Periodic Stratification of Colloids in a Liquid Phase Produced by a Precipitation Reaction and Gel Swelling.

Pattern formation is a frequent phenomenon occurring in animate and inanimate systems. The interplay between the mass transport of the chemical species and the underlying chemical reaction networks generates most patterns in chemical systems. Periodic precipitation is an emblematic example of reaction-diffusion patterns, in which the process generates a spatial periodic structure in porous media. Here, we use the dormant reagent method to produce colloidal particles of Prussian blue (PB) and PB analogues at the liquid-gel interface. The generated particles produced a stable periodic stratification pattern in time in the liquid phase placed on top of the solid hydrogel. The phenomenon is governed by periodic swelling of the gel driven by the osmotic stress and stability of the formed particles. To illustrate the phenomenon, we developed an extended reaction-diffusion model, which incorporated the gel swelling and sedimentation effect of the formed colloids and could qualitatively reproduce the pattern formation in the liquid phase.

A Dormant Reagent Reaction-Diffusion Method for the Generation of Co-Fe Prussian Blue Analogue Periodic Precipitate Particle Libraries.

Liesegang patterns that develop as a result of reaction-diffusion can simultaneously form products with slightly different sizes spatially separated in a single medium. We show here a reaction-diffusion method using a dormant reagent (citrate) for developing Liesegang patterns of cobalt hexacyanoferrate Prussian Blue analog (PBA) particle libraries. This method slows the precipitation reaction and produces different-sized particles in a gel medium at different locations. The gel-embedded particles are still catalytically active. Finally, the applicability of the new method to other PBAs and 2D systems is presented. The method proves promising for obtaining similar inorganic framework libraries with catalytic abilities.

A Quasi Universal Matalon-Packter Law for a Periodically Precipitating System of Iron(II) Hydroxide Involving Volumes and Concentrations of the Invading Electrolyte.

The Matalon-Packter (MP) empirical law of periodically precipitating (Liesegang phenomenon) systems under non-equilibrium conditions describes the dependence of the periodicity (spacing coefficient) on the initial concentration of the outer electrolyte. We aim to present the MP law in a more generalized form using a realistic approach wherein mass transfer in the gel column plays a role instead of the initial concentrations. This work is an attempt to make such progress. The Liesegang bands of Fe(OH)2 were studied by varying the reservoir concentrations (c) and volumes (V) of the outer electrolyte (NH4OH). The spacing coefficient was found to be a function of the volume and concentration of the outer electrolyte. It was observed that the amount of chemical substance (cV) and the average molar diffusion flux (Fdiff) of the ions of the outer electrolyte could be a unifying quantity for expressing the MP law instead of the initial electrolyte concentration. We demonstrated that a single model is possible for a system, irrespective of the V value. Three different volumes were employed, and the calculations were performed under small, intermediate, and larger reservoir volume regimes. Interestingly, a single model was observed for the diffusion coefficients for all of the Fdiff values.

Bioinspired Control of Calcium Phosphate Liesegang Patterns Using Anionic Polyelectrolytes.

The Liesegang phenomenon is a spontaneous pattern formation, which is a periodic distribution of the precipitate discovered in diffusion-limited systems. Over the past century, it has been experimentally attempted to control the periodicity of patterns and structures of precipitates by varying the concentration of the hydrogel or electrolytes, adding organic or inorganic impurities, and applying an electric or pH field. In this work, the periodic patterns of calcium phosphate were manipulated with an anionic macromolecular additive inspired by bone mineralization in which various noncollagenous proteins are involved in the formation of a polymer-induced liquid precursor. The periodic patterns were systematically controlled by adjusting the amount of poly(acrylic acid), and they were numerically simulated by adjusting the threshold concentration of nucleation. The change of the pattern is explained by improved stability and directional diffusion of the intermediate.

Phase separation mechanism for a unified understanding of dissipative pattern formation in a Liesegang system.

Dissipative patterns with solid-phase transitions are ubiquitous in nature. Despite their ubiquitous nature, there is no unified understanding of the non-equilibrium self-assembly mechanisms of such pattern formation. The Liesegang pattern (LP) is a typical model that has the potential to describe dissipative pattern formation arising from the nonlinear coupling of directional mass transport of water-soluble substances into a porous media with their solid-phase transition processes. However, the conventional mechanism in a Liesegang system lacks practicality because most of the existing studies have focused only on the transition mechanism of nucleation from the molecular to the solid state. In this study, we demonstrate a novel experimental system based on a phase transition and separation mechanism that does not require nucleation, namely, the pH-induced aggregation of gold nanoparticles modified with 11-mercaptoundecanoic acid (MUA-Au NPs) by H+ diffusion in a solid hydrogel. Combined experiments and numerical simulations reveal that pattern formation is driven by the macroscopic phase-separation mechanism. Furthermore, the pattern periodicity obtained from both experiments and simulations follows the classical spacing law of LP, namely, the LP morphology is determined without the need for nucleation. Therefore, we can show that the formation of LPs can be described in a unified mechanism, regardless of whether nucleation occurs. This finding opens the possibility that the chemical Liesegang system can be applied as a practical model for proving the mechanisms of similar dissipative pattern formation.

Shape changes and budding of giant vesicles induced by an internal chemical trigger: an interplay between osmosis and pH change.

Shape transformation and budding of phospholipid/fatty acid giant hybrid vesicles can be induced by an internal chemical stimulus (pH change) when coupled with an osmotic shock. In particular, an autocatalytic enzymatic reaction set (urea-urease system), confined in the lumen of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)/oleic acid (HOA) vesicles, can force the budding of the hosting vesicle, when properly fed by a trans-membrane substrate infusion. Herein, we elucidate the budding mechanism by simulating the shape changes of a vesicle during the enzymatic reaction. The area-difference-elasticity (ADE) theory is thus implemented to minimize the surface elastic energy and obtain the equilibrium shape at different values of the reduced volume and different values of the reduced preferred area difference (Δa0). Simulations, together with control experiments, unambiguously show that to obtain an effective vesicle shape transformation, the osmotic stress and the pH change in the lumen of the vesicle must act in synergy at the same timescale. Osmotic pressure induces a vesicle deflation (volume loss), while the pH change affects the preferred area difference between the outer and the inner membrane leaflets.

Pattern Formation in Precipitation Reactions: The Liesegang Phenomenon.

Pattern formation is a frequent phenomenon in physics, chemistry, biology, and materials science. Bottom-up pattern formation usually occurs in the interaction of the transport phenomena of chemical species with their chemical reaction. The oldest pattern formation is the Liesegang phenomenon (or periodic precipitation), which was discovered and described in 1896 by Raphael Edward Liesegang, who was a German chemist and photographer who was born 150 years ago. The purpose of this feature article is to provide a comprehensive overview of this type of pattern formation. Liesegang banding occurs because of the coupling of the diffusion process of the reagents with their chemical reactions in solid hydrogels. We will discuss several phenomena observed and discovered in the past century, including reverse patterns, precipitation patterns with dissolution (due to complex formation), helicoidal patterns, and precipitation waves. Additionally, we will review all existing models of the Liesegang phenomenon including pre- and postnucleation scenarios. Finally, we will highlight several applications of periodic precipitation.

Carbon Dioxide-Driven Coupling in a Two-Compartment System: Methyl Red Oscillator.

Strategies for designing autonomous oscillatory systems have gained much attention in the past few decades. A broadly accepted and used strategy for the generation of forced oscillations in the originally non-oscillatory subsystems is to couple a pH (driving) oscillator to a pH-sensitive substance (forced oscillatory subsystem) in a one-compartment system. The forced oscillatory subsystem comprises pH-sensitive components, which inevitably generate negative feedback and affect the characteristics of the driving oscillatory system. Here, we present a different approach by separating the driving and forced oscillatory systems into a two-compartment system using a silicone membrane, and the forced oscillations of the absorbance of a pH-sensitive chemical species (methyl red dye) were realized by the transport of carbon dioxide through the membrane generated periodically by the driving pH oscillator. The transported carbon dioxide produced the pH change in the separated compartment by carbon dioxide-hydrogen carbonate-carbonate equilibria and created forced oscillations of a pH-sensitive chemical species manifested in the oscillation of its absorbance at a fixed wavelength. This approach avoids any feedback from the forced oscillatory system to the driving system via the cross-membrane transport of the chemical species from the forced to the driving oscillatory system. Additionally, we present that this carbon dioxide coupling to the methyl red dye can be used to estimate the carbon dioxide content in both liquid and gas phases.

Nanocrystals Assembled by the Chemical Reaction of the Dispersion Solvent.

The development of methods to pattern nanocrystals with different sizes and shapes remains a challenge. In this study, we demonstrate a unique class of bottom-up approaches to assemble nanocrystals into patterns. Our approach for patterning nanocrystals focuses on the utilization and control of the chemical reaction of solvents surrounding nanocrystals. The photopolymerization of solvent molecules through a photomask creates time-dependent concentration gradients of the solvents. Dispersed nanocrystals such as silver nanowires (AgNWs) migrate and are gradually organized and integrated into the polymerizing films based on the concentration gradients. The AgNW-embedded film properties are determined by the organized AgNW structures and include light transmission and electrical conductivity. Overall, the demonstrated method is very simple, widely applicable to various nanocrystals and solvents, and can thus contribute to the development of a new class of nanocrystal patterning methods.

Autonomous Chemical Modulation and Unidirectional Coupling in Two Oscillatory Chemical Systems.

Controlling and coupling of out-of-equilibrium reaction networks have great importance in chemistry and biology. We provide an example for the ideal master-slave coupling between two pH oscillators (the sulfite-bromate and the hydrogen peroxide-sulfite pH oscillators operated in continuous-flow stirred tank reactors). The coupling between the reactors was realized by transport of carbon dioxide through a silicon membrane, which is a common chemical species in both systems. We showed that by using this strategy, the master system can generate forced pH oscillations in the slave system. We could control the amplitude and frequency of the oscillations in the slave system and reversibly drive the transition in the oscillations between the regular and chaotic regimes. Using this coupling strategy, we could present an example of amplitude modulation in a coupled chemical system.

Existence of a Precipitation Threshold in the Electrostatic Precipitation of Oppositely Charged Nanoparticles.

Oppositely charged nanoparticles precipitate rapidly only at the point of electroneutrality, wherein their charges are macroscopically compensated. We investigated the aggregation and precipitation of oppositely charged nanoparticles at concentrations ranging from 10 to 10-3  mm (based on gold atoms) by using UV/Vis measurements. We employed solutions of equally sized (4.6 nm) gold nanoparticles, which were functionalized and stabilized with either positively or with negatively charged alkanethiols. Results showed that oppositely charged nanoparticles do not precipitate if their concentration is below a certain threshold even if the electroneutrality condition is fulfilled. This finding suggests a universal behavior of chemical systems comprising oppositely charged building blocks such as ions and charged nanoparticles.

From Master-Slave to Peer-to-Peer Coupling in Chemical Reaction Networks.

Design strategy through linking a driving pH oscillator (master system) to a pH sensitive complexation, precipitation, or protonation equilibrium (slave system) has been widely used to create and control concentration oscillations of chemical entities (e.g., monovalent cations, DNA, nanoparticles) not participating in the pH oscillatory system. No systematic investigation has been carried out on how the components of these equilibria affect the characteristics of the driving pH oscillators, and this feedback effect has been often neglected in previous studies. Here we show that pH sensitive species (hydrogen carbonate, EDTA) through a pH-dependent equilibrium could significantly affect the characteristics (time period and amplitude) of the driving pH oscillators. By varying the concentration of those species we are able to control the strength of the chemical feedback from slave system to master system thus introducing a transition from master-slave coupling to peer-to-peer coupling in linked chemical systems. To illustrate this transition and coupling strategies we investigate two coupled chemical systems, namely, the bromate-sulfite pH oscillator and carbonate-carbon dioxide equilibrium and the hydrogen peroxide-thiosulfate-copper(II) and EDTA complexation equilibrium. As a sign of the peer-to-peer coupling the characteristics of the driving oscillatory systems can be tuned by controlling the feedback strength, and the oscillations can be canceled above a critical value of this parameter.

Probing the mystery of Liesegang band formation: revealing the origin of self-organized dual-frequency micro and nanoparticle arrays.

Periodic precipitation processes in gels can result in impressive micro- and nanostructured patterns known as periodic precipitation (or Liesegang bands). Under certain conditions, the silver nitrate-chromium(vi) system exhibits the coexistence of two kinds of Liesegang bands with different frequencies. We now present that the two kinds of bands form independently on different time scales and the pH-dependent chromate(vi)-dichromate(vi) equilibrium controls the formation of the precipitates. We determined the spatial distribution and constitution of the particles in the bands using focused ion beam-scanning electron microscopy (FIB-SEM) and scanning transmission X-ray spectromicroscopy (STXM) measurements. This provided the necessary empirical input data to formulate a model for the pattern formation; a model that quantitatively reproduces the experimental observations. Understanding the pattern-forming process at the molecular level enables us to tailor the size and the shape of the bands, which, in turn, can lead to new functional architectures for a range of applications.

Self-assembly of like-charged nanoparticles into Voronoi diagrams.

The self-assembly of nanoscopic building blocks into higher order macroscopic patterns is one possible approach for the bottom-up fabrication of complex functional systems. Macroscopic pattern formation, in general, is determined by the reaction and diffusion of ions and molecules. In some cases macroscopic patterns emerge from diffusion and interactions existing between nanoscopic or microscopic building blocks. In systems where the distribution of the interaction-determining species is influenced by the presence of a diffusion barrier, the evolving macroscopic patterns will be determined by the spatiotemporal evolution of the building blocks. Here we show that a macroscopic pattern can be generated by the spatiotemporally controlled aggregation of like-charged carboxyl-terminated gold nanoparticles in a hydrogel, where clustering is induced by the screening effect of the sodium ions that diffuse in a hydrogel. Diffusion fronts of the sodium ions and the induced nanoparticle aggregation generate Voronoi diagrams, where the Voronoi cells consist of aggregated nanoparticles and their edges are aggregation-free and nanoparticle-free zones. We also developed a simple aggregation-diffusion model to adequately describe the evolution of the experimentally observed Voronoi patterns.

Growth of nanoparticles and microparticles by controlled reaction-diffusion processes.

The synthesis of different sizes of nanoparticles and microparticles is important in designing nanostructured materials with various properties. Wet synthesis methods lack the flexibility to create various sizes of particles (particle libraries) using fixed conditions without the repetition of the steps in the method with a new set of parameters. Here, we report a synthesis method based on nucleation and particle growth in the wake of a moving chemical front in a gel matrix. The process yields well-separated regions (bands) filled with nearly monodisperse nanoparticles and microparticles, with the size of the particles varying from band to band in a predictable way. The origin of the effect is due to an interplay of a precipitation reaction of the reagents and their diffusion that is controlled in space and time by the moving chemical front. The method represents a new approach and a promising tool for the fast and competitive synthesis of various sizes of colloidal particles.

Self-Assembly of Charged Nanoparticles by an Autocatalytic Reaction Front.

In this work we present that aggregation of charged and pH sensitive nanoparticles can be spatiotemporally controlled by an autonomous way using the chlorite-tetrathionate autocatalytic front, where the front regulates the electrostatic interaction between nanoparticles due to protonation of the capping (carboxylate-terminated) ligand. We found that the aggregation and sedimentation of nanoparticles in liquid phase with the effect of reversible binding of the autocatalyst (H(+)) play important roles in changing the front stability (mixing length) and the velocity of the front in both cases when the fronts propagate upward and downward. Calculation of interparticle interactions (electrostatic and van der Waals) with the measurement of front velocity revealed that the aggregation process occurs fast (within a few seconds) at the front position.

Targets, ripples and spirals in a precipitation system with anomalous dispersion.

We present a novel reaction-diffusion system that exhibits three-dimensional superdiffusive traveling waves without utilizing any external forces. These waves include single circular targets, spirals, and ripples as well as phase-like waves. The system is based on the interplay of the precipitation reaction of mercuric iodide in a gel medium, its polymorphic transformation to a different crystalline form, and its redissolution in excess iodide. A phase diagram is constructed as a function of the initial concentrations of the reagents. The spatiotemporal evolution of these waves is thoroughly analyzed and seems to be a consequence of an anomalous dispersion relationship. Pattern selection and wavelengths of propagating waves are found to depend on initial concentrations of the reactants. The breakup of the waves is also investigated. While the breakdown of ripples and spirals is shown to be a consequence of a Doppler-like instability in conjunction with anomalous dispersion, the targets undergo a boundary defect-mediated breakup.

Propagating fronts and morphological instabilities in a precipitation reaction.

Precipitation processes are essential in many natural systems, especially in biomineralization and in geological pattern formation. We observe temporal oscillations in the total mass of the precipitate, the formation of propagating and annihilating waves, and morphological instabilities in a thin precipitation layer in a two-side-fed gel reactor containing the AlCl3/NaOH reaction-diffusion system. Contrary to the standard Liesegang patterns, these structures form in the lateral direction at the meeting of the counterpropagating diffusion fronts of the electrolytes. The two main ingredients of the system are the amphoteric precipitate and the cross gradient of the chemicals due to the fixed boundary conditions. Simulations with a four-variable precipitation/redissolution model qualitatively reproduce the oscillations in the total mass of the precipitate and point out the stratified three-dimensional structure of the precipitate.

Maze solving using fatty acid chemistry.

This study demonstrates that the Marangoni flow in a channel network can solve maze problems such as exploring and visualizing the shortest path and finding all possible solutions in a parallel fashion. The Marangoni flow is generated by the pH gradient in a maze filled with an alkaline solution of a fatty acid by introducing a hydrogel block soaked with an acid at the exit. The pH gradient changes the protonation rate of fatty acid molecules, which translates into the surface tension gradient at the liquid-air interface through the maze. Fluid flow maintained by the surface tension gradient (Marangoni flow) can drag water-soluble dye particles toward low pH (exit) at the liquid-air interface. Dye particles placed at the entrance of the maze dissolve during this motion, thus exhibiting and finding the shortest path and all possible paths in a maze.

Label-free in situ optical monitoring of the adsorption of oppositely charged metal nanoparticles.

The mechanism of alternating deposition of oppositely charged gold nanoparticles (AuNPs) was investigated by optical waveguide lightmode spectroscopy (OWLS). OWLS allows monitoring of the kinetics of layer-by-layer (LbL) adsorption of positively and negatively charged nanoparticles in real time without using any labels so that the dynamics of layer formation can be revealed. Positively charged NPs that are already deposited on a negatively charged glass substrate strongly facilitate the adsorption of the negatively charged particles. The morphology of the adsorbed layer was also investigated with atomic force microscopy (AFM). AFM revealed that the interaction between oppositely charged particles results in the formation of NP clusters with sizes varying between 100 and 6000 NPs. The cluster size distribution is found to be an exponentially decaying function, and we propose a simple theory to explain this finding.