Convective Instability of the Limiting Current of the Triiodide Reduction in an Electrolytic Cell with Horizontal Electrodes

The instability of the limiting current of cathodic reaction in the system I^– ₃ – I^–– Pt with excess of KI is studied experimentally in a cell with two horizontal one-side electrodes. The observed velocity oscillation fluctuations at average frequency of about 0.01 Hz are typical for convective instability of solution within a boundary layer of the cathode whose working surface faces upward. The limits of existence of different types of convective instability in the system are determined in a Cartesian space of partial Rayleigh numbers for solution components KI and I₂.     

低浓度三分子模型差速流动引起的化学不稳定性

建立了低浓度三分子反应模型反应-流动-扩散方程,理论分析了出现差速流动化学不稳定的条件,得到了临界流动速率c和扰动波包的群速度vg,讨论了扰动增长率与流速的关系,并理论研究了出现不稳定时系统的时、空结构.研究结果表明,化学反应在低浓度条件下也可能出现差速流动引起的化学不稳定.     

Features of the real structure of pseudoboehmites: Violations of the structure and layer packing caused by crystallization water

Rietveld structure refinement and simulation of the diffraction patterns of partially disordered materials are used to study the real structure of nanoscale pseudoboehmite samples obtained by different technologies. The effect of various violations in the structure of these nanomaterials on diffraction patterns is analyzed. The introduction of corrections for the Lorentz and polarization factors in the determination of the cell parameter b by the position of the 020 diffraction peak in the pattern is shown to be important. A model for the atomic structure of pseudoboehmite is proposed. The model involves additional water molecules as compared to the structure of boehmite. The water molecules in the interlayer space of the layered boehmite structure are found to violate its regularity, which results in a decrease in the size of crystallites.     

On the different types of states of a one dimensional system of electrons in the Hartree-Fock method

We consider the different types of ground states of one-dimensional lattice gas of electrons. Interactions between electrons on the same lattice point and on neighboring lattice points are taken into account. The treatment is based on Hartree-Fock approximation for an unbounded system. Regions of the parameter space of the electron-electron interaction are found corresponding to the existence of mixed solutions (i.e., diagonal and nondiagonal long-range order are present stimultaneously). It is shown that the ground state of the system always corresponds to one of the pure types of order (only diagonal or only nondiagonal long-range order) and that diagonal order is present in the ground state. Conditions for the stability of the pure solutions against various perturbations are found.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 5, pp. 513–520, September–October, 1989.The authors thank V. Ya. Krivnov for useful discussions.     

Negative-tension instability of scroll waves and winfree turbulence in the oregonator model

Excitable media support self-organized scroll waves which can be unstable and give rise to three-dimensional wave chaos. Winfree turbulence of scroll waves results from the negative-tension instability of scroll waves; it plays an important role in the cardiac tissue where it may lead to ventricular fibrillation. By numerical simulations of the Oregonator model, we show that this instability and, thus, the Winfree turbulence may also be observed in the Belousov-Zhabotinsky reaction. The region in the parameter space, where the instability takes place, is determined, and a relationship between the negative-tension instability and the meandering behavior of spiral waves is found. The application of global periodic forcing to control such turbulence in the Oregonator model is discussed.     

Role of ohmic losses in appearance of dynamic instabilities in model electrochemical system with cylindrical electrode under potentiostatic conditions

The impedance spectroscopy technique was used for theoretical studies of the conditions of appearance of Hopf instability and saddle-node instability in a model electrochemical system with a preceding homogeneous chemical reaction in the Nernst diffusion layer and electrocatalytic reaction on the surface of a cylindrical electrode under potentiostatic conditions. It is shown that the value of the ohmic resistance parameter in the system can affect the number of bifurcation points and bifurcation frequency. An increase in the ohmic resistance parameter results in the narrowing of the region of Hopf bifurcation giving rise to spontaneous periodical current oscillations and expansion of the region of saddle-node instability leading to bistability. There are threshold values of the ohmic resistance parameters critical for appearance and disappearance of the dynamic instabilities under consideration.     

A simplified model of oscillating electrolytes

Unstable electrophoretic transport leading to oscillations in concentration profiles occur in certain electrolyte systems known as oscillating electrolytes whose eigenmobilities are complex valued. The study of the nonlinear behavior of such systems is of great interest but is constrained due to a high degree of complexity in the governing equations. Here we present a simplified model of unstable electrophoretic transport in a binary system that reduces the governing equations to two partial differential equations only and does away with other equations that characterize acid–base dissociation reactions and electroneutrality. We present analytical expressions for electromigration fluxes and validate the model with full nonlinear simulations. The model exhibits similar nonlinear behavior as the actual unstable electrophoretic system under various initial disturbances. For comparison, we also show that similar modeling for a stable system predicts concentration profiles that quantitatively agree with its nonoscillating dynamics. Moreover, the unique feature of electromigration flux in oscillating electrolytes that unfolds from the modeling led us to find an elegant explanation of the instability mechanism. Our theory gives a qualitative understanding of the existence and growth of large oscillation patterns in oscillating electrolytes.     

Flow-alignment and viscosity rules for single-phase binary mesomorphic mixtures

A macroscopic model for incompressible homogeneous (single phase) binary nematic mixtures, under isothermal conditions is given. The rheological model is a generalization of the standard Ericksen's nematorheological model for single component uniaxial rod-like nematic liquid crystals. Its special cases include single component orthorhombic biaxial nematics and single component uniaxial nematics. The theory is used to formulate rules for the rotational viscosity and the reactive parameter of nematic mixtures in the presence of weak flows. The predicted mixture rules for the reactive parameter and rotational viscosity are analysed as a function of concentration and rotational viscosity ratio for various monomeric and polymeric mixtures, and for rod-rod, disc-disc, and rod-disc nematic mixtures. The mixture rules are used to compute alignment phase diagrams and alignment transition (orientational instability) thresholds.     

Properties of combustion waves in the model with competitive exo- and endothermic reactions

In this paper we investigate the properties of the travelling combustion wave solutions in a diffusion-thermal model with a two-step competitive exo–endothermic reaction mechanism in one spatial dimension under adiabatic conditions. The model is analysed both numerically and analytically using asymptotic analysis. It is demonstrated that depending on the parameter values, the flame speed as a function of parameters is either a single-valued monotonic function or a double-valued c-shaped function with the turning point type of behaviour. For the case of single-valued flame speed, two flame regimes are identified: the regime with exo- and endothermic reaction domination. Two different routes to extinction are found as well as regions of the existence of combustion waves in the parameter space. Prospects of further work are also discussed.     

The effect of the order of the autocatalysis on the transverse stability of reaction fronts

A linear stability analysis of planar reaction fronts to transverse perturbations is considered for a system based on an autocatalytic reaction of general order p. Dispersion curves, plots of the growth rate sigma against a transverse wavenumber k, are obtained for a range of values of p and D, where D is the ratio of the diffusion coefficients of autocatalyst and substrate. A value D(0) of D, dependent on p, is found at which sigma(max), the maximum value of sigma in the unstable regime, is largest, with D(0) increasing as p is increased. An asymptotic analysis for small wavenumbers is derived, which enables the region in the (p, D) parameter space for instability to be determined. An analysis for D small is undertaken, which leads to upper bounds on the wavenumber for a possible instability.     

Precise simulation of the freezing transition of supercritical Lennard-Jones

The fluid-solid transition of the Lennard-Jones model is analyzed along a supercritical isotherm. The analysis is implemented via a simulation method which is based on a modification of the constrained cell model of Hoover and Ree. In the context of hard-sphere freezing, Hoover and Ree simulated the solid phase using a constrained cell model in which each particle is confined within its own Wigner-Seitz cell. Hoover and Ree also proposed a modified cell model by considering the effect of an external field of variable strength. High-field values favor configurations with a single particle per Wigner-Seitz cell and thus stabilize the solid phase. In previous work, a simulation method for freezing transitions, based on constant-pressure simulations of the modified cell model, was developed and tested on a system of hard spheres. In the present work, this method is used to determine the freezing transition of a Lennard-Jones model system on a supercritical isotherm at a reduced temperature of 2. As in the case of hard spheres, constant-pressure simulations of the fully occupied constrained cell model of a system of Lennard-Jones particles indicate a point of mechanical instability at a density which is approximately 70% of the density at close packing. Furthermore, constant-pressure simulations of the modified cell model indicate that as the strength of the field is reduced, the transition from the solid to the fluid is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the Lennard-Jones system is obtained by analyzing the field-induced fluid-solid transition of the modified cell model in the high-pressure, zero-field limit. The simulations are implemented under constant pressure using tempering and histogram reweighting techniques. The coexistence pressure and densities are determined through finite-size scaling techniques for first-order phase transitions which are based on analyzing the size-dependent behavior of susceptibilities and dimensionless moment ratios of the order parameter.     

Numerical Study of Electroconvective Instability of Binary Electrolyte in a Cell with Plane Parallel Electrodes

Electroconvective instability of a binary electrolyte in a cell with plane parallel electrodes is studied using a numerical method. When a direct current is passed through the cell, a space charge and an electrical force acting upon the solution form under certain conditions. If the electric force density reaches a critical value, convective instability emerges in the cell, leading to the formation of nonequilibrium dissipative structures similar to Rayleigh–Benard cells in a nonuniformly heated liquid. The critical parameter _crit, at which instability emerges in the system, is determined. Dependences of _crit on the ratio between the diffusion coefficients for electrolyte cations and anions and on the current passed through solution are determined.     

Numerical Study of Rayleigh–Benard Instability of a Binary Electrolyte in a Cell with Plane Parallel Electrodes Taking into Account the Space Charge

An electrochemical system consisting of two plane horizontal electrodes of the same metal and the interelectrode space filled with solution of a salt of this metal is considered. The conditions of emergence of Rayleigh–Benard convective instability in this system are investigated using a numerical method. Two reasons for the instability are taken into account: the buoyant force and the electrical force caused by a very small space charge formed near the electrode, at which the electrochemical reaction proceeds at the limiting diffusion current. The instability emergence conditions are characterized by critical values of two parameters corresponding to the aforementioned forces. The mutual effect of these forces on the instability emergence and an essential role of the ratio between the diffusion coefficients of electrolyte cations and anions are revealed.     

Self-assembly and elastic instability in polymer flows

This paper is devoted to the discussion of problems related to elastic instability arising in polymer flows. A new model of the rotary dynamics of macromolecules in shear fields of different geometries is proposed. The model is based on the nonlinear finite-difference Schródinger equation describing the process of self-assembly for the system of bonded macromolecules as rotators. It is shown that the self-assembly of macromolecules is accompanied by the chaos-order transition that creates prerequisites for the flow elastic instability obeying the bifurcation mechanism. The self-assembly of macromolecules in shear fields is accompanied by the growth of the space scale in the molecular correlation and can lead to formation of rheological spiral and fibril superlattices.     

Selkov模型不同扩散和流速下非Turing不稳定化学反应机制

建立了Selkov模型中间反应物具有不同扩散和不同流速条件下的反应-扩散-流动方程,理论分析了非Turing不稳定形成的条件,求得其参数区间,对Andresen的结论作了拓展.研究还发现,在振荡Hopf区域之外,静止波动(空间周期结构FDS)仍然可以存在.因而,此结构存在的参数空间大于Andresen的结果.同时,还将此种不稳定参数区间与Turing不稳定和差速流动引起不稳定(DIFI)的结果进行了比较,结果发现静态FDS值总是处于DIFI临界曲线相应的最小值之上,这表明动力学机制是由DIFI不稳定造成的,DIFI不稳定区是产生静止波FDS不稳定结构的必要条件.     

A realistic kinetic Monte Carlo simulation of the faceting of a Pt(110) surface under reaction conditions

The faceting process on Pt(110) is studied with the help of a kinetic Monte Carlo model taking into account realistic Pt-Pt, Pt-CO, and Pt-O interactions. The activation energies of the allowed atomic steps are estimated using available computational and experimental data. The model well reproduces the region in the parameter space where faceting occurs. Under kinetic instability conditions, the simulated faceted pattern forms a periodic hill and valley structure with a lateral periodicity of approximately 140-170 A, which is comparable with experimental data. The simulations reproduce the development of faceting on a realistic time scale.     

从多重定态到化学振荡

通过对化学反应体系动力学模型的分析, 论证了通过在多重定态体系中引入适当慢反馈步骤设计化学振荡体系的可能性, 提出了这类体系的动力学方程具有振荡解的判据以及在参数平面内划分振荡区域的方法。采用这种途径具体分析了一氧化碳在铂催化剂上氧化产生振荡现象的机理。     

Numerical Simulation of Rayleigh–Bènard Instability in Solutions Containing Ions of Three Types

The conditions for appearance of a Rayleigh–Benard instability (RBI) induced by a constant current between two horizontal electrodes in solution containing electroactive ions and indifferent electrolyte (system with three kinds of ions) are analyzed. It is taken into account that all the components take part in the formation of buoyant forces. The problem is solved for a stationary case (as an expansion to a series by a small parameter), and then equations for low perturbations are solved by the Galerkin method. The calculation is performed with a program that accounts for any number of members in a Galerkin expansion. A diagram is obtained, which determines conditions for the RBI emergence in terms of ratios of partial Raleigh numbers. The ratio of diffusion coefficients for supporting cations and anions significantly affects position of the boundary dividing ranges of convective stability and RBI in a diagram of nonequilibrium phase transitions.     

Turbulent states in a reaction-diffusion system with period-doubling bifurcations

We investigate the spatially extended Hastings–Powell model in one and two dimensions with constant diffusion coefficients and nonflux boundary conditions. Nowave zones, spirals and chaos are found. An absolute instability of the spirals produces a transition to chaos. A constant number of defects, linearly increasing with the bifurcation parameter of the system is found, i.e. there do not exist defect-creation or defect-destruction events. Defects behave as hard disks, with translational degrees of freedom, which result from a cooperative interaction between pairs of defects.     

Periodic and chaotic behavior of substrate-inhibited enzymatic reactions with hydrogen ions production

A two-compartment model of an enzyme system with substrate inhibition kinetics and hydrogen ion production is investigated. The model is used to study the bifurcation, instability, and chaotic behavior of the system. The investigation, although in a restricted region of the parameters’ space, has uncovered a good part of the rich dynamic characteristics of this system, including: period doubling sequences leading to chaos, banded chaos, fully developed chaos, interior crisis, tangent bifurcation leading to intermittency, periodic windows interrupting chaotic regions, and alternating periodic chaotic sequences. The results relate to the phenomena occurring in physiological experiments, such as the periodic stimulation of neural cells and the voltagegated ion channel dynamics.