Poissonian stationary distribution in a class of detailed balanced reactions

We investigate those detailed balanced (vectorial) complex chemical reactions that belong to the class of simple Markovian population processes and show that there is no chemical reaction with independent reaction rates having a Poissonian stationary distribution. There exists, however, a manifold of reactions with dependent (as given) reaction rates and with Poissonian stationary distribution.

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Calcium complex grease as a low-polarity stationary phase

Considerable and unexpected thermal stability has been found with a calcium complex hydrocarbon grease proposed as a non-polar stationary phase. Although the polarity is unsatisfactory, improved stability has been achieved by the addition of an antioxidant. The use of an antioxidant increased significantly the thermal stability of low-polarity hydrogenated Apiezon M, which has been reported as an acceptable non-polar basic stationary phase for use of high temperatures.     

Kinetic insights over a PEMFC operating on stationary and oscillatory states

Kinetic investigations in the oscillatory state have been carried out in order to shed light on the interplay between the complex kinetics exhibited by a proton exchange membrane fuel cell fed with poisoned H(2) (108 ppm of CO) and the other in serie process. The apparent activation energy (E(a)) in the stationary state was investigated in order to clarify the E(a) observed in the oscillatory state. The apparent activation energy in the stationary state, under potentiostatic control, rendered (a) E(a) ≈ 50-60 kJ mol(-1) over 0.8 V < E < 0.6 V and (b) E(a) ≈ 10 kJ mol(-1) at E = 0.3 V. The former is related to the H(2) adsorption in the vacancies of the surface poisoned by CO and the latter is correlated to the process of proton conductivity in the membrane. The dependence of the period-one oscillations on the temperature yielded a genuine Arrhenius dependence with two E(a) values: (a) E(a) around 70 kJ mol(-1), at high temperatures, and (b) E(a) around 10-15 kJ mol(-1), at lower temperatures. The latter E(a) indicates the presence of protonic mass transport coupled to the essential oscillatory mechanism. These insights point in the right direction to predict spatial couplings between anode and cathode as having the highest strength as well as to speculate the most likely candidates to promote spatial inhomogeneities.     

Finding complex balanced and detailed balanced realizations of chemical reaction networks

Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not “encoded” in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability of the underlying reaction kinetic system when further conditions are also fulfilled. In this paper, efficient numerical procedures are given for finding complex balanced or detailed balanced realizations of mass action type chemical reaction networks or kinetic dynamical systems in the framework of linear programming. The procedures are illustrated on numerical examples.     

Global stability of complex balanced mechanisms

We prove that the ω‐limit set of any solution of a complex balanced chemical reaction mechanism contains either a unique, positive complex balanced equilibrium point, or boundary complex balanced equilibrium points. Then, using this result, we are able to provide global stability results for three enzymatic mechanisms. This revised version was published online in July 2006 with corrections to the Cover Date.     

Kinetic equations for thermal dissociation processes

Relationships between average degree of transformation and time of dissociation were derived for polydisperse granular materials with account to the type of grain size distribution. It has been checked, under what conditions the kinetic curves obtained by numeric solution of those relationships may be described in terms of equations D1 α²=kt , F2 [1/(1 - α) - 1 =kt] and F3 [1/(1 - α)² - 1=kt]. This revised version was published online in August 2006 with corrections to the Cover Date.     

Multiple stationary point representations in MC SCF calculations

By using a complete second-order Newton-Raphson multiconfigurational self-consistent field (MC SCF) procedure combined with the Fletcher restricted step constraint algorithm and a modification of the surface walking procedure of Simons et al., an MC SCF energy hypersurface at fixed geometry has been examined in considerably more detail than had been done previously. By calculational example, it is shown that there may exist several MC SCF stationary points which fulfill all four structural criteria we require of a state for being a “good” representation of an exact state. The problem with the existence of several stationary point solutions may be reduced if care is taken in the selection of the MC SCF configuration space. Calculational examples also demonstrate that near-lying stationary points exist which fulfill some, but not all, of these four structural criteria. Hence, stationary points should be obtained with a global MC SCF method which automatically eliminates convergence to as many as possible of these unwanted stationary points. Upon convergence, structural criteria which are not automatically fulfilled should be examined in detail.     

Kinetic analysis of complex reactions

TG and DSC techniques have been extensively used to study complex solid state reactions. For complex reactions (constituting of all exothermic or all endothermic one step first order individual reactions), it has been shown that the results of TG and DSC instruments may not be identical. This is because the TG instrument is incapable of correctly recording the true effective reaction rate of complex reactions (if the reaction rate is not proportional to the total amount of reactants). This may happen when the reaction rates of the individual reactions in the composite reaction mixture are significantly different. In this communication it has also been suggested that the Friedman analysis of obtaining activation energy (E) may be inapplicable for complex or composite reaction due to the fact that, there may be no unique effective constant conversion at various heating rates.

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Zusammenfassung TG- und DSC-Techniken wurden in großem Umfang zur Untersuchung komplexer Festkörperreaktionen herangezogen. Für (alle exotherme oder alle endotherme individuelle Einschritt-Reaktionen erster Ordnung in sich einschließende) komplexe Reaktionen wurde gezeigt, daß die Ergebnisse von TG- und DSC-Geräten nicht notwendigerweise identisch sind, weil das TG-Gerät die wahre effektive Reaktionsgeschwindigkeit komplexer Reaktionen nicht korrekt zu registrieren imstande ist (wenn die Reaktionsgeschwindigkeit nicht proportional der Gesamtmenge der Reaktanten ist). Dies kann der Fall sein, wenn die Reaktionsgeschwindigkeiten der individuellen Reaktionen im Reaktionsgemisch significant unterschiedlich sind. In der vorliegenden Publikation wird auch darauf hingewiesen, daß die Friedman-Analyse zur Ermittlung der Aktivierungsenergie (E) bei komplexen Reaktionen nicht unbedingt anwendbar ist, da die Konversion von der Aufheizgeschwindigkeit abhängig sein kann.

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The author would like to thank the reviewer for his comments.     

Kinetic analysis of a photosensitive chelator and its complex with Zn(II)

The reversible sequestration and release of metal ions is an important objective in biological and environmental research. Unfortunately, although there have been dramatic examples of metal ion activity control, there are very few quantitative investigations of stoichiometry, equilibria and kinetics. A significant contributor to this lack of quantitative work is the complexity of many photochromic systems. Therefore, we have attempted to create a simple, reversible photochromic metal-ion chelator that can be analyzed quantitatively. The chelator should have certain other attributes as well, namely, that it binds to divalent metal ions (because of their extreme biological importance) and that it binds metal ions in the dark so that light is used to release metal ions rather than sequester them. The photochromic chelator (1) binds to divalent metal ions [Zn(II), Cu(II), Pb(II), Hg(II), Fe(II), Co(II) and Cd(II); other metal ions have not yet been tested] in the dark with a significant binding strength. In both methanol (by spectrophotometry) and methanol-water (by voltammetry), the stoichiometry of the 1-Zn(II) complex is 2:1. The binding constant (K1K2) is on the order of 10(12)-10(14) M(-2) in methanol and 5.0 x 10(8) M(-2) in 50% aqueous methanol. The chelator 1 is photolabile, yielding 2 with a quantum efficiency of 0.91. In a solution containing excess Zn(II), so that over 99% of the ligand exists as the monodentate complex, photolysis produces 2 with a quantum efficiency of 0.15. A kinetic analysis leads to the conclusion that the complex itself is photolabile.     

Kinetic stability of complex molecular clusters

This investigation is concerned with modeling the evaporation, or decay, of n-nonane molecular clusters. We use a unique cluster decay model that was first developed to estimate the decay time scale of argon clusters using molecular-dynamics simulations. In this study we seek to enhance the model so that it represents a more complex cluster decay dynamic, suitable for n-nonane clusters. Experimental measurements of nucleation rates of n-nonane droplets have been used to deduce the rate at which a molecule escapes from the cluster. Typically for an n-nonane cluster containing 40 molecules, at an experimental temperature of 225 K, the empirical decay time, which is the inverse of the decay rate, is estimated to be 50 ns. For this time scale, the direct observation of n-nonane cluster decay from a molecular-dynamics trajectory is not feasible, since decay events are so rare. However, the cluster decay model uses a combination of molecular dynamics and stochastic dynamics in order to resolve the problem associated with long decay time scales. The model is based on a Langevin treatment that views cluster decay as single-particle escape from a confining potential of mean force. It is used to predict kinetic decay times of n-nonane clusters. We discover this result differs significantly from a classically derived decay time scale determined from a continuum thermodynamic treatment of the population balance equations of clusters. However, the dynamically generated results obtained from the kinetic decay model compare more favorably than the classical results with the empirical decay times that are deduced from experimental measurements of n-nonane clusters.     

Kinetic equations of isotope transfer by elementary reaction

On the basis of matrices of transfer of atoms kinetic equations of isotope transfer between the components participating in elementary reactions have been derived.

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Kinetic analysis of aluminum complex formation with different soil fulvic acids

A fluorescence technique was used to investigate the complex formation kinetics of aluminum with fulvic acids isolated from different forest soil environments. In the pH range of 2.4–3.6, all of the fulvic acids were found to contain two kinetically distinguishable components, which define two types of average aluminum binding sites. Both of these average sites on all of the fulvic acids conformed to a bidentate chelating binding site kinetic analysis, from which average rate and equilibrium parameters were obtained. Evidence indicated that the difference in reaction rate between the two types of aluminum binding sites on the fulvic acids was due to a steric strain, whereby aluminum was repelled from the slower reacting sites. In comparing this study with a similar kinetic study carried out in acetate buffered solutions, it was found that the presence of buffer changed both the overall mechanism by which aluminum reacted with fulvic acid, and the nature of the sites on fulvic acid that bind aluminum.     

Modified tight-binding equations for electron wave functions in crystals with point defects

A system of tight-binding equations for the electron wave function in infinite, semi-infinite, or interface crystals with point defects is transformed to a finite system for the coefficients of specially constructed converging and diverging waves. The solution of this finite system allows the construction of the electron wave function over all space. This makes it possible to calculate the electronic structure of a defect and its “images” in the various experimental methods used for studying defects in the bulk, on the surface, and at the interface of crystals, without conventional structural simplifications. The proposed method is applied to the calculation of point defects in a two-dimensional square lattice. G. K. Boreskov Institute of Catalysis, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 6, pp. 985–993, November–December, 1996. Translated by I. Izvekova     

Kinetic equations of isotope redistribution in an elementary reaction

Kinetic equations for the redistribution of isotopic molecules in an elementary reaction have been derived on the basis of atom distribution matrices.

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On coordinate transformations in steepest descent path and stationary point locations

Two aspects of the problems of calculating steepest descent paths and locating stationary points on surfaces E( X ), which are sources of some confusion in the literature, are addressed. These include writing proper expressions for the gradient and Hessian, and their transformation properties relative to coordinate transformations, based on the invariance of the surface E( X ). The appropriate transformation is derived, based on a constrained energy minimization condition, to achieve what we call the Hessian eigenvalue representation. This not only allows decoupling of the variables, but also points to the minimization direction and preserves the eigenvalues of the Hessian. These results allow one to use the steepest descent path and stationary point location algorithms in any coordinate system and obtain invariant results. The validity of these considerations are also confirmed through numerical examples. The stationary condition with constrained kinematic path length is also shown to yield a Hessian eigenvalue representation for the normal modes for small vibrations. Lastly, we have constructed a mathematically consistent definition of mass-weighted Cartesians where the intrinsic reaction path of Fukui is a steepest descent path. © 1992 John Wiley & Sons, Inc.     

Rapid determination of complex mixtures by dual-column gas chromatography with a novel stationary phase combination and spectrometric detection

Fast GC separations of a broad range of analytes are demonstrated using a capillary column coated with a novel immobilized ionic liquid (IIL) stationary phase. Both completely cross-linked and partially cross-linked columns were evaluated, yielding approximately 1600 and approximately 2000 theoretical plates per meter, respectively. Enhanced separation is demonstrated using a dual-column ensemble comprised of an IIL column, a commercially coated Rtx-1 column, and a pneumatic valve connecting the inlet to the junction point between the two columns. Enhanced separation of 20 components, with two sets of co-eluting peaks is shown in approximately 150 s, while sacrificing only a length of time equivalent to the sum of the stop flow pulses, or about 15.5 s. A novel application of a band trajectory model that shows band position as a function of analysis time as analytes move through the column ensemble is employed to determine pulse application times. The model predicts component retention times within a few seconds. Another method of selectivity enhancement of the IIL stationary phase-coated columns is demonstrated using a differential mobility spectrometer (DMS) that provides a second dimension separation based on ion mobility in a high-frequency electrical field. The DMS is able to separate all but one set of co-eluting components from the IIL column. The separation of 13 components found in the headspace above U.S. currency is demonstrated using the IIL column in a dual-column ensemble as well as with the DMS.     

Determining the independent parameters in stationary kinetic equations for linear mechanisms

Coloring methods in graph theory are used in estimating the number of parameters to be determined in a kinetic model corresponding to a linear mechanism. The estimates are based on determining the numbers of differently colored frameworks. Examples are discussed of isomerization and an enzymatic reaction catalyzed by ammonoacyl-MRNA synthetase.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, No. 2, pp. 187–191, March–April, 1987.     

Kinetic parameters of thermal decomposition of complex of β-cyclodextrin with water

The apparent kinetic parameters of the thermal decomposition of the-cyclodextrin-water complex were estimated from thermogravimetric data. Various calculation methods were used and the results compared. All methods except the Kissinger method gave a reaction order near to zero and an activation energy in the range 60 to 65 kJ/mol. Some trials were made to extrapolate the activation energy values to semi-isothermal conditions (65.7 kJ/mol). The loss in weight indicated the presence of 11 water molecules in the complex. This was liberated in single stage, despite its occurrence as two distinct types, as shown by crystallographic studies.

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Zusammenfassung Auf Grundlage von thermogravimetrischen Daten wurden die scheinbaren kinetischen Parameter des Thermozerfalles von-Cyclodextrin-Wasser- Komplexen geschätzt. Die durch verschiedene Rechenmethoden erhaltenen Ergebnisse wurden in Tabelle 3 verglichen. Mit Ausnahme der Kissinger-Methode ergaben alle Verfahren eine Reaktionsordnung von annähernd Null und eine Aktivierungsenergie im Bereich 60–65 kJ/mol. Ausserdem wurde versucht, die Aktivierungsenergiewerte auf halbisotherme Bedingungen zu extrapolieren (65.7 kJ/mol). Der Masseverlust weist elf Wassermoleküle im Komplex nach, die in einem einzigen Schritt abgegeben werden, ungeachtet dessen, dass kristallographische Untersuchungen die Wassermoleküle zwei verschiedenen Typen zuordnen.

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