Precipitation Pattern Formation Research Articles

Formation of Precipitation Ellipsoidal Disks and Spheres in the Wake of a Planar Diffusion Front.

Pattern formation is one of the examples of self-organization. In the generation of patterns, the coupling between the mass transport of the chemical species and their chemical reactions plays an important role. Periodic precipitation (Liesegang phenomenon) is a type of pattern formation in which layered precipitation structures form in the wake of the diffusion front. Here, we show a new type of precipitation pattern formation in zeolitic imidazolate framework-67 in a solid hydrogel column in a test tube manifested in the generation of precipitation ellipsoidal disks and spheres in the wake of the planar diffusion front of the outer electrolyte (2-methylimidazole). To increase the probability of the emergence of ellipsoidal disks and spheres, the surfaces of the borosilicate test tubes were chemically treated and functionalized. To support the experimental findings, we developed a reaction-diffusion model that qualitatively describes the formation of precipitate ellipsoidal disks and spheres in a test tube.

Chemical Tracking of Temperature by Concurrent Periodic Precipitation Pattern Formation in Polyacrylamide Gels.

In nature, nonequilibrium systems reflect environmental changes, and these changes are often “recorded” in their solid body as they develop. Periodic precipitation patterns, aka Liesegang patterns (LPs), are visual sums of complex events in nonequilibrium reaction–diffusion processes. Here we aim to achieve an artificial system that “records” the temperature changes in the environment with the concurrent LP formation. We first illustrate the differences in 1-D LPs developing at different temperatures in terms of band spacings, which can demonstrate the time, ramp steepness, and extent of a temperature change. These results are discussed and augmented by a mathematical model. Using scanning electron microscopy, we show that the average size of the CuCrO4 precipitate also reflects the temperature changes. Finally, we show that these changes can also be “recorded” in the 2-D and 3-D LPs, which can have applications in long-term temperature tracking and complex soft material design.

Spontaneous precipitation pattern formation by crystallites of Mn-Fe-based Prussian blue analogues in agarose gel.

Precipitation patterns spontaneously formed by Mn–Fe-based Prussian blue analogues (Mn–Fe PBAs) in agarose gel were investigated over wide concentration ranges for the outer (0.10 ≤ [Mn2+] ≤ 0.70 M) and inner electrolytes (0.01 ≤ [[Fe(CN)6]3−] ≤ 0.35 M). The precipitation patterns were classified into five types: continuous in the inner electrolyte gel, continuous in the outer electrolyte gel, a very short band close to the gel boundary, periodic bands in the inner electrolyte gel, and filament-like patterns in the inner electrolyte gel. The concentrations found to be suitable for applications as pulsatile 137Cs adsorbent delivery materials, for which the periodic patterns were most distinct and frequently occurring, were [Mn2+] ≈ 0.55 M and [[Fe(CN)6]3−] ≈ 0.10 M. The filament-like pattern, reported here for the first time, was generated near the cylindrical gel surface in a local, stochastic, and two-dimensional manner. Scanning electron microscopy (SEM) images of the periodic band patterns indicate that the Mn–Fe PBA precipitates in periodic patterns consist of cubic crystallites (3–10 μm, each side), suggesting significant contributions from Ostwald ripening to the precipitation process. In contrast, precipitates in the filament-like pattern consist of relatively smaller cubic crystallites (≲1 μm, each side), implying an important role of rapid nucleation in the formation of this structure. SEM observations also suggest that, overall, agarose gels support crystallite ripening more effectively, and hence also better suppress the formation of definite periodic bands, than water-glass gels. These findings provide useful information for future applications of self-assembled Mn–Fe PBA patterns in gels.

Osmotic contribution to the flow-driven tube formation of copper-phosphate and copper-silicate chemical gardens.

We have produced hollow copper-containing precipitate tubes using a flow-injection technique, and characterized their linear and volume growth. It is shown that the ratio of the volume increase rate to that of pumping is constant independent of the chemical composition. It is also found that osmosis significantly contributes to the tube growth, since the inward flux of chemical species dominates during the precipitate pattern formation. The asymmetric hydrodynamic field coupled with the inherent concentration and pH gradients results in different particle morphology on the two sides of the precipitate membrane. While the tubes have a smooth outer surface, the inner walls are covered with nanoflowers for copper phosphate and with nanoballs for copper silicate.

Thermodynamic stability of driven open systems and control of phase separation by electro-autocatalysis.

Motivated by the possibility of electrochemical control of phase separation, a variational theory of thermodynamic stability is developed for driven reactive mixtures, based on a nonlinear generalization of the Cahn-Hilliard and Allen-Cahn equations. The Glansdorff-Prigogine stability criterion is extended for driving chemical work, based on variations of nonequilibrium Gibbs free energy. Linear stability is generally determined by the competition of chemical diffusion and driven autocatalysis. Novel features arise for electrochemical systems, related to controlled total current (galvanostatic operation), concentration-dependent exchange current (Butler-Volmer kinetics), and negative differential reaction resistance (Marcus kinetics). The theory shows how spinodal decomposition can be controlled by solo-autocatalytic charge transfer, with only a single faradaic reaction. Experimental evidence is presented for intercalation and electrodeposition in rechargeable batteries, and further applications are discussed in solid state ionics, electrovariable optics, electrochemical precipitation, and biological pattern formation.

Chemical waves in heterogeneous media.

Formation of precipitation patterns and wave propagation in excitable media have attracted considerable scientific interest in the context of nonlinear chemical kinetics because of a new approach to micro and nanofabrication, in addition to some biological aspects. All precipitation patterns share common morphological characteristics, namely the formed patterns are stationary and no dynamical patterns can be observed in these classical precipitation systems (e.g., Liesegang phenomenon). However, it has been recently shown that in several circumstances dynamic patterns (chemical waves) can exist in purely inorganic precipitation systems similar to the well-known and studied (excitable) waves in Belousov-Zhabotinsky reaction. In this study, we show how to fine-tune the pattern characteristics in precipitation systems, such as the wavelength and the pattern morphology by changing the concentrations of the reagents, and we demonstrate chemical waves on a moving 3D spherical precipitation layer. We show that such precipitation waves have anomalous transport property, specifically superdiffusive nature, and it can be controlled by the initial concentration of the inner electrolyte. Moreover, we present several precipitation systems in which chemical wave propagation inside a moving precipitation layer can emerge. This observation points out the generality and robustness of similar behavior in diffusion-precipitation systems.

Mesoscopic Study of the Effects of Gel Concentration and Materials on the Formation of Precipitation Patterns

A mesoscopic model based on the lattice Boltzmann method (LBM) is proposed to simulate the formation of Liesegang precipitation patterns and investigate the effects of gel on the morphology of the precipitates. In this model, nucleation is introduced on the basis of Ostwald's supersaturation theory, and subsequent crystal growth on the precipitate surface is simulated using a crystal growth model by taking into account the heterogeneous reaction on the surface of the precipitate. This model can capture the porous structures of the precipitates and can take into account the effects of the gel concentration and material by adjusting the gel porosity and nucleation threshold. The density of the precipitate nodes in the model is limited. A wide range of precipitation patterns is predicted under different gel concentrations, including regular bands, treelike patterns, and for the first time with numerical models, transition patterns between regular bands and treelike patterns. Both the spacing law and the width law are carefully investigated with different gel concentrations and gel materials, and the obtained α in the width law (w(n) ≈ x(n)(α), where x(n) and w(n) are the position and the width of the nth band, respectively) is in the range of 0.58-0.67, sandwiched by previously predicted ranges.

Hexagonal CNN and its applications in sphalerite banding texture simulation

A cellular nonlinear network (CNN) has been developed in the literature to characterize complexity, especially for reaction-diffusion dynamic systems. This CNN includes models that describe periodic precipitation and banding pattern formation in minerals. Banding textures are commonly observed in mineral crystals, including sphalerite crystals in Mississippi Valley-type deposits. A CNN model in a hexagonal coordinate system is developed in this paper to simulate the process for the hexagonal growth of minerals such as sphalerite. The model involves dividing the hexagonal space into triangular cells for which a coupling law can be defined. The model was used by referring to the initial conditions in the literature. The agreement of the simulated results with the observations demonstrates that the CNN model introduced in this paper is reasonable and can be used to interpret the mechanism for hexagonal growth of various textures such as banding in sphalerite.

Theoretical and experimental investigation of immunoprecipitation pattern formation in gel medium

We present the results of our comprehensive study of precipitation pattern formation by interacting immunogenic proteins in a gel medium. Formation of immunoprecipitation patterns was studied both theoretically and experimentally. Based on a system of reaction-diffusion equations, continuous deterministic description provides a quantitative model of reaction kinetics. Discrete stochastic microscopic description was used to supplement the results of reaction-diffusion model by mimicking product aggregation that contributes to a deeper understanding of the mechanism that governs the phenomenon. Our studies have shown that the mechanism of immunoprecipitation pattern formation is specific for protein precipitation and differs from such mechanisms for any inorganic or biological substances. By microscopic examination, we demonstrated that immunoprecipitation patterns can have a microstructure. We found that the microscopic structure of immunoprecipitation patterns results from multicomponent composition of antiserum.

Precipitation Pattern Formation in the Copper(II) Oxalate System with Gravity Flow and Axial Symmetry

Chemical systems that are far from thermodynamic equilibrium may form complex temporal and spatiotemporal structures. In our paper, we present unusual precipitation patterns that have been observed in the system of Cu(II)-oxalate. Starting with a pellet of copper sulfate immersed in or by pumping copper sulfate solution into a horizontal layer of sodium oxalate solution, we have observed the formation of a precipitate ring and an array of radially oriented thin fingers. The development of these patterns is related to the internal structure of the different crystals, the gravity flow, and the circular symmetry of the experimental arrangement.

Pattern transition between periodic Liesegang pattern and crystal growth regime in reaction–diffusion systems

The pattern transition between periodic precipitation pattern formation (Liesegang phenomenon) and pure crystal growth regimes is investigated in silver nitrate and potassium dichromate system in mixed agarose–gelatin gel. Morphologically different patterns were found depending on the quality of the gel, and transition between these typical patterns can be controlled by the concentration of gelatin in mixed gel. Effect of temperature and hydrodynamic force on precipitation pattern structure was also investigated.

Encoding information into precipitation structures

Material design at submicron scales would be profoundly affected if the formation ofprecipitation patterns could be easily controlled. It would allow the direct building ofbulk structures, in contrast to traditional techniques which consist of removingmaterial in order to create patterns. Here, we discuss an extension of our recentproposal of using electrical currents to control precipitation bands which emerge inthe wake of reaction fronts in A+ + B– → C reaction–diffusion processes. Our main result, based on simulating thereaction–diffusion–precipitation equations, is that the dynamics of the charged agents canbe guided by an appropriately designed time-dependent electric current so that, in additionto the control of the band spacing, the width of the precipitation bands can also be tuned.This makes straightforward the encoding of information into precipitation patterns and, asan amusing example, we demonstrate the feasibility by showing how to encode a musicalrhythm.

Self-organization in nonlinear dynamical systems and its relation to the materials science

This review paper presents briefly the main concepts of nonlinear dynamics and their exemplary manifestations in selected systems, including those important from the point of view of materials science. It is an extended version of the conference presentation. The conditions of instabilities leading to spontaneous formation of dissipative structures are given. Principles of nonlinear dynamics are illustrated with several examples from the homogeneous and heterogeneous and physical and chemical systems: pattern formation in the convective motion of fluids subject to various kinds of driving forces, periodic precipitation phenomena, oscillations, and pattern formation in the Belousov–Zhabotinski (BZ) reaction and the catalytic oxidation of thiocyanate ions with hydrogen peroxide, as well as bistability and tristability in the electrochemical reduction of azide complexes of nickel(II). The application of nonlinear dynamics in materials science is first exemplified by its role in polymerization reactions. Such processes can either exhibit internal couplings leading to oscillations or can be coupled with the chemical oscillatory process through, e.g., the covalent bonding of its catalyst to the polymer network. Other selected examples of the application of nonlinear dynamics in materials science, referring to electrochemical processes, were briefly reviewed. Nonlinear dynamics appears to be useful for designing new materials, including those at the nanoscale.

Temporal and Spatial Organization of Chemical and Hydrodynamic Processes. The System Pb2+−Chlorite−Thiourea

Precise spatio-temporal organization of chemical, hydrodynamic, and mechanical processes is typical for biological systems where particular chemical reactions have to accrue in precisely assignment place and time. It is rarely studied and observed in chemical systems. We report unusual precipitation pattern formation of PbSO(4) in chemical media (Pb(2+)-Chlorite-Thiourea System). We have found that there is a region in a plane of initial concentrations of chlorite ions and thiourea where precipitation of lead sulfate appears in a form of ring if a pellet of lead nitrate is placed into the system. The whole process may be divided into three stages: movement of first circular front of lead containing solution, formation of a ringlike pattern of lead sulfate, and finally, propagation of this pattern resulting in a formation of ring with final inside diameter. Our experiments indicate that the following values are reproducible and quantify the PbSO(4) ring evolution: induction time, radius of the ring birth, speed of ring propagation toward the center, and final inside radius of the ring. Numerical solution of kinetic equations allowed us to give a qualitative explanation for the phenomenon observed. Formation and evolution of the PbSO(4) rings are caused by interplay of concentration gradients in the system and chemical reactions that occur in excitable chlorite-thiourea system. Chemical reactions and hydrodynamic processes form a complex causal network that made morphogenesis of this unusual pattern possible.

Precipitation Pattern Formation in the Presence of Imposed Concentration Gradients

AbstractThis study explored precipitation pattern formation under conditions where the inner electrolyte was inhomogeneously distributed. Depending on the imposed concentration gradient, various new precipitation structures such as bifurcated segments, budding patterns, and Liesegang rings segregated with broken circles have been observed. The analysis illustrates that, despite the presence of an imposed concentration gradient, the location of Xn of the nth band and its time of formation tn still satisfy a simple law, but the spacing (Xn+1/Xn) of the precipitation bands departs from a linear relationship once broken rings are developed in the medium.

Steady states and linear stability analysis of precipitation pattern formation at geothermal hot springs

A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match the measured shapes near the vent at the top of observed travertine domes well. Closer to the base of the dome, the solutions deviate from observations and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.

Pattern Formation and Self-Organization in a Simple Precipitation System

Various types of pattern formation and self-organization phenomena can be observed in biological, chemical, and geochemical systems due to the interaction of reaction with diffusion. The appearance of static precipitation patterns was reported first by Liesegang in 1896. Traveling waves and dynamically changing patterns can also exist in reaction-diffusion systems: the Belousov-Zhabotinsky reaction provides a classical example for these phenomena. Until now, no experimental evidence had been found for the presence of such dynamical patterns in precipitation systems. Pattern formation phenomena, as a result of precipitation front coupling with traveling waves, are investigated in a new simple reaction-diffusion system that is based on the precipitation and complex formation of aluminum hydroxide. A unique kind of self-organization, the spontaneous appearance of traveling waves, and spiral formation inside a precipitation front is reported. The newly designed system is a simple one (we need just two inorganic reactants, and the experimental setup is simple), in which dynamically changing pattern formation can be observed. This work could show a new perspective in precipitation pattern formation and geochemical self-organization.

Dynamics of Precipitation Pattern Formation at Geothermal Hot Springs

We formulate and model the dynamics of spatial patterns arising during the precipitation of calcium carbonate from a supersaturated shallow water flow. The model describes the formation of travertine deposits at geothermal hot springs and rimstone dams of calcite in caves. We find explicit solutions for travertine domes at low flow rates, identify the linear instabilities which generate dam and pond formation on sloped substrates, and present simulations of statistical landscape evolution.

Periodic precipitation pattern formation in hydrothermally treated metamict zircon

For more than 100 years mineralogists, physicists, chemists, geologists, and biologists have discussed the formation of periodic Liesegang patterns observed in natural and experimental systems. Spectacular examples of minerals showing complex periodic patterns are agate, malachite, and sphalerite. Here we report the first observation of Liesegang-like patterns in hydrothermally treated metamict (i.e., amorphous) zircon. The structures observed show curved bands, radial sets of pocketlike wave fronts or irregular curved patterns in both cathodoluminescence and backscattered electron images. They are composed of alternating zones of crystallographically well-aligned, polycrystalline zircon along with remnant amorphous pockets and a phase assemblage of randomly oriented zircon crystallites, monoclinic ZrO2, and amorphous SiO2, as revealed by transmission electron microscopy. Analyses by secondary ion mass spectrometry and electron microprobe reveal that the latter zones are characterized by higher hydrogen concentrations and higher Zr-Si ratios. Both zones are also distinguishable by a distinctly different crystallite size. We propose a possible pattern-forming mechanism that is based on a feedback of hydrogen diffusion, zircon nucleation, and the displacement of hydrogen atoms from growing crystallites.

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).