Spontaneous Formation of Microgroove Arrays on the Surface of p‐Type Porous Silicon Induced by a Turing Instability in Electrochemical Dissolution

Self‐organization plays an imperative role in recent materials science. Highly tunable, periodic structures based on dynamic self‐organization at micrometer scales have proven difficult to design, but are desired for the further development of micropatterning. In the present study, we report a microgroove array that spontaneously forms on a p‐type silicon surface during its electrodissolution. Our detailed experimental results suggest that the instability can be classified as Turing instability. The characteristic scale of the Turing‐type pattern is small compared to self‐organized patterns caused by the Turing instabilities reported so far. The mechanism for the miniaturization of self‐organized patterns is strongly related to the semiconducting property of silicon electrodes as well as the dynamics of their surface chemistry.     

Hydrodynamic Instabilities Driven by Acid-base Neutralization Reaction in Immiscible System

The hydrodynamic instabilities driven by an acid-base neutralization reaction, in contact along a plane interface, placed in a Hele-Shaw cell under the gravitational field are reported.The system consists of the heavier aqueous tetramethyle-ammonium hydroxide below the lighter layer of organic phase with propionic acid as reacting specie. The effect of chemical composition on hydrodynamic instabilities during interfacial mass transfer accompanied by a neutralization reaction is investigated. Depending on the initial concentration of the reacting species, Marangoni convection in the form of roll cells or trains of waves is observed. Mach-Zehnder interferometer is used to measure the change in base concentration at the time of instability formation. The results show that the instabilities resulted from the convection flow are more efficient to the mechanism of mass transfer and can drastically alter pattern formation in the system.     

Turing pattern formation in anisotropic medium

Diffusion of reacting species in chemical and biochemical systems in anisotropic medium is markedly different from those occurring in isotropic medium, therefore approximating diffusion coefficients as constants may not be desirable as this has dynamical consequences. This paper is devoted to the analytical and numerical investigation of the development of spatial patterns in such systems. To this end we consider a general reaction–diffusion system with concentration-dependent diffusion and formulate a scheme to derive the general form of envelope equation for such systems. The theory is applied to the chlorite–iodide–malonic acid system, a standard paradigm for activator–inhibitor mechanism, to derive the instability condition in terms of the anisotropy parameters (\(\kappa _{i}, i = u, v\) that impart concentration-dependence to the diffusion coefficients) and identify the supercritical and subcritical Turing regions in the bifurcation diagram. The theoretical predictions are in good agreement with the numerical simulations.     

On the origin of Turing instability

A reaction–diffusion system consisting of one, two or three chemical species and taking place in an arbitrary number of spatial dimensions cannot exhibit Turing instability if none of the reaction steps express cross‐inhibition. A corollary of this result – obtained by elementary calculations – underlines the importance of nonlinearity in the formation of stationary structures, a kind of self‐organization on a chemical basis. Relations to global stability of reaction–diffusion systems, and results on multispecies systems are also mentioned. The statements are not restricted to mass action type models. As a by‐product, the solution of a basic inverse problem of formal kinetics is also presented which extends a previous result by Hárs and Tóth (1981) to models with arbitrary – including rational – functions as reaction rates so often occurring, e.g., in enzyme kinetics.     

Turing pattern amplitude equation for a model glycolytic reaction-diffusion system

For a reaction-diffusion system of glycolytic oscillations containing analytical steady state solution in complicated algebraic form, Turing instability condition and the critical wavenumber at the Turing bifurcation point, have been derived by a linear stability analysis. In the framework of a weakly nonlinear theory, these relations have been subsequently used to derive an amplitude equation, which interprets the structural transitions and stability of various forms of Turing structures. Amplitude equation also conforms to the expectation that time-invariant amplitudes are independent of complexing reaction with the activator species.     

The Model of “Minimal Oscillator” Derived from the Kinetic Mechanism of the H2O2–NaSCN–NaOH–CuSO4 Dynamical System

Dissipative chemical reactions, which involve oscillatory variations of the concentrations of the intermediates in time, are usually characterized with complicated kinetic mechanisms. However, the essential source of the oscillations can often be reduced to only a few reaction steps providing the alternative domination of the positive and negative feedback loops. In an extreme case such a reduction leads to the so–called “minimal oscillator,” the concept used in the past for the well‐known Belousov‐Zhabotinsky (BZ) reaction. In the present work, we construct such a minimal system for the (discovered by M. Orbán) H₂O₂–NaSCN–NaOH–CuSO₄ homogeneous oscillator, in which instabilities originate from kinetic mechanism substantially different from that proposed for the BZ system. The methodology involves intuitive analysis of the reaction mechanism, supported by numerical calculations and spectrophotometric measurements. We show how the actual, only three‐variable model evolves from our previously elaborated: nine‐ and five–variable mechanisms and prove that its further reduction to two–variable one is not possible. Thus the present work is a final step in our searches for the “minimal Orbán oscillator”.     

Nanoscale changes induce microscale effects in Turing patterns

A water-in-oil microemulsion loaded with a reaction-diffusion chemical system (Belousov-Zhabotinsky reaction) is able to exhibit Turing patterns that are believed to be responsible for differentiation processes in Nature. Using polymers, such as polyethylene oxide, longer than the droplet size changes the distribution of droplets due to cluster formation. This difference in the nanoscale has relevant consequences in the observed the Turing pattern's wavelength, which is three orders of magnitude larger than the droplet size.     

庚酸甲酯高温燃烧化学动力学机理的系统简化和分析

采用详细化学反应动力学机理的系统简化方法, 对庚酸甲酯高温燃烧化学动力学机理进行了系统简化. 首先采用两步直接关系图法(Directed relation graph method, DRG)和主成分分析(Principle component analysis, PCA)方法对由1087个物种、4592步可逆反应组成的庚酸甲酯燃烧的详细机理进行框架简化, 得到了包含108个物种, 547步基元反应的框架机理. 在此框架机理基础上, 进一步采用计算奇异值摄动法(Computational singular perturbation, CSP)对框架机理进行时间尺度分析, 再选取30个准稳态物种, 采用准稳态近似(Quasi steady state approximation, QSSA)方法构建了包含78个物种、74步总包反应的全局简化机理. 模拟结果表明, 在较宽的参数范围内, 框架机理和全局简化机理均能重现庚酸甲酯高温燃烧时的点火延迟、物种浓度分布和熄火等燃烧特性. 此外, 基于框架机理阐明了庚酸甲酯高温燃烧的反应路径和对点火有重要影响的基元反应. 与详细机理相比, 框架机理保留了良好的精确性和全局性, 可以很好地反映庚酸甲酯的燃烧特性, 有助于对生物柴油的燃烧过程的理解.     

529—Chemical reactions and oscillating potential difference variations at an oil-water interface

Oscillatory potential and difference interfacial tension variation can be observed at an oil-water interface containing charge species when the conditions are such that hydrodynamic instabilities can occur. We propose a mechanism based on an experimental study accountable for the relaxation-type oscillations observed. It involves the coupling of a chemical reaction occurring in the bulk in the vicinity of the interface with an interfacial transfer by diffusion and adsorption-desorption processes.     

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.     

Pentanary cross-diffusion in water-in-oil microemulsions loaded with two components of the Belousov-Zhabotinsky reaction

We measure cross-diffusion coefficients in a five-component system, an aerosol OT (AOT) water-in-oil microemulsion loaded with two constituents of the Belousov-Zhabotinsky (BZ) reaction (H(2) O/AOT/BZ1/BZ2/octane). The species BZ1 is either NaBr, an inhibitor of the BZ reaction, or ferroin, a catalyst for the reaction. As species BZ2, we choose Br(2) , an intermediate in the reaction. The cross-diffusion coefficients between BZ1 and BZ2 are found to be negative, which can be understood in terms of complexation between these species. Using a four-variable model for the BZ reaction, we find that the cross-diffusion coefficients measured here can lead to a noticeable shift in the onset of Turing instability in the BZ-AOT system.     

Density functional calculations for predicting structures and vibrational frequencies of aluminum chloride-fluoride complexes

Quantum chemical calculations are used to study AlCl_y−xF_x^3−y (y = 5 or 6, x = 0,…,y) species that can occur in aluminum electrorefining melts. These theoretical studies are included in a wider research program concerning the chemical instabilities in the bulk of molten salts during the refinement process. Stabilization energies, equilibrium geometries and vibrational frequencies of the complexes are calculated using the Delley functional methodology described in Ref. [1] (B. Delley, J. Chem. Phys., 92 (1990) 508). These computational simulations, discussed and compared with the experimental results demonstrate that density functional calculations can be reliably used in the study of complexes existing in molten salts. Quantum chemical calculations are accurate tools for theoretically predicting structures, physical and chemical properties and vibrational frequencies of known entities as well as unknown compounds.     

Application of chemical graph theory for automated mechanism generation

We present an application of the chemical graph theory approach for generating elementary reactions of complex systems. Molecular species are naturally represented by graphs, which are identified by their vertices and edges where vertices are atom types and edges are bonds. The mechanism is generated using a set of reaction patterns (sub-graphs). These subgraphs are the internal representations for a given class of reaction thus allowing for the possibility of eliminating unimportant product species a priori. Furthermore, each molecule is canonically represented by a set of topological indices (Connectivity Index, Balaban Index, Schulz TI Index, WID Index, etc.) and thus eliminates the probability for regenerating the same species twice. Theoretical background and test cases on combustion of hydrocarbons are presented.     

铂电极BZ反应系双电层稀疏区中的Turing结构

将扩散流作为场函数, 考虑φ电势的空间分布, 建立了铂电极BZ反应系在双电层稀疏区的动力学演化机制, 确立了纳入稀疏区φ电势效应的反应-扩散型演化方程. 采用Boltzmann分布近似, 解决了演化方程中含φ电势的流项的线性化问题; 导出了可在算法上实现的三变量体系线性化算子本征值的解析形式. 分别以静态铂电极BZ反应系双电层稀疏区和对应的纯粹BZ反应系作为参考模型系, 分析了经空间对称性破缺产生Turing结构的参数范围. 数值模拟发现, φ电场的存在使铂电极BZ反应系的输运过程在静态双电层稀疏区趋于电化学平衡时, 在对应的纯粹BZ反应体系中可呈现的Turing结构已趋于消失; 而在电流强度不太大的恒流不可逆铂电极BZ反应体系双电层稀疏区中, 鲜明稳定的Turing结构又重新出现在原参数区间内. 同时, 在静态双电层稀疏区不出现Turing结构的参数范围内也可找到类似的恒流稳定空间结构.     

Analysis on First-stage Ignition of n-Heptane at Low Temperatures with a Lumped Skeletal Mechanism

Two-stage ignition exists in the low-temperature combustion process of n-heptane and the first-stage ignition also shows a negative temperature coefficient(NTC) phenomenon. To study key reactions and understand chemical principles affecting the first-stage ignition of n-heptane, a lumped skeletal mechanism with 62 species is obtained based on the detailed NUIGMech1.0 mechanism using the directed relation graph method assisted by sensitivity analysis and isomer lumping. The lumped mechanism shows good performance on ignition delay time under wide conditions. The study revealed that the temperature after the first-stage ignition is higher and a larger amount of fuel is consumed at lower initial temperatures. The temperature at the first-stage ignition is relatively insensitive to the initial temperature. Further sensitivity analysis and reaction path analysis carried out based on the lumped mechanism show that the decomposition of RO₂ to produce alkene and HO₂is the most important reaction to inhibit the first-stage ignitions. The chain branching explosion closely related to the first-stage ignition will be terminated when the rate constant for the RO₂ decomposition is larger than that of the isomerization of RO₂ to produce QOOH. The NTC behavior as well as other characteristics of the first-stage ignition can be rationalized from the competition between these two reactions.     

Triplet organometallic reactivity under ambient conditions: an ultrafast UV pump/IR probe study.

The reactivity of triplet 16-electron organometallic species has been studied in room-temperature solution using femtosecond UV pump IR probe spectroscopy. Specifically, the Si-H bond-activation reaction of photogenerated triplet Fe(CO)(4) and triplet CpCo(CO) with triethylsilane has been characterized and compared to the known singlet species CpRh(CO). The intermediates observed were studied using density functional theory (DFT) as well as ab initio quantum chemical calculations. The triplet organometallics have a greater overall reactivity than singlet species due to a change in the Si-H activation mechanism, which is due to the fact that triplet intermediates coordinate weakly at best with the ethyl groups of triethylsilane. Consequently, the triplet species do not become trapped in alkyl-solvated intermediate states. The experimental results are compared to the theoretical calculations, which qualitatively reproduce the trends in the data.     

Kinetic Evidence for a Non‐Langmuir‐Hinshelwood Surface Reaction: H/D Exchange over Pd Nanoparticles and Pd(111)

The mechanism of hydrogen recombination on a Pd(111) single crystal and well‐defined Pd nanoparticles is studied using pulsed multi‐molecular beam techniques and the H₂/D₂ isotope exchange reaction. The focus of this study is to obtain a microscopic understanding of the role of subsurface hydrogen in enhancing the associative desorption of molecular hydrogen. HD production from H₂ and D₂ over Pd is investigated using pulsed molecular beams, and the temperature dependence and reaction orders are obtained for the rate of HD production under various reaction conditions designed to modulate the amount of subsurface hydrogen present. The experimental data are compared to the results of kinetic modeling based on different mechanisms for hydrogen recombination. We found that under conditions where virtually no subsurface hydrogen species are present, the HD formation rate can be described exceptionally well by a classic Langmuir–Hinshelwood model. However, this model completely fails to reproduce the experimentally observed high HD formation rates and the reaction orders under reaction conditions where subsurface hydrogen is present. To analyze this phenomenon, we develop two kinetic models that account for the role of subsurface hydrogen. First, we investigate the possibility of a change in the reaction mechanism, where recombination of one subsurface and one surface hydrogen species (known as a breakthrough mechanism) becomes dominant when subsurface hydrogen is present. Second, we investigate the possibility of the modified Langmuir–Hinshelwood mechanism with subsurface hydrogen lowering the activation energy for recombination of two hydrogen species adsorbed on the surface. We show that the experimental reaction kinetics can be well described by both kinetic models based on non‐Langmuir–Hinshelwood‐type mechanisms.     

Development of a chemical structure comparison method for integrated analysis of chemical and genomic information in the metabolic pathways

Cellular functions result from intricate networks of molecular interactions, which involve not only proteins and nucleic acids but also small chemical compounds. Here we present an efficient algorithm for comparing two chemical structures of compounds, where the chemical structure is treated as a graph consisting of atoms as nodes and covalent bonds as edges. On the basis of the concept of functional groups, 68 atom types (node types) are defined for carbon, nitrogen, oxygen, and other atomic species with different environments, which has enabled detection of biochemically meaningful features. Maximal common subgraphs of two graphs can be found by searching for maximal cliques in the association graph, and we have introduced heuristics to accelerate the clique finding and to detect optimal local matches (simply connected common subgraphs). Our procedure was applied to the comparison and clustering of 9383 compounds, mostly metabolic compounds, in the KEGG/LIGAND database. The largest clusters of similar compounds were related to carbohydrates, and the clusters corresponded well to the categorization of pathways as represented by the KEGG pathway map numbers. When each pathway map was examined in more detail, finer clusters could be identified corresponding to subpathways or pathway modules containing continuous sets of reaction steps. Furthermore, it was found that the pathway modules identified by similar compound structures sometimes overlap with the pathway modules identified by genomic contexts, namely, by operon structures of enzyme genes.     

On the origin of Turing instability

A reaction–diffusion system consisting of one, two or three chemical species and taking place in an arbitrary number of spatial dimensions cannot exhibit Turing instability if none of the reaction steps express cross‐inhibition. A corollary of this result – obtained by elementary calculations – underlines the importance of nonlinearity in the formation of stationary structures, a kind of self‐organization on a chemical basis. Relations to global stability of reaction–diffusion systems, and results on multispecies systems are also mentioned. The statements are not restricted to mass action type models. As a by‐product, the solution of a basic inverse problem of formal kinetics is also presented which extends a previous result by Hárs and Tóth (1981) to models with arbitrary – including rational – functions as reaction rates so often occurring, e.g., in enzyme kinetics. This revised version was published online in July 2006 with corrections to the Cover Date.