Alginate microparticles and nanoparticles crosslinked with Ca+2 ions are frequently employed in biomedical applications. Here we use microemulsion polymerization to prepare alginate nanoparticles (nanogels) using different crosslinking ions (Ca+2, Sr+2, Ba+2) to encapsulate a model protein, urease enzyme (jackbeans). With alginate concentrations of 0.2 wt% in the aqueous phase, emulsion droplets showed good stability and narrow, monomodal distributions with radii ∼65 ± 10 nm. The size of the nanogel varies with the crosslinking cation and its affinity for the mannuronate and guluronate units in the linear alginate chain. The nanogels were further characterized using dynamic light scattering, scanning electron microscopy, energy dispersive X-ray spectrometry and zeta potential. This work demonstrates the potential application of Ba-alginate as an alternative matrix for nano-encapsulation of proteins and its use for biomedical applications.Download high-res image (82KB)Download full-size image

Existing models of the ferrocyanide–iodate–sulfite (FIS) reaction seek to replicate the oscillatory pH behavior that occurs in open systems. These models exhibit significant differences in the amplitudes and waveforms of the concentration oscillations of such intermediates as I–, I3–, and Fe(CN)63– under identical conditions and do not include several experimentally found intermediates. Here we report measurements of sulfite concentrations during an oscillatory cycle. Knowing the correct concentration of sulfite over the course of a period is important because sulfite is the main component that determines the buffer capacity, the pH extrema, and the amount of oxidizer (iodate) required for the transition to low pH. On the basis of this new result and recent experimental findings on the rate laws and intermediates of component processes taken from the literature, we propose a mass action kinetics model that attempts to faithfully represent the chemistry of the FIS reaction. This new comprehensive mechanism reproduces the pH oscillations and the periodic behavior in [Fe(CN)63–], [I3–], [I–], and [SO32–]T with characteristics similar to those seen in experiments in both CSTR and semibatch arrangements. The parameter ranges at which stationary and oscillatory behavior is exhibited also show good agreement with those of the experiments.

The hydrogen ion is arguably the most ubiquitous and important species in chemistry. It also plays a key role in nearly every biological process. In this Account, we discuss systems whose behavior is governed by oscillations in the concentration of hydrogen ion. The first chemical oscillators driven by changes in pH were developed a quarter century ago. Since then, about two dozen new pH oscillators, systems in which the periodic variation in pH is not just an indicator but an essential prerequisite of the oscillatory behavior, have been discovered. Mechanistic understanding of their behavior has grown, and new ideas for their practical application have been proposed and, in some cases, tested.Here we present a catalog of the known pH oscillators, divide them into mechanistically based categories based on whether they involve a single oxidant and reductant or an oxidant and a pair of reductants, and describe general mechanisms for these two major classes of systems. We also describe in detail the chemistry of one example from each class, hydrogen peroxide–sulfide and ferricyanide–iodate–sulfite. Finally, we consider actual and potential applications. These include using pH oscillators to induce oscillation in species that would otherwise be nonoscillatory, creating novel spatial patterns, generating periodic transitions between vesicle and micelle states, stimulating switching between folded and random coil states of DNA, building molecular motors, and designing pulsating drug delivery systems. We point out the importance for future applications of finding a batch pH oscillator, one that oscillates in a closed system for an extended period of time, and comment on the progress that has been made toward that goal.

Coupled chemical oscillators are usually studied with symmetric coupling, either between identical oscillators or between oscillators whose frequencies differ. Asymmetric connectivity is important in neuroscience, where synaptic strength inequality in neural networks commonly occurs. While the properties of the individual oscillators in some coupled chemical systems may be readily changed, enforcing inequality between the connection strengths in a reciprocal coupling is more challenging. We recently demonstrated a novel way of coupling chemical oscillators, which allows for manipulation of individual connection strengths. Here we study two identical, pulse-coupled Belousov–Zhabotinsky (BZ) oscillators with unequal connection strengths. When the pulse perturbations contain KBr (inhibitor), this system exhibits simple out-of-phase and complex oscillations, oscillatory-suppressed states as well as temporally periodic patterns (N:M) in which the two oscillators exhibit different numbers of peaks per cycle. The N:M patterns emerge due to the long-term effect of the inhibitory pulse-perturbations, a feature that has not been considered in earlier works. Time delay was previously shown to have a profound effect on the system’s behaviour when pulse coupling was inhibitory and the coupling strengths were equal. When the coupling is asymmetric, however, delay produces no qualitative change in behaviour, though the 1:2 temporal pattern becomes more robust. Asymmetry in instantaneous excitatory coupling via AgNO3 injection produces a previously unseen temporal pattern (1:N patterns starting with a double peak) with time delay and high [AgNO3]. Numerical simulations of the behaviour agree well with theoretical predictions in asymmetrical pulse-coupled systems.

While living systems have developed highly efficient ways to convert chemical energy (e.g., ATP hydrolysis) to mechanical motion (e.g., movement of muscle), it remains a challenge to build muscle-like biomimetic systems to generate mechanical force directly from chemical reactions. Here we show that a continuous flow of reactant solution leads to by far the largest volume change to date in autonomous active gels driven by the Belousov–Zhabotinsky reaction. These results demonstrate that microfluidics offers a useful and facile experimental approach to optimize the conditions (e.g., fabrication methods, counterions, flow rates, concentrations of reagents) for chemomechanical transduction in active materials. This work thus provides much needed insights and methods for the development of chemomechanically active systems based on combining soft materials and microfluidic systems.

We employ high-performance liquid chromatography with evaporative light scattering and mass spectrometric detection (HPLC/ELSD and LC/MS) to monitor the dynamic behavior of L-Pro, L-Hyp, and L-Pro–L-Hyp in 70% aqueous methanol. The individual amino acid solutions show evidence of oscillatory oligomerization. In the binary solution, the behavior is controlled by the dynamics of L-Pro oligomerization. A simple model involving oligomerization, formation of catalytic oligomer aggregates and cross-catalysis provides qualitative insight into the process.

A photosensitive self-oscillating gel that incorporates the Belousov–Zhabotinsky reaction can undergo rhythmic mechanical oscillations. We exploit the dependence of the oscillation frequency on light intensity to generate both photophobic and phototropic movement of the gel under differential illumination. Our findings may be used in designing intelligent sensors that can execute biomimetic behaviours.

We study the use of post-self-assembly cross-linking to combine molecular nanofibers of hydrogelators with copolymers to generate oscillatory materials using the Belousov–Zhabotinsky reaction. The formation of nanofibers from designed hydrogelators provides multiple polymerizable sites for copolymerizing with N-isopropylacrylamide and for attaching a catalytic ruthenium bipyridine complex on the copolymer. The combination of supramolecular self-assembly with copolymerization offers a versatile and facile approach for generating soft materials that have large pores in the gel network and robust mechanical integrity. These larger pores facilitate the diffusion of the reactants and accelerate the chemical oscillation by about a factor of 4 relative to a poly(NIPAAm-Ru) gel that contains no molecular nanofibers.

Patterns containing multiple length scales arise in a variety of natural systems such as lateral veins in leaves, fingerprints, wrinkled skin, and dendritic crystals. Here we observe period-doubling and bursting instabilities in the spatial extent of wave propagation in a gel-filled capillary tube open at one end and containing the Belousov–Zhabotinsky (BZ) reaction–diffusion system. We analyze the relationship between the multiple propagation distances of pulse waves and the local kinetics of the reaction–diffusion system. Simulations with a five-variable Oregonator model qualitatively mimic the multiple length scale patterns of pulse propagation observed in our experiments, suggesting that the study of these phenomena in reaction–diffusion systems may be helpful in understanding complex multiple length scale dynamical behaviors in nature.Keywords: Belousov−Zhabotinsky reaction; multiscale dissipative structures; Oregonator model; pulse waves; reaction-diffusion;

Evolution is a characteristic feature of living systems, and many fundamental processes in life, including the cell cycle, take place in a periodic fashion. From a chemistry perspective, these repeating phenomena suggest the question of whether reactions in which concentrations oscillate could provide a basis and/or useful models for the behavior of organisms, and perhaps even their ability to evolve.In this Account, we examine several aspects of the behavior of the prototype oscillating chemical reaction, the Belousov–Zhabotinsky (BZ) system, carried out in microemulsions, arrays of micrometer-sized aqueous droplets suspended in oil, or hydrogels. Each of these environments contains elements of the compartmentalization that likely played a role in the development of the first living cells, and within them we observe behaviors not found in the BZ reaction in simple aqueous solution. Several of these phenomena resemble traits displayed by living organisms. For example, the nanodroplets in a BZ microemulsion “communicate” with each other through a phenomenon analogous to quorum sensing in bacteria to produce a remarkable variety of patterns and waves on length scales 105 times the size of a single droplet. A photosensitive version can “remember” an imposed image. Larger, micrometer-sized droplets exhibit similarly rich behavior and allow for the observation and control of individual droplets. These droplets offer promise for building arrays capable of computation by varying the strength and sign of the coupling between drops. Gels that incorporate a BZ catalyst and are immersed in a solution containing the BZ reactants change their shape and volume in oscillations that follow the variation in the redox state of the catalyst. Using this phenomenon, we can construct phototactic gel “worms” or segments of gel that attract one another.Whether such systems will provide more realistic caricatures of life, and whether they can serve as useful materials will largely depend on the successful integration of various properties, including communication, motion, and memory, which we observed in separate experiments. Theoretical approaches that couple reaction and diffusion processes to mechanical and other material properties are likely to play a key role in this integration, and we describe one such approach. The evolution of systems of coupled chemical oscillators presents another challenge to the development of these systems, but one that we expect to be solved.

We designed and synthesised two new polymerizable ruthenium complexes that catalyse the Belousov–Zhabotinsky (BZ) oscillating reaction and incorporated them into a copolymer to form hydrogels. The periodic oxidation and reduction of the attached ruthenium complex in the BZ reaction induces hydrating and dehydrating effects, respectively, that result in self-oscillatory volume changes of the hydrogel. We evaluated the correlation between the chemomechanical oscillation properties of the hydrogel and the proximity of the catalyst to the polymer backbone. Our results indicate that, like the change of such macroscopic parameters as temperature, reactant concentrations and pH, varying the microscopic distance between the catalyst and the polymeric chain provides a new way to tailor the chemomechanical behaviour, e.g., the initiation time, the frequency of oscillation, and the volume change of BZ hydrogels. Moreover, variation of the catalysts offers a new means to control the microstructure of the copolymer by expanding the range of monomer ratios. Modulation of molecular structure appears to be an effective way to alter the reaction–diffusion profile of species within heterogeneous chemoresponsive gels, thus contributing to the development of multifunctional, active soft materials capable of converting chemical energy into controllable mechanical forces.

After a polymerizable hydrogelator self-assembles in water to form molecular nanofibers, post-self-assembly cross-linking allows the catalyst of the Belousov–Zhabotinsky (BZ) reaction to be attached to the nanofibers, resulting in a hydrogel that exhibits concentration oscillations, spiral waves, and concentric waves. In addition to the first report of the observation of BZ spiral waves in a hydrogel that covalently integrates the catalyst, we suggest a new approach to developing active soft materials as chemical oscillators and for exploring the correlation between molecular structure and far-from-equilibrium dynamics.

All pH-oscillators reported to date function only under open (flow reactor) conditions. We describe an approach to generating pH-oscillations in a closed system by starting from an open system pH-oscillator, finding semibatch conditions under which it oscillates with an inflow of a single reactant to an otherwise closed reactor containing the remaining components, and replacing this inflow with a layer of silica gel impregnated with the key reactant. We present data showing the successful application of this technique to the BrO3––Mn2+–SO32–, IO3––Fe(CN)64––SO32–, and BrO3––Fe(CN)64––SO32– systems. In all three cases, sulfite ion is the species that is replenished via dissolution from the gel layer.

Spatiotemporal pattern formation in the electrocatalytic oxidation of sulfide on a platinum disk is investigated using electrochemical methods and a charge-coupled device (CCD) camera simultaneously. The system is characterized by different oscillatory regions spread over a wide potential range. An additional series resistor and a large electrode area facilitate observation of multiple regions of kinetic instabilities along the current/potential curve. Spatiotemporal patterns on the working electrode, such as fronts, pulses, spirals, twinkling eyes, labyrinthine stripes, and alternating synchronized deposition and dissolution, are observed at different operating conditions of series resistance and sweep rate.

We report the successful use of Ru(II)(terpy)2 (1, terpy = 2,2′:6′,2′′-terpyridine) as a catalyst in the Belousov−Zhabotinsky (BZ) oscillating chemical reaction. We also examine several additional Ru(II) complexes, Ru(II)(bipy)2(L′)2 (2, L′ = 4-pyridinecarboxylic acid; bipy = 2,2′-bipyridine) and Ru(II)(bipy)2(L′′) (3, L′′ = 4,4′-dicarboxy-2,2′-bipy; 4, L′′ = N-allyl-4′-methyl-[2,2′-bipy]-4-carboxamide; 5, L′′ = bipy), for catalyzing the BZ reaction. While 2 is unable to trigger BZ oscillations, probably because of the rapid loss of L′ in a BZ solution, the other bipyridine-based Ru(II)-complexes can catalyze the BZ reaction, although their catalytic activity is adversely affected by slow ligand substitution in a BZ solution. Nevertheless, the successfully tested Ru(II)(terpy)2 and Ru(II)(bipy)2(L′′) catalysts may provide useful building blocks for complex functional macromolecules.

We employ high-performance liquid chromatography with diode array, evaporative light scattering, and mass spectrometric detection to monitor the oligomerization of l-lactic acid in pure acetonitrile and in 70% aqueous ethanol. The production of higher oligomers appears to proceed in an oscillatory fashion. A model is presented that involves the formation of aggregates (micelles), which catalyze the oligomerization.

We have carried out species determination and kinetic analysis in the hydrogen peroxide−thiosulfate reaction by means of capillary electrophoresis and high performance liquid chromatography. In addition to thiosulfate, dithionate, trithionate, and tetrathionate, other polythionates such as pentathionate and hexathionate were detected during the oxidation process. The polythionates found are sensitive to the pH, with the average length of the sulfur chain decreasing with increasing pH. By varying the pH and the concentrations of the reactants, we find that the reaction is first order with respect to each of the reactants with rate constant k = 0.025 M−1 s−1. With HOS2O3−, HSO3−/SO32−, S3O62−, S4O62−, and S5O62− as key intermediates that are eventually oxidized to sulfate, a proposed 14-step kinetic model simulates the reaction process, including the evolution of the thiosulfate and tetrathionate concentrations at various pHs.

We investigate the effect of changing temperature in the ferroin-catalysed Belousov–Zhabotinsky (BZ) reaction dispersed in the water nanodroplets of a water-in-oil aerosol OT (AOT) microemulsion, which undergoes a temperature-induced percolation transition at about 38 °C. We observe stationary Turing patterns at temperatures in the range 15–35 °C and bulk oscillations at T = 40–55 °C. When a temperature gradient ΔT is applied normal to a thin layer of the BZ–AOT reaction mixture, the range of patterns observed is dramatically expanded. Anti-phase oscillatory Turing patterns, leaping waves, and chaotic waves emerge, depending on the temperature gradient and the average temperature. These new patterns originate from the coupling between a low temperature Turing mode and a high temperature Hopf mode. Simulations with a simple model of the BZ–AOT system give good agreement with our experimental results.

Oscillations in the concentration of divalent ions Cd2+, Ca2+, Zn2+, Co2+ and Ni2+ are induced by adding these species to the BrO3−–SO32− chemical oscillator in a flow reactor. Producing periodic pulses in the concentrations of these non-redox ions extends our earlier approach to generating forced periodic behavior. Instead of driving pH-dependent equilibrium reactions of the target ion by a pH oscillator backward and forward, we now couple a redox core oscillating reaction to two consecutive reactions taking place between the components of the oscillator and the target element. In the systems examined here, the oscillatory reductant SO32− binds the free metal ion in a MSO3 precipitate, reducing its level to a minimal value when [SO32−] is high, followed by release of the metal ion when the sulfite is oxidized by BrO3−.

In earlier studies, we showed that certain low-molecular-weight carboxylic acids (profens, amino acids, hydroxy acids) can undergo spontaneous in vitro chiral conversion accompanied by condensation to from oligomers, and we proposed two simple models to describe these processes. Here, we present the results of investigations using non-chiral high-performance liquid chromatography with diode array detector (HPLC-DAD) and mass spectrometry (MS) on the dynamics of peptidization of S-, R-, and rac-phenylglycine dissolved in 70% aqueous ethanol and stored for times up to one year. The experimental results demonstrate that peptidization of phenylglycine can occur in an oscillatory fashion. We also describe, and carry out simulations with, three models that capture key aspects of the oscillatory condensation and chiral conversion processes.

Many phenomena of biological, physical, and chemical importance involve synchronization of oscillatory elements. We explore here, in several geometries, the behavior of diffusively coupled, nanoliter volume, aqueous drops separated by oil gaps and containing the reactants of the oscillatory Belousov−Zhabotinsky (BZ) reaction. A variety of synchronous regimes are found, including in- and antiphase oscillations, stationary Turing patterns, and more complex combinations of stationary and oscillatory BZ drops, including three-phase patterns. A model consisting of ordinary differential equations based on a simplified description of the BZ chemistry and diffusion of messenger (primarily inhibitory) species qualitatively reproduces most of the experimental results.Keywords (keywords): antiphase oscillation; Belousov-Zhabotinsky reaction; in-phase oscillation; synchronized oscillators; Turing patterns;

We study the oxidation dynamics of thiosulfate ions by hydrogen peroxide in the presence of trace amounts of copper(II) using the reaction temperature as a control parameter in a continuous flow stirred tank reactor. The system displays period-doubling, aperodic, and mixed-mode oscillations at different temperatures. We are able to simulate these complex dynamics with a model proposed by Kurin-Csörgei et al. The model suggests that the Cu2+-containing term is not essential for the observed oscillations. We find small-amplitude and high-frequency oscillations in the catalyst-free experimental system. The reaction between H2O2 and S2O32− contains the core mechanism of the H2O2−S2O32−−Cu2+ and H2O2−S2O32−−SO32- oscillatory systems, while the Cu2+ and SO32− modulate the feedback loops so as to strengthen the oscillatory dynamics.

Two-dimensional Liesegang patterns formed when the boundary between electrolytes is polygonal display a variety of patterns, such as dislocations (radial alleys of gaps), branches (anastomoses) and spirals, many of which can be found in nature. Each vertex of the polygon can produce a pair of dislocation lines or branch lines. The effect caused by a vertex decreases with the number of vertices. Double-armed spirals are observed in experiments with a pentagonal boundary. Hexagons, which begin to approach smooth circular boundaries, do not give rise to dislocations, but instead yield concentric precipitation rings. A simple model of nucleation growth enables us to simulate dislocations and spirals consistent with those seen in our experiments.

Cross-diffusion, the phenomenon in which a gradient in the concentration of one species induces a flux of another chemical species, has generally been neglected in the study of reaction–diffusion systems. We summarize experiments that demonstrate that cross-diffusion coefficients can be quite significant, even exceeding “normal,” diagonal diffusion coefficients in magnitude in systems that involve ions, micelles, complex formation, excluded volume effects (e.g., surface or polymer reactions) and other phenomena commonly encountered in situations of interest to chemists. We then demonstrate with a series of model calculations that cross-diffusion can lead to spatial and spatiotemporal pattern formation, even in relatively simple systems. We also show that, in the absence of cross-diffusion among the reacting species, introduction of a nonreactive species that induces appropriate cross-diffusive fluxes with reactive species can lead to pattern formation.

The BrO3−−SO32−−Fe(CN)64− (BSF) pH-oscillatory system is coupled to the Al(OH)3 precipitation equilibrium (BSFA system) and studied in a stirred flow reactor. The dynamic behavior of the BSFA system differs significantly from that of the BSF system. In addition to the large-amplitude pH oscillations found in the BSF system, new small-amplitude and mixed-mode oscillations occur. A detailed mechanism of the BSFA system is developed and investigated.

We explored the temperature-dependent dynamics of the electrochemical oxidation of thiourea under potential-control mode and found complex oscillations with one large peak and one small peak per period. Adjusting the temperature caused the relative amplitudes and positions of the two peaks to vary. Experiments showed that there were two distinct oscillatory regimes as a function of the external current, and at some temperatures, three-frequency quasiperiodic oscillations occurred for current densities between the two oscillatory windows. We examined the species present and the component reactions by employing cyclic voltammetry and electrolysis−HPLC−MS in the two oscillatory regimes. Adsorption and desorption of multiple species, including water and chloride, contribute to the rich dynamical phenomena that were observed.

We describe an improved Taylor dispersion method for four-component systems, which we apply to measure the main- and cross-diffusion coefficients in an Aerosol OT water-in-oil microemulsion loaded with one of the reactants of the Belousov−Zhabotinsky (BZ) reaction, water(1)/AOT(2)/R(3)/octane(4) system, where R is malonic acid or ferroin. With [H2O]/[AOT] = 11.8 and volume droplet fraction φd = 0.18, when the microemulsion is below the percolation transition, the cross-diffusion coefficients D13 and D23 are large and positive (D13/D33 ≅ 14, D23/D33 ≅ 3) for malonic acid and large and negative for ferroin (D13/D33 ≅ −112, D23/D33 ≅ −30) while coefficients D31 and D32 are small and negative for malonic acid (D31/D33 ≅ −0.01, D32/D33 ≅ −0.14) and small and positive for ferroin (D31/D33 ≅ 5 × 10−4, D32/D33 ≅ 8 × 10−3). These data represent the first direct determination of cross-diffusion effects in a pattern-forming system and of the full matrix of diffusion coefficients for a four-component system. The results should provide a basis for modeling pattern formation in the BZ−AOT system.

We employ reversed-phase ion-pair high-performance liquid chromatography to quantitatively characterize the oxidation kinetics of thiourea oxidation by hydrogen peroxide. The HPLC technique makes it possible to monitor the concentrations of a variety of sulfur-containing species with different oxidation states and to elucidate the relative phase relations among them. The experimental results are in good agreement with simulations from an 8-step reaction mechanism.

Waves and patterns in living systems are often driven by biochemical reactions with enzymes as catalysts and regulators. We present a reaction–diffusion system catalyzed by the enzyme glucose oxidase that exhibits traveling wave patterns in a spatially extended medium. Fronts and pulses propagate as a result of the coupling between the enzyme-catalyzed autocatalytic production and diffusion of hydrogen ions. A mathematical model qualitatively explains the experimental observations.

We describe a new type of solitary waves, which propagate in such a manner that the pulse periodically disappears from its original position and reemerges at a fixed distance. We find such jumping waves as solutions to a reaction–diffusion system with a subcritical short-wavelength instability. We demonstrate closely related solitary wave solutions in the quintic complex Ginzburg–Landau equation. We study the characteristics of and interactions between these solitary waves and the dynamics of related wave trains and standing waves.

We consider the response of complex systems to stimuli and argue for the importance of both sensitivity, the possibility of large response to small stimuli, and robustness, the possibility of small response to large stimuli. Using a dynamic attractor network model for switching of patterns of behavior, we show that the scale-free topologies often found in nature enable more sensitive response to specific changes than do random networks. This property may be essential in networks where appropriate response to environmental change is critical and may, in such systems, be more important than features, such as connectivity, often used to characterize network topologies. Phenomenologically observed exponents for functional scale-free networks fall in a range corresponding to the onset of particularly high sensitivities, while still retaining robustness.

•Copper(I) oxide nanoparticles can be synthesized by a simple reaction-diffusion process.•The mean diameter and the size dispersion of the particles are controlled by two experimental parameters.•The synthetic approach is a modification of that used to produce Liesegang rings.Copper (I) oxide nanoparticles are synthesized by a simple reaction-diffusion process involving Cu+ ions and sodium hydroxide in gelatin. The mean diameter and the size dispersion of the nanoparticles can be controlled by two experimental parameters, the percent of gelatin in the medium and the hydroxide ion concentration. UV–visible spectroscopy, transmission electron microscopy and X-ray diffraction are used to analyze the size, morphology, and chemical composition of the nanoparticles generated.

A photosensitive self-oscillating gel that incorporates the Belousov–Zhabotinsky reaction can undergo rhythmic mechanical oscillations. We exploit the dependence of the oscillation frequency on light intensity to generate both photophobic and phototropic movement of the gel under differential illumination. Our findings may be used in designing intelligent sensors that can execute biomimetic behaviours.

Coupled chemical oscillators are usually studied with symmetric coupling, either between identical oscillators or between oscillators whose frequencies differ. Asymmetric connectivity is important in neuroscience, where synaptic strength inequality in neural networks commonly occurs. While the properties of the individual oscillators in some coupled chemical systems may be readily changed, enforcing inequality between the connection strengths in a reciprocal coupling is more challenging. We recently demonstrated a novel way of coupling chemical oscillators, which allows for manipulation of individual connection strengths. Here we study two identical, pulse-coupled Belousov–Zhabotinsky (BZ) oscillators with unequal connection strengths. When the pulse perturbations contain KBr (inhibitor), this system exhibits simple out-of-phase and complex oscillations, oscillatory-suppressed states as well as temporally periodic patterns (N:M) in which the two oscillators exhibit different numbers of peaks per cycle. The N:M patterns emerge due to the long-term effect of the inhibitory pulse-perturbations, a feature that has not been considered in earlier works. Time delay was previously shown to have a profound effect on the system’s behaviour when pulse coupling was inhibitory and the coupling strengths were equal. When the coupling is asymmetric, however, delay produces no qualitative change in behaviour, though the 1:2 temporal pattern becomes more robust. Asymmetry in instantaneous excitatory coupling via AgNO3 injection produces a previously unseen temporal pattern (1:N patterns starting with a double peak) with time delay and high [AgNO3]. Numerical simulations of the behaviour agree well with theoretical predictions in asymmetrical pulse-coupled systems.

We investigate the effect of changing temperature in the ferroin-catalysed Belousov–Zhabotinsky (BZ) reaction dispersed in the water nanodroplets of a water-in-oil aerosol OT (AOT) microemulsion, which undergoes a temperature-induced percolation transition at about 38 °C. We observe stationary Turing patterns at temperatures in the range 15–35 °C and bulk oscillations at T = 40–55 °C. When a temperature gradient ΔT is applied normal to a thin layer of the BZ–AOT reaction mixture, the range of patterns observed is dramatically expanded. Anti-phase oscillatory Turing patterns, leaping waves, and chaotic waves emerge, depending on the temperature gradient and the average temperature. These new patterns originate from the coupling between a low temperature Turing mode and a high temperature Hopf mode. Simulations with a simple model of the BZ–AOT system give good agreement with our experimental results.

Two-dimensional Liesegang patterns formed when the boundary between electrolytes is polygonal display a variety of patterns, such as dislocations (radial alleys of gaps), branches (anastomoses) and spirals, many of which can be found in nature. Each vertex of the polygon can produce a pair of dislocation lines or branch lines. The effect caused by a vertex decreases with the number of vertices. Double-armed spirals are observed in experiments with a pentagonal boundary. Hexagons, which begin to approach smooth circular boundaries, do not give rise to dislocations, but instead yield concentric precipitation rings. A simple model of nucleation growth enables us to simulate dislocations and spirals consistent with those seen in our experiments.

Cross-diffusion, the phenomenon in which a gradient in the concentration of one species induces a flux of another chemical species, has generally been neglected in the study of reaction–diffusion systems. We summarize experiments that demonstrate that cross-diffusion coefficients can be quite significant, even exceeding “normal,” diagonal diffusion coefficients in magnitude in systems that involve ions, micelles, complex formation, excluded volume effects (e.g., surface or polymer reactions) and other phenomena commonly encountered in situations of interest to chemists. We then demonstrate with a series of model calculations that cross-diffusion can lead to spatial and spatiotemporal pattern formation, even in relatively simple systems. We also show that, in the absence of cross-diffusion among the reacting species, introduction of a nonreactive species that induces appropriate cross-diffusive fluxes with reactive species can lead to pattern formation.

Oscillations in the concentration of divalent ions Cd2+, Ca2+, Zn2+, Co2+ and Ni2+ are induced by adding these species to the BrO3−–SO32− chemical oscillator in a flow reactor. Producing periodic pulses in the concentrations of these non-redox ions extends our earlier approach to generating forced periodic behavior. Instead of driving pH-dependent equilibrium reactions of the target ion by a pH oscillator backward and forward, we now couple a redox core oscillating reaction to two consecutive reactions taking place between the components of the oscillator and the target element. In the systems examined here, the oscillatory reductant SO32− binds the free metal ion in a MSO3 precipitate, reducing its level to a minimal value when [SO32−] is high, followed by release of the metal ion when the sulfite is oxidized by BrO3−.