; Smith 1984) and competitiveparticle growth (in which larger particles are less solubleand grow at the expense of smaller ones – a phenomenonknown as Ostwald ripening (Mu¨ller & Ross 2003; Sultan& Ortoleva 1993; Ortoleva 1982; Lifshitz & Slyozov1961). Liesegang band patterns tend to obey several exper-imental laws, for example, that the distance between con-secutive bands increases approximately according to ageometric series (Jablczynski 1923). Liesegang band spac-ing is a function of many factors including reactant con-centrations and thresholds for particle formation, andprecipitation patterns can be partially controlled by alteringsuch factors. Periodic precipitation in systems where homo-geneity of the medium or coagulation threshold is variedin the direction of diffusion, rather than kept as a constantvalue, can give rise to regularly spaced bands or ‘revert’patterns (where band spacing decreases with distance) (An-tal et al. 2007; Molna´r et al. 2008; Jahnke & Kantelhardt2010). Local concentrations of ions can be controlled by,for example, an applied time-dependent electric field acrossthe gel, resulting in band formation in predetermined loca-tions (Bena et al. 2008). The physical and chemical prop-erties of the diffusion medium can also have effects on thepattern formation as well. Gradients of factors such as tem-perature or pH that affect precipitation can give rise to

Formation of Liesegang patterns in the presence of an electric field

The effects of an external electric field on the formation of Liesegang patterns are investigated. The patterns are assumed to emerge from a phase separation process in the wake of a diffusive reaction front. The dynamics is described by a Cahn-Hilliard equation with a moving source term representing the reaction zone, and the electric field enters through its effects on the properties of the reaction zone. We employ our previous results [I. Bena, F. Coppex, M. Droz, and Z. Rácz, J. Chem. Phys. 122, 024512 (2005)] on how the electric field changes both the motion of the front, as well as the amount of reaction product left behind the front, and our main conclusion is that the number of precipitation bands becomes finite in a finite electric field. The reason for the finiteness in case when the electric field drives the reagents towards the reaction zone is that the width of consecutive bands increases so that, beyond a distance l(+), the precipitation is continuous (plug is formed). In case of an electric field of opposite polarity, the bands emerge in a finite interval l(-), since the reaction product decreases with time and the conditions for phase separation cease to exist. We give estimates of l(+/-) in terms of measurable quantities and thus present an experimentally verifiable prediction of the "Cahn-Hilliard equation with a moving source" description of Liesegang phenomena.

Simulation of a Crossover from the Precipitation Wave to Moving Liesegang Pattern Formation

Model simulations to investigate the precipitation wave phenomenon and a crossover from the precipitation wave to moving Liesegang patterns were performed. The chemical scheme contains four chemical species via the interaction of precipitation and redissolution (complex formation), in which the precipitation reaction term was based on Ostwald's supersaturation theory. In this article, for the first time, all the features and behaviors of the heterogeneous traveling waves are reproduced, which were observed experimentally in the work of Zrínyi et al. (Zrínyi, et al. J. Phys. Chem. 1991, 95, 1618.). The detailed investigation of the pattern formation showed three possible states of the system, which depend on the initial concentration of the inner and outer electrolytes, respectively. These are the precipitation wave (single moving precipitation band), the moving Liesegang pattern (moving precipitation bands), and the state where these two patterns coexist.

Regular Liesegang patterns and precipitation waves in an open system

We investigate the regular and moving Liesegang pattern formation phenomena in an open system. First, simulations have been performed at fixed coupling between the reactive medium and the reservoir, later this control parameter was varied during the simulations resulting in various phenomena. We predicted and monitored for the first time various--dynamically changing--precipitation structures and a spatial hysteresis phenomenon, which is beyond the scope of the Turing instability. The dynamics of the reaction is well detectable using specific quantities: the total amount of precipitate and its center of gravity.

Front motion in an A+B→C type reaction-diffusion process: Effects of an electric field

We study the effects of an external electric field on both the motion of the reaction zone and the spatial distribution of the reaction product, C, in an irreversible A- + B+ -->C reaction-diffusion process. The electrolytes A identical with (A+,A-) and B identical with (B+,B-) are initially separated in space and the ion-dynamics is described by reaction-diffusion equations obeying local electroneutrality. Without an electric field, the reaction zone moves diffusively leaving behind a constant concentration of C's. In the presence of an electric field which drives the reagents towards the reaction zone, we find that the reaction zone still moves diffusively but with a diffusion coefficient which slightly decreases with increasing field. The important electric field effect is that the concentration of C's is no longer constant but increases linearly in the direction of the motion of the front. The case of an electric field of reversed polarity is also discussed and it is found that the motion of the front has a diffusive as well as a drift component. The concentration of C's decreases in the direction of the motion of the front, up to the complete extinction of the reaction. Possible application of the above results to the understanding of the formation of Liesegang patterns in an electric field is briefly outlined.

Stabilization and destabilization effects of the electric field on stochastic precipitate pattern formation

Stabilization and destabilization effects of an applied electric field on the Liesegang pattern formation in low concentration gradient were studied with numerical model simulations. In the absence of an electric field pattern formation exhibits increasingly stochastic behaviour as the initial concentration difference between the outer and the inner electrolytes ( Δ ) approaches to zero. Our numerical simulation results have shown that, if the electric field promotes the transport of the reaction front of the outer electrolyte into the diffusion column, then the electric field stabilizes the stochastic pattern structure. This means that Liesegang patterns in the simulations will be decreasingly stochastic, in terms of reproducibility of band locations and of the band formation. Destabilization behaviour was observed in the reverse case, if the electric field retards the diffusion of the outer electrolyte. Simulation of pattern formation is presented using concentration perturbations in a deterministic model. The precipitation process is based on ion-product supersaturation theory (Ostwald's model).

Precipitate pattern formation in fluctuating media.

Simulation of the Liesegang pattern formation in low concentration gradient is presented using concentration perturbation in a deterministic model. The precipitation process is based on ion-product supersaturation theory (Ostwald's model). In the classical experiments with high initial concentration gradients, appearance time and locations of the band formation are well reproducible. Decreasing initial concentration gradients results in a more stochastic pattern structure; this means that the reproducibility of the experiments becomes worse. The presented model and the results of the simulations exhibit the same trend, which were demonstrated and investigated experimentally by Kai et al.

Simulation of Liesegang pattern formation using a discrete stochastic model

Simulations of the Liesegang pattern formation are presented that are based on a discrete stochastic model. The diffusion term was modeled by random walk using transition probabilities referring to one and two steps. A semi-stochastic model of the precipitation process was created, using Ostwald’s supersaturation theory. The calculated variance of zone positions and formation time is in good accordance with the experimental observations of Müller et al.

Formation of periodic precipitation patterns: a moving boundary problem

A new scenario for the formation of Liesegang patterns is proposed. The periodic precipitation pattern formation in a gel column is interpreted as a moving boundary problem. The existing time law, space law, and width law are revisited and reformulated on the basis of a moving boundary assumption and more meaningful explanations are given. All the new equations suggested were found to be in good agreement with experimental observations.

Formation of Liesegang patterns in an electric field

Evolution of Liesegang patterns in an electric field was studied experimentally in the AgNO3/K2Cr2O7/gelatine system. The distance of the last (nth) band as a function of their appearance time can be described by the equation Xn = c1t1/2 + c2t + c3. A numerical model, based on Ostwald's supersaturation theory, predicted the same functional law. Experiments showed that the ratio of the distances of two consecutive rings, the spacing coefficient, decreases with increasing electric field strength and this behaviour was also reproduced by the numerical model.

Properties of the asymptotic nA + mB → C reaction-diffusion fronts

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 Galfi and Racz for the case n=m=1. Consequences for the formation of Liesegang patterns are discussed.