Oliver Steinbock

Navigating Complex Labyrinths: Optimal Paths from Chemical Waves

The properties of excitable media are exploited to find minimum-length paths in complex labyrinths. Optimal pathways are experimentally determined by the collection of time-lapse position information on chemical waves propagating through mazes prepared with the Belousov-Zhabotinsky reaction. The corresponding velocity fields provide maps of optimal paths from every point in an image grid to a particular target point. Collisions of waves that were temporarily separated by obstacles mark boundary lines between Significantly different paths with the same absolute distance. The pathfinding algorithm is tested in very complex mazes with a simple reaction-diffusion model.

From Chemical Gardens to Chemobrionics

Chemical gardens in laboratory chemistries ranging from silicates to polyoxometalates, in applications ranging from corrosion products to the hydration of Portland cement, and in natural settings ranging from hydrothermal vents in the ocean depths to brinicles beneath sea ice. In many chemical-garden experiments, the structure forms as a solid seed of a soluble ionic compound dissolves in a solution containing another reactive ion. In general any alkali silicate solution can be used due to their high solubility at high pH. The cation should not precipitate with the counterion of the metal salt used as seed. A main property of seed chemical-garden experiments is that initially, when the fluid is not moving under buoyancy or osmosis, the delivery of the inner reactant is diffusion controlled. Another experimental technique that isolates one aspect of chemical-garden formation is to produce precipitation membranes between different aqueous solutions by introducing the two solutions on either side of an inert carrier matrix. Chemical gardens may be grown upon injection of solutions into a so-called Hele-Shaw cell, a quasi-two-dimensional reactor consisting in two parallel plates separated by a small gap.

External forcing of spiral waves.

The effect of an external rhythm on rotating spiral waves in excitable media is investigated. Parameters of the unperturbed medium were chosen, such that the organizing spiral tip describes meandering (hypocyclic) trajectories, which are the most general shape for the experimentally observed systems. Periodical modulation of excitability in a model of the Belousov-Zhabotinsky (BZ) reaction forces meandering spiral tips to describe trajectories that are not found at corresponding stationary conditions. For different modulation periods, two types of resonance drift, phase-locked tip motion, a spectrum of hypocyclic trajectories, and complex multifrequency patterns were computed. The computational results are complemented by experimental data obtained for periodically changing illumination of the photosensitive BZ reaction. The observed drastic deformation of the tip trajectory is considered as an efficient means to study and to control wave processes in excitable media.

Introduction: Self-organization in nonequilibrium chemical systems

The field of self-organization in nonequilibrium chemical systems comprises the study of dynamical phenomena in chemically reacting systems far from equilibrium. Systematic exploration of this area began with investigations of the temporal behavior of the Belousov-Zhabotinsky oscillating reaction, discovered accidentally in the former Soviet Union in the 1950s. The field soon advanced into chemical waves in excitable media and propagating fronts. With the systematic design of oscillating reactions in the 1980s and the discovery of Turing patterns in the 1990s, the scope of these studies expanded dramatically. The articles in this Focus Issue provide an overview of the development and current state of the field.

Traveling waves in yeast extract and in cultures of Dictyostelium discoideum

Biological self-organization was investigated in a biochemical and a cellular system: yeast extract and cultures of the slime mold Dictyostelium discoideum. In both systems traveling reaction-diffusion waves occur in response to oscillatory reactions. Glycolytic degradation of sugar in a yeast extract leads to the spontaneous formation of NADH and proton waves. Manipulation of the adenine nucleotide pool by addition of purified plasma membrane ATPase favors the formation of both reaction-diffusion waves and phase waves. The results indicate that the energy charge has an important impact for the dynamics of glycolytic patterns. When affecting the lower part of glycolysis by pyruvate addition the frequency of wave generation was increased with concomitant formation of rotating NADH and proton spirals. During morphogenesis of the cellular system Dictyostelium discoideum, circular and spiral shaped aggregation patterns of motile amoeboid cells form in response to traveling cAMP waves. Velocity analysis of the cell movements reveals that the cAMP waves guide the cells towards the site of wave initiation along optimized trajectories. The minimization of aggregation paths is based on a mechanism exploiting general properties of excitation waves. The resulting aggregation territories are reminiscent of Voronoi diagrams.

Compositional analysis of copper–silica precipitation tubes

Silica gardens consist of hollow tubular structures that form from salt crystals seeded into silicate solution. We investigate the structure and elemental composition of these tubes in the context of a recently developed experimental model that allows quantitative analyses based on predetermined reactant concentrations and flow rates. In these experiments, cupric sulfate solution is injected into large volumes of waterglass. The walls of the resulting tubular structures have a typical width of 10 microm and are gradient materials. Micro-Raman spectroscopy along with energy dispersive X-ray fluorescence data identify amorphous silica and copper(ii) hydroxide as the main compounds within the inner and outer tube surfaces, respectively. Upon heating the blueish precipitates to approximately 150 degrees C, the material turns black as copper(ii) hydroxide decomposes to copper(ii) oxide. Moreover, we present high resolution transmission electron micrographs that reveal polycrystalline morphologies.

Bubble‐Templated and Flow‐Controlled Synthesis of Macroscopic Silica Tubes Supporting Zinc Oxide Nanostructures

Reaction–transport coupling can self-organize inorganic structures with complex, hierarchical architectures that in some cases extend beyond the nanometer scale into the macroscopic world. A simple but nonetheless interesting example is the hollow-tube motif which is found in cement, biomineralized shells of algae, ferrotubes, speleotherms and hydrothermal vents. Arguably one of the best laboratory models for the study of tube formation is a class of reactions known as chemical or silica “gardens”. These reactions produce millimeter-scale precipitation tubes that can grow upward at rates of millimeters per second. Recent studies of these hollow structures have demonstrated applications of metallosilica tubes as Brønsted acid catalysts and simple microfluid devices. Herein, we present the synthesis of similar tubes using a flow injection method with gas bubbles as directional guides and templates. The bubbles are pinned to the interfacial reaction zone of the growing tubes. The resulting materials are very straight tubes consisting of silica-supported zinc oxide nanostructures and show interesting luminescence and photocatalytic properties. The prototypical experiment underlying our investigations consists of crystals seeded into aqueous solutions containing anions such as borates, phosphates, carbonates, or silicates; herein we present experiments involving silicates. Furthermore, many different salts can be used as the seed, with the exception of Group 1 elements. Tube morphogenesis starts with the formation of a colloidal and semipermeable membrane around the dissolving seed. Osmotic pressure differences induce a cross-membrane flux of water and subsequently rupture the membrane. From the breach site a buoyant jet of salt solution is ejected which templates the tube-forming co-precipitation of amorphous silica and metal hydroxides (or oxides). Figure 1a shows a precipitation structure formed from a zinc(II) sulfate crystal seeded into 2.5m silicate solution. The tube is reminiscent of an erratic string of beads. Figure 1b shows a micrograph of a similar tube obtained by scanning electron microscopy (SEM). The average diameter of the tube is about 1 mm. Clearly, such irregular and uncontrolled structures have very limited value as hollow support systems and cannot be extended over long distances. Our method overcomes these limitations by replacing the seed particle with a seed solution injected at constant flow rates. Furthermore, we place a buoyant gas bubble into the initial, colloidal

Hollow Microtubes and Shells from Reactant-Loaded Polymer Beads†

The production of complex micrometer-scale structures by spatial control of chemical reactions and physical transformations is unambiguously demonstrated by living systems. For example, certain marine algae surround themselves with intricate arrays of calcite-based plates or tubes, while radiolarians stabilize their extravagant shapes with internal microspikes and perforated shells made of silica. These structures are clearly the result of complicated and genetically regulated cellular functions, but also involve generic physicochemical mechanisms that create spatial complexity from emergent phenomena. These nonequilibrium phenomena should also exist in nonbiological systems, but the number of examples established to date is quite small. In chemistry, the production of nanoand microstructures with complex shapes typically relies on sol–gel, precipitation and other solidification processes such as vapor deposition. Classic examples of macroscopic complexity are Liesegang rings and the formation of so-called “silica gardens”. The latter example is known to many as a chemistry toy and demonstration experiment, and leads to millimeter-sized, hollow tubes in aqueous solutions of silicates, borates, or carbonates from small, submerged salt seeds. Most common inorganic compounds can be used as seed particles with the exception of alkali-metal salts. Hollow precipitation tubes are also observed on corroding metals, in setting cement, in caves as “soda straw” speleotherms, and on the ocean floor as “black smokers”. The length scales of these tubular precipitation structures span three orders of magnitude. Ritchie et al. recently studied silica tube formation from small polyoxometalate-based solid grains and observed tube radii as small as several micrometers. Even smaller silica tubes (0.1 mm) have been synthesized using organic-crystal templating and liquid-crystal phase transformations. Clearly, such length scales make these hollow tubes interesting targets for various applications. Herein, we report a novel approach to silica microstructures. Our approach is based on compartmentalizing the two reactant solutions in a controlled and quantifiable fashion. For these experiments, we produce agarose beads as a microvessel by using a conventional emulsification technique. The gel beads are then loaded diffusively with copper sulfate and finally exposed to a large volume of sodium silicate solution. The resulting dynamics are illustrated by the brightfield micrographs in Figure 1 (see the

Complex Shapes and Dynamics of Dissolving Drops of Dichloromethane

There is a growing interest in synthetic, chemical systems capable of undergoing autonomous shape changes and/or self-motion. Important examples include solid objects such as catalytic Au/Pt nanorods, mechanically responsive gels driven by oscillating reactions, and liquid systems in which self-motion is induced by surface-tension gradients. The latter class of systems includes iodine/iodide-containing oil droplets on glass surfaces under aqueous solutions of stearyltrimethylammonium chloride as well as drop motion on an alkylsilane-treated silicon surface with spatial “wettability” changes. Droplet motion on air–water interfaces is usually driven by aMarangoni effect involving temperature or concentration gradients. A typical example are pentanol droplets on water, which depending on the drop volume, perform erratic or unidirectional motion and also show very disorganized forms of droplet fission. This fission can extend from the millimeter-scale down to nanoscopic micelles. Herein, we investigate the dynamics of water-saturated dichloromethane (CH2Cl2, 25 mL) droplets on aqueous solutions of cetyltrimethylammonium bromide (CTAB). Figure 1 is a qualitative phase diagram describing the macroscopic dynamics in the CH2Cl2/CTAB system in terms of the elapsed reaction time and the surfactant concentration. The data are representative for the fourth and fifth drops added. The diagram shows a variety of complex drop shapes and dynamics that we identified to be the most characteristic ones. For each concentration we have studied the dynamics of five successive drops. In general these dichloromethane-accumulating experiments reveal no marked differences; however, the fourth and fifth drops deviate from their predecessors during the late stages of dissolution. These altered dynamics typically match the behavior of drops at a slightly higher CTAB concentration. The life time of the dichloromethane drops varies systematically between approximately 20 and 90 s. This large range is mainly caused by changes in the initial induction period during which drops are stationary and have a circular rim. Complex phenomena are found only for surfactant concentrations above a critical value [CTAB]crit 0.25 mmolL . In the absence of surfactant or below [CTAB]crit, the drops spread out over a large area and solubilize rapidly (< 15 s) without noteworthy macroscopic features. For surfactant concentration close to [CTAB]crit (left column in Figure 1), the initial dichloromethane drops are relatively flat. We also observe that the water surface around the drop supports a disk-shaped film. The macroscopic dynamics involve several successive stages: During the first stage, the edge of the film breaks into small droplets that are continuously ejected and quickly disappear. Then the drop abruptly moves away from the center of the film to maneuver back and forth along a nearly stationary line. During these lateral oscillations, each directional change causes the expulsion of a line of small droplets. After a while, the drop starts to move steadily along a circular orbit larger than its own diameter. Finally all motion ceases, the drop becomes circular again, shrinks and vanishes. At a surfactant concentration of 0.5 mmolL 1 (second column in Figure 1), the dichloromethane drops undergo a similar sequence of motion patterns. However, the dynamics Figure 1. Qualitative description of the drop evolution in the CH2Cl2/ CTAB system at five different concentrations of the surfactant CTAB. The typical life time of the dissolving droplets ranges between 20 and 90 s. The time axis is not to scale as the diagram emphasizes distinct, successive states in the drop evolution. Single arrows indicate rotation of the drop around its geometrical center. The double arrow indicates that the drop moves back and forth along a fixed line. The field of view of all frames corresponds to 13 13 mm.

Chemical spiral rotation is controlled by light-induced artificial cores

Abstract Dynamic features of spiral-shaped excitation waves rotating around unexcitable disks are investigated experimentally. The spiral patterns are observed in the ruthenium-catalyzed Belousov-Zhabotinsky reaction (bromination of malonic acid), in which the excitability depends on the intensity of applied illumination. Measurements are performed with a novel technique, which uses an argon laser beam for manipulation of wave propagation and creation of unexcitable disks, serving as artificial spiral cores. Rotation period, wavelength and velocity of spirals increase monotonically when the core radius is enlarged by expanding the diameter of the laser beam (0.1–3.0 mm). Rapid change of the core size is followed by a continuous relaxation process into a new dynamic state. The transient wavelengths and velocities scanned during this process provide data for a fast calculation of the dispersion relation for the investigated medium.