Dynamics of chemical reactions and nonphysical steady states

Data on the position of nonphysical (lying beyond the region of determination) steady states are shown to be of use for understanding the dynamic behavior of chemical reactions, in particular, the reasons for slow relaxations.

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Analysis of fluctuations in chemical reactions with several steady states

The effect of fluctuations in nonequilibrium systems is treated in terms of the stochastic theory. A solution of the fundamental equation is analyzed using the Monte-Carlo method /1, 2/. The results are compared with the conclusions following from the equations corresponding to a phenomenological model.

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Experimental and theoretical investigations of steady and transient states in systems of ion exchange bipolar membranes

The electrochemical characteristics of one commercial bipolar ion exchange membrane and of two home-made bipolar membranes are investigated over a range of current densities up to 2 kA m⁻². Studies are performed using galvano-potentiometry (i/V) and impedance spectrometry methods. The temperature dependence of i/V curves enables the determination of the activation energies related to the overall electrochemical process of H⁺ and OH⁻ production by water dissociation at the membrane junction. The physical analysis of the experimental data is made on the basis of a neutral layer model for the membrane junction. The theoretical treatment leads first to establish a thermodynamic framework insuring the validity of the criteria used in the interpretation of the results in terms of the model. Application of current electrochemical kinetic concepts at steady state involves the idea that, in the presence of an efficient catalyst, a quasi-reversible state of the water dissociation reaction may be achieved at the junction. A theoretical approach is developed for treating the data obtained with transient measurements in absence of co-ion transport. This study reveals the intrinsic roles played in the overall process of respectively: (a) the H⁺ and OH⁻ ion transport; (b) the electrical double layers at the membrane junction boundaries; and (c) the chemical mechanism of water dissociation.     

Temporal asymmetry of fluctuations in nonequilibrium steady states

Temporal asymmetries of fluctuation paths in nonequilibrium microscopic shearing systems are observed for the first time. Inspired by theories that predict asymmetry of fluctuation paths in stochastic dynamics, we focus on deterministic reversible particle models, which represent a small part of a macroscopic system. We have monitored and measured the asymmetry of the fluctuation paths of various observables as they go away from and towards the mean. The understanding of such asymmetries may scatter light on how irreversibility emerges from the microscopic reversible dynamics and on the behavior of mesoscopic (nanoscale) systems.     

Multiplicity of steady states in oxidative heterogeneous catalysis

Typical mechanisms of heterogeneous catalytic reactions and their kinetíc models that are characterized by a plurality of steady states are considered. Models of adsorption that lead to a plurality of equilibrium adsorption states are discussed.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 4, pp. 285–300, July–August, 1992.     

Entropy production as a universal functional of reaction rate: chemical networks close to steady states

Entropy production rate (EPR) is the fundamental theoretical quantity in non-equilibrium thermodynamics whereas reaction rate is the primary experimental quantity for a chemical system out-of-equilibrium. In this work, we explore a connection between the above two quantities for general reaction networks. Both cyclic and linear networks of arbitrary dimension are studied, along with a mixed variety. The systems can attain a non-equilibrium steady state (NESS) under chemiostatic condition, which becomes the state of true thermodynamic equilibrium when detailed balance holds. We show that there exists a universal functional relationship of the EPR with reaction rate close to steady states for all the networks considered. Near a NESS, the former varies linearly with the reaction rate. On the other hand, around a true equilibrium, it varies quadratically with the latter. Numerical experiments justify our analytical findings quite transparently.     

Sensitivity amplification in the phosphorylation-dephosphorylation cycle: nonequilibrium steady states, chemical master equation, and temporal cooperativity

A new type of cooperativity termed temporal cooperativity [Biophys. Chem. 105, 585 (2003); Annu. Rev. Phys. Chem. 58, 113 (2007)] emerges in the signal transduction module of phosphorylation-dephosphorylation cycle (PdPC). It utilizes multiple kinetic cycles in time, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein. In the present paper, we thoroughly investigate both the deterministic (microscopic) and stochastic (mesoscopic) models and focus on the identification of the source of temporal cooperativity via comparing with allosteric cooperativity. A thermodynamic analysis confirms again the claim that the chemical equilibrium state exists if and only if the phosphorylation potential DeltaG=0, in which case the amplification of sensitivity is completely abolished. Then we provide comprehensive theoretical and numerical analysis with the first-order and zero-order assumptions in PdPC, respectively. Furthermore, it is interestingly found that the underlying mathematics of temporal cooperativity and allosteric cooperativity are equivalent, and both of them can be expressed by "dissociation constants," which also characterizes the essential differences between the simple and ultrasensitive PdPC switches. Nevertheless, the degree of allosteric cooperativity is restricted by the total number of sites in a single enzyme molecule that cannot be freely regulated, while temporal cooperativity is only restricted by the total number of molecules of the target protein that can be regulated in a wide range and gives rise to the ultrasensitivity phenomenon.     

On the multiplicity criterion for steady states in catalytic reactions

CNDO/2 studies of NH₃ adsorption in terms of cluster models of the-Al₂O₃ surface sites have revealed that coordinatively unsaturated aluminium ions occupying tetrahedral and octahedral sites are Lewis acids that are stronger in the former case. NH₃ molecule adsorption on these sites is accompanied by an increase in the H–N–H bond angle and a weakening of the N–H bond.

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/2 , -Al₂O₃ , , , , . NH₃ H–N–H N–H.

     

β-Modification of polypropylene and its two-component systems

β-modification and multi-component systems ofβ-polypropylene were prepared both under laboratory and processing conditions. Characteristic features of crystallization, melting, and annealing ofβ-PP are summarized. The very distinct memory effect in the melting and annealing ofβ-PP is also presented. The existence of a lower and an upper limit temperature ofβ-PP formation is demonstrated. The structural stability and the orientation-inducedβα-recrystallization ofβ-PP are analyzed. Preparation and properties of polymer blends and filled composites fromβ-PP are introduced, too.     

Limiting phenomena and multiplicity of steady states in gas-phase oxidation processes

It was found that in a chain-branching oxidation reaction of hydrogen at low pressures, there is a concentration range of the reagents over which there are three steady states: the boundaries of this range determine the positions of the limiting transitions between the regions of slow and rapid occurrence of the process. The dependences of the position of the limiting transitions in noncatalytic oxidation reactions of hydrogen and of oxidation of CO on platinum metals on the rate constants of the elementary stages of these processes have been compared. At different ratios of the rate constants of the heterogeneous-homogeneous catalytic process, the dependences of the reaction rate on the concentration of the reagent may contain a break, or may have the form of a loop or hystereses, both clockwise and counterclockwise.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 1, pp. 28–33, January–February, 1987.     

Simple catalytic mechanism permitting a multiplicity of catalyst steady states

The conditions of the existence of several steady states for a three-step mechanism, viz. a catalytic trigger (consecutive), are discussed.

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Histidine kinases and two-component signal transduction systems.

The phosphorylation of histidine is the first step in many signal transduction cascades in bacteria, yeast and higher plants. The transfer of a very reactive phosphoryl group from phosphorylated histidine kinase to an acceptor is an essential step in many cellular signaling responses.     

Forward and reverse excitation energy transport in concentrated two-component systems

The experimental and numerical study of the forward and reverse energy transport in concentrated two-component solutions is presented. Experimental results are compared with those of diagrammatic and hopping theories. It is shown that the effect of direct acceptor excitation by the light beam is important in the presence of the reverse transfer and it must be taken into account to describe correctly the experimental results within the framework of any theoretical model. This effect leads in particular to the decrease in the donor emission anisotropy and to the increase in its quantum yield. Our analysis indicates the advantage of the diagrammatic model over the hopping approach.     

Wavelet transform of quantum chemical states

By using the technique of integral within an ordered product of operators, we recast classical wavelet transform to a matrix element of the squeezing‐displacing operator U(μ,s) between the mother wavelet vector 〈ψ| and the state vector |f〉 to be transformed, i.e., we propose that 〈ψ|U(μ,s)|f〉 can be considered as a new kind of spectrum for analyzing the quantum state |f〉. In this way, we propose the wavelet‐ transform spectrum for quantum chemical states. As an example, we carry out the numerical calculation of wavelet‐transform spectrum for the binomial state. It seems to us that this kind of spectrum can be used to recognize a variety of quantum chemical states. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Dynamic properties of a heterogeneous catalytic reaction with several steady states

For the simplest catalytic mechanism (three-stage) permitting several steady states of the surface, a qualitative analysis of the properties of its kinetic model trajectories has been performed. Types of the steady states have been determined. Absence of oscillations (damped and undamped) has been shown.

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Для простейшего каталитического механизма (трехстадийного), допускающего несколько стационарных состояний поверхности, проведен качественный анализ свойств траекторий его кинетической модели. Определены типы стационарных состояний. Показано отсутствие осцилляций (затухающих и незатухающих).

     

The simplest catalytic mechanism permitting several steady states of the surface

The conditions for the existence of several steady states of the surface have been found for the simplest mechanism without the assumption of autocatalysis and without the effect of the medium on the catalyst. A possibility has been shown for the explanation of the multiplicity of steady states, found experimentally in the kinetic region, in terms of mechanisms including interactions between various intermediates.

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On bound states in two-body systems

The application of the Σ-separation method to the calculation of multicenter two-electron molecular integrals with Slater-type basis functions is reported. The approach is based on the approximation of a scalar component of the two-center atomic density by a two-center expansion over Slater-type functions. A least-squares fit was used to determine the coefficients of the expansion. The angular multipliers of the atomic density were treated exactly. It is shown that this approach can serve as a sufficiently accurate and fast algorithm for the calculation of multicenter two-electron molecular integrals with Slater-type basis functions. © 1995 John Wiley & Sons, Inc.