Turing patterns in the chlorine dioxide-iodine-malonic acid reaction with square spatial periodic forcing

We use the photosensitive chlorine dioxide-iodine-malonic acid reaction-diffusion system to study wavenumber locking of Turing patterns to two-dimensional "square" spatial forcing, implemented as orthogonal sets of bright bands projected onto the reaction medium. Various resonant structures emerge in a broad range of forcing wavelengths and amplitudes, including square lattices and superlattices, one-dimensional stripe patterns and oblique rectangular patterns. Numerical simulations using a model that incorporates additive two-dimensional spatially periodic forcing reproduce well the experimental observations.     

Spatial bistability and waves in a reaction with acid autocatalysis

The phenomenon of spatial bistability has recently been proposed for a comprehensive understanding of a number of chemical patterns observed in open spatial reactors consisting of thin films of gel diffusively fed from one side. We study experimentally and numerically this phenomenon in the tetrathionate-chlorite reaction characterized by an acid superautocatalysis. We focus on the similarities and differences with previous studies on the chlorine dioxide-iodide reaction. In addition, we show that this reaction, which is only bistable in a continuous stirred tank reactor, can exhibit oscillatory and traveling waves when diffusion comes into play. Our computations suggest that the nonstationary behaviour originates from differential diffusive transport.     

Locking of Turing patterns in the chlorine dioxide-iodine-malonic acid reaction with one-dimensional spatial periodic forcing

We use the photosensitive chlorine dioxide-iodine-malonic acid reaction-diffusion system to study wavenumber locking of Turing patterns with spatial periodic forcing. Wavenumber-locked stripe patterns are the typical resonant structures that labyrinthine patterns exhibit in response to one-dimensional forcing by illumination when images of stripes are projected on a working medium. Our experimental results reveal that segmented oblique, hexagonal and rectangular patterns can also be obtained. However, these two-dimensional resonant structures only develop in a relatively narrow range of forcing parameters, where the unforced stripe pattern is in close proximity to the domain of hexagonal patterns. Numerical simulations based on a model that incorporates the forcing by illumination using an additive term reproduce well the experimental observations. These findings confirm that additive one-dimensional forcing can generate a two-dimensional resonant response. However, such a response is considerably less robust than the effect of multiplicative forcing.     

Friction-induced pattern formation and Turing systems

We investigate the possibility of Turing-type pattern formation during friction. Turing or reaction-diffusion systems describe variations of spatial concentrations of chemical components with time due to local chemical reactions coupled with diffusion. Turing systems can lead to a variety of complex spatial patterns evolving with time. During friction, the patterns can form at the sliding interface due to the mass transfer (diffusion), heat transfer, various tribochemical reactions, and wear. We present simulation data showing the possibility of such pattern formation. On the other hand, existing experimental data suggest that in situ tribofilms can form at the frictional interface due to a variety of friction-induced chemical reactions (oxidation, the selective transfer of Cu ions, etc.). These tribofilms as well as other frictional "secondary structures" can form various patterns (islands or honeycomb domains). This mechanism of pattern formation can be attributed to the Turing systems.     

Modeling chlorite-iodide reaction dynamics using a chlorine dioxide-iodide reaction mechanism

The mechanism of Lengyel, Li, Kustin, and Epstein (J. Am. Chem. Soc. 1996, 118, 3708) for the oscillatory chlorine dioxide-iodide reaction accurately models the reaction in closed and open systems. We investigated whether this mechanism minus the single reaction involving chlorine dioxide models the chlorite-iodide reaction equally well. It agrees qualitatively with clock reaction results. As for open system dynamics, the mechanism predicts the existence of two steady states and bistability in very nearly the same regions where these features are found experimentally in the pH range 2-4. A discrepancy in the range of bistability emerges as pH decreases, and it cannot be remedied by taking into account chlorous acid decomposition. That we were unable to locate an oscillatory region is of greater significance. Because the chlorite-iodide reaction is sensitive to mixing effects, we incorporated a two-parameter model of imperfect mixing but still found no oscillations at physically reasonable parameter values. These discrepancies strongly suggest that to obtain predictive utility for the chlorite-iodide reaction, revision of the chlorine dioxide-iodide mechanism is required.     

Multiple types of spatio-temporal oscillations induced by differential diffusion in the Landolt reaction

The acid autoactivated iodate-sulfite redox reaction (Landolt reaction) exhibits bistability but no oscillatory dynamics when operated in a continuous stirred tank reactor (CSTR). However, it has been previously found experimentally that this reaction can exhibit both spatial bistability and oscillations when carried out in a one side diffusely fed spatial reactor. The precise origin of the oscillatory instability remained mainly elusive. We unambiguously show, in numerical simulations based of a kinetic model recently proposed by Csek?et al., J. Phys. Chem., 2008, 112, 5954), that the observed oscillations are due to the faster diffusion of the proton relative to the other feed species (long range activation instability). Furthermore, our calculations account for the previous experimental observation of two different oscillatory modes. The first one is associated to localized front oscillations, as already reported in another reaction. The other one is a periodic switch between the two states of the spatial bistability and affects the system as a whole. This oscillatory mode was undocumented in the previous studies of long range activation instabilities. More complex dynamical behaviors that mix these two types of oscillations are also reported.     

Particle dynamics simulations of Turing patterns

The direct simulation Monte Carlo method is used to reproduce Turing patterns at the microscopic level in reaction-diffusion systems. In order to satisfy the basic condition for the development of such a spatial structure, we propose a model involving a solvent, which allows for disparate diffusivities of individual reactive species. One-dimensional structures are simulated in systems of various lengths. Simulation results agree with the macroscopic predictions obtained by integration of the reaction-diffusion equations. Additional effects due to internal fluctuations are observed, such as temporal transitions between structures of different wavelengths in a confined system. For a structure developing behind a propagating wave front, the fluctuations suppress the induction period and accelerate the formation of the Turing pattern. These results support the ability of reaction-diffusion models to robustly reproduce axial segmentation including the formation of early vertebrae or somites in noisy biological environments.     

Formation and control of Turing patterns and phase fronts in photonics and chemistry

We review the main mechanisms for the formation of regular spatial structures (Turing patterns) and phase fronts in photonics and chemistry driven by either diffraction or diffusion. We first demonstrate that the so-called ‘off-resonance’ mechanism leading to regular patterns in photonics is a Turing instability. We then show that negative feedback techniques for the control of photonic patterns based on Fourier transforms can be extended and applied to chemical experiments. The dynamics of phase fronts leading to locked lines and spots are also presented to outline analogies and differences in the study of complex systems in these two scientific disciplines.     

Aromatic chlorination of omega-phenylalkylamines and omega-phenylalkylamides in carbon tetrachloride and alpha,alpha,alpha-trifluorotoluene

The aromatic halogenation of simple alkylbenzenes with chlorine proceeds smoothly in acetic acid but is much less efficient in less polar solvents. By contrast chlorination of omega-phenylalkylamines, such as 3-phenylpropylamine, occurs readily in either acetic acid, carbon tetrachloride or alpha,alpha,alpha-trifluorotoluene, and in the latter solvents gives high proportions of ortho-chlorinated products. These effects are attributable to the involvement of N-chloroamines as reaction intermediates, with intramolecular delivery of the chlorine electrophile. Omega-phenylalkylamides, such as 3-phenylpropionamide, also easily undergo aromatic chlorination in carbon tetrachloride and alpha,alpha,alpha-trifluorotoluene. These reactions generally show a first-order dependence on the substrate concentration, but not on the amount of chlorine. With carbon tetrachloride, very similar reaction rates are observed with chlorine concentrations ranging from 0.1-1.5 M. In alpha,alpha,alpha-trifluorotoluene, the rates reach a plateau at a chlorine concentration of approximately 0.2 M. These features indicate that the reactions proceed via the formation of intermediates which evidence suggests may be the corresponding O-chloroimidates. Irrespective of the mechanistic details, the reactions are remarkably rapid, being faster than analogous reactions in acetic acid and three to four orders of magnitude more rapid than reactions of simple alkylbenzenes in carbon tetrachloride. Therefore, chlorination of the amines and amides may be accomplished without the need for highly polar solvents, added catalysts or large excesses of chlorine, which are often employed for electrophilic aromatic substitutions. Although the use of carbon tetrachloride is becoming increasingly impractical due to environmental concerns, the trifluorotoluene is a suitable alternative.     

Surface-catalyzed chlorine and nitrogen activation: mechanisms for the heterogeneous formation of ClNO, NO, NO2, HONO, and N2O from HNO3 and HCl on aluminum oxide particle surfaces

It is well-known that chlorine active species (e.g., Cl(2), ClONO(2), ClONO) can form from heterogeneous reactions between nitrogen oxides and hydrogen chloride on aerosol particle surfaces in the stratosphere. However, less is known about these reactions in the troposphere. In this study, a potential new heterogeneous pathway involving reaction of gaseous HCl and HNO(3) on aluminum oxide particle surfaces, a proxy for mineral dust in the troposphere, is proposed. We combine transmission Fourier transform infrared spectroscopy with X-ray photoelectron spectroscopy to investigate changes in the composition of both gas-phase and surface-bound species during the reaction under different environmental conditions of relative humidity and simulated solar radiation. Exposure of surface nitrate-coated aluminum oxide particles, from prereaction with nitric acid, to gaseous HCl yields several gas-phase products, including ClNO, NO(2), and HNO(3), under dry (RH < 1%) conditions. Under humid more conditions (RH > 20%), NO and N(2)O are the only gas products observed. The experimental data suggest that, in the presence of adsorbed water, ClNO is hydrolyzed on the particle surface to yield NO and NO(2), potentially via a HONO intermediate. NO(2) undergoes further hydrolysis via a surface-mediated process, resulting in N(2)O as an additional nitrogen-containing product. In the presence of broad-band irradiation (λ > 300 nm) gas-phase products can undergo photochemistry, e.g., ClNO photodissociates to NO and chlorine atoms. The gas-phase product distribution also depends on particle mineralogy (Al(2)O(3) vs CaCO(3)) and the presence of other coadsorbed gases (e.g., NH(3)). These newly identified reaction pathways discussed here involve continuous production of active ozone-depleting chlorine and nitrogen species from stable sinks such as gas-phase HCl and HNO(3) as a result of heterogeneous surface reactions. Given that aluminosilicates represent a major fraction of mineral dust aerosol, aluminum oxide can be used as a model system to begin to understand various aspects of possible reactions on mineral dust aerosol surfaces.     

Synthesis in the 2-mercaptobenzothiazole series V. Thiazolidino[2, 3-b]-benzothiazolines

Reaction of 2-mercaptobenzothiazoles substituted at position 6 by chlorine, dimethylsulfamido, benzamido, and nitro groups, with chlorobromoalkanes, is used to synthesize the corresponding 6-substituted 2-(-chloroalkylmercapto)benzothiazoles. Oxidation of these compounds with hydrogen peroxide in acetic acid converts them to sulfoxides and sulfones, while heating in nitrobenzene cyclizes them to 6 substituted 2,3-dihydrothiazolo[2,3-b]benzothiazolium chlorides. The latter and previously obtained quaternary salts are converted by sodium borohydride into derivatives of a new tricyclic system, thiazolidino[2,3-b]benzothiazoline.For Part IV see [1].     

Effect of gel network on pattern formation in the ferrocyanide-iodate-sulfite reaction

Stationary patterns have been researched experimentally since the discovery of the Turing pattern in the chlorite-iodide-malonic acid (CIMA) reaction and the self-replicating spot pattern in the ferrocyanide-iodate-sulfite (FIS) reaction. In this study, we reproduced the pattern formation in the FIS reaction by using poly(acrylamide) gels. Gels with different swelling ratios were prepared to use as a medium. The effect of the swelling ratio was compared with the effect of thickness. It was found that the swelling ratio greatly influenced pattern formation. Oscillating spot patterns appeared at high swelling ratios, and lamellar patterns appeared at a low swelling ratio. Self-replicating spot patterns appeared in between the two areas. The front velocities, which were observed in the initial stage of pattern formation, depended on the swelling ratio. Furthermore, this dependence obeys the free volume theory of diffusion. These results provide evidence that the change in front velocities is caused by a change in diffusion. Pattern formation can be controlled not only by thickness but also by swelling ratio, which may be useful for creating novel pattern templates.     

Pattern formation in the iodate-sulfite-thiosulfate reaction-diffusion system

Sodium polyacrylate-induced pH pattern formation and starch-induced iodine pattern formation were investigated in the iodate-sulfite-thiosulfate (IST) reaction in a one-side fed disc gel reactor (OSFR). As binding agents of the autocatalyst of hydrogen ions or iodide ions, different content of sodium polyacrylate or starch has induced various types of pattern formation. We observed pH pulses, striped patterns, mixed spots and stripes, and hexagonal spots upon increasing the content of sodium polyacrylate and observed iodine pulses, branched patterns, and labyrinthine patterns upon increasing the starch content in the system. Coexistence of a pH front and an iodine front was also studied in a batch IST reaction-diffusion system. Both pH and iodine front instabilities were observed in the presence of sodium polyacrylate, i.e., cellular fronts and transient Turing structures resulting from the decrease in diffusion coefficients of activators. The mechanism of multiple feedback may explain the different patterns in the IST reaction-diffusion system.     

Superlattice patterns and spatial instability induced by delay feedback

Various oscillatory superlattice patterns in a reaction-diffusion system are observed by means of delay feedback (DF) in the parametric domain where the system without DF displays uniform bulk oscillation. By varying DF parameters within an appropriate range, the system undergoes transitions to oscillatory hexagons, stripes and squares, and square superlattices with different wavenumbers are also obtained. Linear stability analysis reveals that the patterns do not result from the Turing instability and a possible mechanism of pattern formation is suggested and proved analytically: DF induces instability of a homogeneous limit cycle with respect to spatial perturbations even if the Turing instability does not occur, so that oscillatory patterns possessing the corresponding spatial modes are produced. The different behavior of the dominant characteristic multiplier seems to be connected to the pattern selection. Here it is clearly demonstrated that DF can play a destabilizing role in spatially extended system instead of stabilizing the periodic orbits or turbulent states, which most earlier works have usually focused on.     

Dancing waves in reaction-diffusion systems

The mechanism of pattern formation in reaction-diffusion systems is treated as an interesting subject, generally for understanding self-organization observed in living systems and natural phenomena. Several spatial patterns appear in the reaction-diffusion systems where an activator and an inhibitor coexist as an intermediate, as represented by a traveling wave, a stationary wave called a Turing structure, etc. Here, we show new kinds of waves in reaction-diffusion systems, which exhibit reciprocating motion without colliding into each other or blinking periodically. These patterns have never been observed in the conventional numerical models, although experimentally oscillating spots have been often observed. Our model demonstrates that other than the ratio of diffusion coefficients for both intermediates, the thickness of reaction media acts to generate inhibitory effect. The spatial factor of the medium contributes to new pattern formation in reaction-diffusion systems. For the design of new functional materials, the concept might be useful as a simple controlling method for pattern dynamics.     

Reaction of P(III) chlorides with aldehydes: II. Reaction of primary intermediates with aprotic nucleophiles: Ethylene oxide,acetals, trialkyl orthoformates,and trialkyl phosphites

Structure of primary intermediates of the reaction of P(III) chlorides with aliphatic aldehydes was confirmed by their reactions with such aprotic reagents like ethylene oxide, trialkyl phosphites, acetals, and trialkyl orthoformates. Principle difference in the reactions of these nucleophiles with intermediates containing active chlorine atom at P(III) and those not containing was established. The former as well as all the other P(III) chlorides react directly with nucleophiles, while the latter slowly decompose into aldehyde and P(III) chloride, and the latter reacts with the nucleophile.     

Chlorine atom and ClO wall reaction products

The products of the heterogeneous reactions of chlorine atoms and chlorine oxide radicals with acid coated Pyrex walls have been directly determined for the first time. Contrary to the usual assumption that chlorine atoms recombine to form Cl₂, we find that the major product is HCl, with small amounts of perchlorate also formed. Similarly, ClO radicals form HCl rather than Cl₂. The source of hydrogen for these reactions is probably the water always found in this type of vacuum system. These results may change the interpretation of flow tube experiments with chlorine atoms. Application to the H + HCl reaction is discussed as an example.     

Hydration of Cl<Superscript>–</Superscript> ion in a planar nanopore with hydrophilic walls. 1. Molecular structure

Computer simulation has been employed to obtain equilibrium molecular configurations, as well as spatial and angular distributions of water molecules, under the action of the field of a single-charged chlorine anion in a model planar nanopore with structureless walls at room temperature. A detailed many-body model of intermolecular interactions calibrated in accordance with experimental data relative to the free energy of hydration in water vapor has been used. The effect of the hydrophilicity of the walls on the ion hydration shell consists in its disintegration into two parts, i.e., molecules retained exclusively due to the interactions with the ion and those adsorbed on the walls. In the regime of strong interactions with the walls, two relatively stable states arise with asymmetric distribution of molecules between opposite walls. The existence of the two metastable states destabilizes the position of ions inside a pore and is expected to accelerate their adsorption on the walls.     

Self‐Organized Stationary Patterns in Networks of Bistable Chemical Reactions

Experiments with networks of discrete reactive bistable electrochemical elements organized in regular and nonregular tree networks are presented to confirm an alternative to the Turing mechanism for the formation of self‐organized stationary patterns. The results show that the pattern formation can be described by the identification of domains that can be activated individually or in combinations. The method also enabled the localization of chemical reactions to network substructures and the identification of critical sites whose activation results in complete activation of the system. Although the experiments were performed with a specific nickel electrodissolution system, they reproduced all the salient dynamic behavior of a general network model with a single nonlinearity parameter. Thus, the considered pattern‐formation mechanism is very robust, and similar behavior can be expected in other natural or engineered networked systems that exhibit, at least locally, a treelike structure.