A generalization of Wegscheider's condition. Implications for properties of steady states and for quasi-steady-state approximation

A generalization of Wegschcider's condition concerning equilibrium constants in chemically reacting systems is formulated, which is then proved to be a necessary and sufficient condition for detailed balancing. In order to include a large multitude of rate laws, a generalized mass action kinetics is considered which comprises usual mass action kinetics and all reversible enzyme kinetics and which is consistent with basic postulates of irreversible thermodynamics for ideal mixtures. Reaction systems of arbitrary stoichiometry are considered. They may contain reactants with fixed concentrations, as is characteristic for models of biochemical reaction networks. Existence, uniqueness, and global asymptotic stability of equilibrium states for reaction systems endowed with generalized man action kinetics are proved. Using these results, he generalized Wegscheider condition is shown to be a sufficient criterion for the applicability of the quasi-steady-state approximation.     

Positive equilibria of weakly reversible power law kinetic systems with linear independent interactions

In this paper, we extend our study of power law kinetic systems whose kinetic order vectors (which we call “interactions”) are reactant-determined (i.e. reactions with the same reactant complex have identical vectors) and are linear independent per linkage class. In particular, we consider PL-TLK systems, i.e. such whose T-matrix (the matrix with the interactions as columns indexed by the reactant complexes), when augmented with the rows of characteristic vectors of the linkage classes, has maximal column rank. Our main result states that any weakly reversible PL-TLK system has a complex balanced equilibrium. On the one hand, we consider this result as a “Higher Deficiency Theorem” for such systems since in our previous work, we derived analogues of the Deficiency Zero and the Deficiency One Theorems for mass action kinetics (MAK) systems for them, thus covering the “Low Deficiency” case. On the other hand, our result can also be viewed as a “Weak Reversibility Theorem” (WRT) in the sense that the statement “any weakly reversible system with a kinetics from the given set has a positive equilibrium” holds. According to the work of Deng et al. and more recently of Boros, such a WRT holds for MAK systems. However, we show that a WRT does not hold for two proper MAK supersets: the set PL-NIK of non-inhibitory power law kinetics (i.e. all kinetic orders are non-negative) and the set PL-FSK of factor span surjective power law kinetics (i.e. different reactants imply different interactions).     

Capillary rise kinetics of some building materials

The presence of water in masonry is one of the main factors in deterioration. Capillary rise is the most usual mechanism of water penetration into building materials. In this study the kinetics of the capillary rise phenomenon was studied for various building materials: four stones, two bricks, and six plasters. A first-order kinetic model was proposed, in which the equilibrium moisture height derived from Darcy law. The capillary height time constant found to be strongly affected by the material characteristics. Moreover, the capillary height time constant can be predicted if the average pore radius of the materials is known.     

Kinetic approach to chemical reactions and inelastic transitions in a rarefied gas

A kinetic approach is presented for the analysis of a gas mixture with two kinds of nonconservative interactions. In a bimolecular chemical reaction, mass transfer and energy of chemical link arise, and in inelastic mechanical encounters, molecules get excited or de‐excited due to their quantized structure. Molecules undergo transitions between energy levels also by absorption and emission of photons of the self‐consistent radiation field. From the kinetic Boltzmann‐type equations, the problem of equilibria and of their stability is addressed. A detailed balance principle is proved and a Lyapunov functional is constructed; mass action law and Planck's law of radiation are recovered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermodynamic Analysis of Chemically Reacting Mixtures and Their Kinetics: Example of a Mixture of Three Isomers

Thermodynamics provides consequences of and restrictions on chemically reacting mixtures, particularly their kinetics, which have not been fully explored. Herein, a comprehensive thermodynamic analysis is illustrated for a reacting mixture of three isomers. The rate equation is first derived on the basis of the results of nonequilibrium continuum thermodynamics of linear fluids, and is then subjected to the requirement of consistency with entropic inequality (the second law). This consistency test involves the correct representation of the reaction rate as a function of affinities. It is shown that entropic inequality restricts the signs or values of coefficients in the constitutive equations for reaction rates/rate constants. The use of reverse rate constants and the identification of thermodynamic and kinetic equilibrium constants are not necessary in this approach. Although the presented thermodynamic analysis works only for independent reactions, the rates of dependent reactions are not excluded from having effects on kinetics. It is shown that the rates of dependent reactions are combined from the rates of independent reactions differently than dependent reactions are combined from independent reactions. The results are compared to the classical mass‐action rate equations, and new restrictions on the values of the classical rate constants are derived.     

Law of Mass Action Type Chemical Mechanisms for Modeling Autocatalysis and Hypercycles: Their Role in the Evolutionary Race

One of our most appealing challenge is to unravel the role of a presumably autocatalytic system in controlling the origin and spreading of Life on our entire planet. Here we show that in the simplest autocatalytic loop involving reactions capable of self-replication and obeying law of mass action kinetics, concentration growth of the autocatalyst may be characterized by parametrization of direct and autocatalytic pathways rather than by kinetic orders of the autocatalyst. Extending this model by feasible elementary steps allows us to outline super-exponential growth where kinetic order of the autocatalyst is higher than unity. Furthermore, it is shown in case of the simplest hypercycle that such a situation might appear where the otherwise more sluggish autocatalytic route receives a decisive support from the crosscatalytic pathway to become an apparently stronger autocatalytic loop even if the other route contains a more efficient autocatalysis. If the hypercycle is performed under flow conditions selection of autocatalyst depends on kinetic and flow parameters influenced by external factors mimicking that the most adaptive loop of hypercycle eventually finds its wining way in the evolutionary race.     

Decay kinetics of the excited S1 state of the cyanine dye Cy(+)I(-) (thiacarbocyanine iodide): the computation of quantum yields for different pathways

This work explains the unordinary solvent effect which was observed in the photochemical decay kinetics for the cyanine dye thiacarbocyanine iodide (Cy(+)I(-)) in binary solvent mixtures toluene/dimethylsulfoxide. The interpretation is formulated in terms of the probability density F(R) describing the distribution of interionic distances R in the ion pair Cy(+)I(-) and depending on the solvent composition. The proper normalization of this distribution is expressed via the degree of association α for the ion pair in a given solvent mixture. The α values are, in turn, extracted by means of the mass action law from the ionic association constants computed in a separate publication. The detailed kinetic scheme includes the empirical parametrization of the R-dependent kinetic constants for different decay channels. The multiparameter fitting procedure represents, with the reasonable parameter values, the dependence of the observed quantum yields on the solvent composition.     

A kinetic expression for the pyrolytic decomposition of polytetrafluoroethylene

Despite the fact that the thermal decomposition of polytetrafluoroethylene has been extensively studied over the past six decades, some inconsistencies regarding the kinetic parameters, e.g. the order of the reaction, remain. Representative kinetic data are essential for practical purposes such as reactor design and scaling. In general the literature data refer to homogeneous bulk heating, whereas the case of the non-homogeneous heating of a single particle has not received attention. Data (reaction rate and pre-exponential factor) applicable to this latter case were experimentally determined from isothermal thermogravimetric analyses of the depolymerisation reaction of PTFE. The kinetic data obtained on coarse granules (800-1000 μm) are reported here. The rate law is consistent with a shrinking particle kinetic model, with chemical kinetics controlling phase-boundary movement. The mass loss rate is directly proportional to surface area. A rate law applicable to this case, and useable for geometries of arbitrary shape, is derived.     

Convolution potential sweep voltammetry V. Determination of charge transfer kinetics deviating from the Butler-Volmer behaviour

Convolution potential sweep voltammetry is applied to the analysis of charge transfer kinetics. The possibility of using the method without assuming a priori the validity of a given kinetic law, e.g. the Butler-Volmer law as usually done, is illustrated on the example of the reduction of tert-nitrobutane in acetonitrile and dimethylformamide. It is found that the post-factum experimental kinetics indeed deviate significantly from the Butler-Volmer behavior, involving a dependence of the transfer coefficient α upon the electrode potential. It is shown that the experimental variations of α match the orders of magnitude predicted by the Marcus theory. A procedure is proposed and applied for determining the reversible half-wave potential for redox couples in which one species is not quite stable chemically by combining the cyclic voltammetry and CPSV data.     

Carbothermal synthesis of titanium nitride (TiN): Kinetics and mechanism

Constant rate thermal analysis (CRTA) has been used for studying the kinetics of the carbothermal reduction of anatase in nitrogen. It is noteworthy to point out the ability of CRTA method for discriminating the kinetic law of solid-state reactions with considerably higher precision than conventional (TG, DTA, isothermal etc.) methods. The precise control of the reaction rate implies either direct or indirect control of both the partial pressure of CO generated in the reaction and the heat evolution rate, which allows to minimize the influence of heat and mass transfer phenomena. It has been shown that this synthesis is best described by a Johnson–Mehl–Avrami (with n = 2) kinetic model with an activation energy that fall in the range 162–165 kJ mol⁻¹. Finally the results reported here constitute the first attempt to use the new CRTA method to study the kinetics of the carbothermal synthesis of TiN. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 566–571, 2005     

Kinetics and Mechanism of Bilirubin Oxidation by Benzoyl Peroxide in Dimethyl Sulfoxide

The kinetics of the redox reaction of bilirubin by the action of benzoyl peroxide in dimethyl sulfoxide was analyzed. It is shown that the first reaction product is biliverdin, which oxidizes to purpurin and further to choletelin. The kinetic and activation parameters of the oxidation reactions were obtained. A kinetic model of the process was proposed. An assumed route of the reaction is related to the exchange interaction of CH protons of methylene and methine spacers with free radicals in the rate‐limiting step with the further destruction of the “ridge‐tile” pigment conformation. The mechanism steps are confirmed by quantum‐chemical calculations and HPLC. It is found that in organic solvents the end products of bilirubin oxidation are not monopyrrolic derivatives. The data obtained will be useful in constructing antioxidant action models of the pigment.     

Optimizing electrode-attached redox-peptide systems for kinetic characterization of protease action on immobilized substrates. Observation of dissimilar behavior of trypsin and thrombin enzymes

In this work, we experimentally address the issue of optimizing gold electrode attached ferrocene (Fc)-peptide systems for kinetic measurements of protease action. Considering human α-thrombin and bovine trypsin as proteases of interest, we show that the recurring problem of incomplete cleavage of the peptide layer by these enzymes can be solved by using ultraflat template-stripped gold, instead of polished polycrystalline gold, as the Fc-peptide bearing electrode material. We describe how these fragile surfaces can be mounted in a rotating disk configuration so that enzyme mass transfer no longer limits the overall measured cleavage kinetics. Finally, we demonstrate that, once the system has been optimized, in situ real-time cyclic voltammetry monitoring of the protease action can yield high-quality kinetic data, showing no sign of interfering effects. The cleavage progress curves then closely match the Langmuirian variation expected for a kinetically controlled surface process. Global fit of the progress curves yield accurate values of the peptide cleavage rate for both trypsin and thrombin. It is shown that, whereas trypsin action on the surface-attached peptide closely follows Michaelis-Menten kinetics, thrombin displays a specific and unexpected behavior characterized by a nearly enzyme-concentration-independent cleavage rate in the subnanomolar enzyme concentration range. The reason for this behavior has still to be clarified, but its occurrence may limit the sensitivity of thrombin sensors based on Fc-peptide layers.     

Role of the third strand in the binding of proflavine and pt-proflavine to poly(rA).2poly(rU): a thermodynamic and kinetic study

The interactions of triple strands of poly(rA).2poly(rU) with proflavine (PR) and the proflavine cis-platinum derivative [{PtCl (tmen)} 2{NC 13H 7(NCH 2CH 2) 2}] (+) (PRPt) are examined at pH 7.0, T = 25 degrees C, and 0.2 M ionic strength by spectrophotometry, spectrofluorometry, circular dichroism, viscosimetry, stopped-flow, and T-jump relaxation techniques. The melting experiments demonstrate that both drugs tend to destabilize the triplex structure, although the PRPt effect is more relevant. By contrast, both drugs tend to slightly stabilize the duplex structure. The viscosity and circular dichroism measurements show that, at a low dye-to-polymer ratio ( C D/ C P), the binding is intercalative, whereas at high C D/ C P values, the external binding dominates. The binding kinetics and equilibria have been investigated over the C D/ C P region, where intercalation is operative. Both drugs bind to the RNA triplex according to the excluded site model. With PR, two kinetic effects have been observed, whereas with PRPt, only one has been observed. The results are interpreted according to the reaction schemes D + S right arrow over left arrow DS I, with PRPt, and D + S right arrow over left arrow DS I right arrow over left arrow DS II, with PR. The electrostatic contribution to the formation activation energy for DS I is similar (40%) for both systems. The results suggest that DS I is a partially intercalated species. Absence of the second step with PRPt is put down to groove interaction of the Pt-containing moiety, which prevents the PR residue from further penetration through the base pairs to form the fully intercalated complex, DS II. Comparison with the binding of the same drugs to the duplex reveals that the occupation of the major groove in poly(rA).2poly(rU) by the third strand plays a critical role in the kinetic behavior.     

Determination of the Kinetic and Thermodynamic Parameters of Adsorption Processes by a Volume Step Thermal Method

A volume step method measuring the pressure and the adsorbent temperature of an adsorbent-adsorbate system has been developped. It is shown that this method allows the determination of all the relevant parameters of an adsorption process, kinetic as well as thermodynamic in case of Linear Driving Force mass transfer. The method for determining the parameters can be extended to the case of diffusive mass transfer if the mass transfer kinetics is faster than the heat transfer kinetics. An example is given, showing the determination of the diffusion coefficient of carbon dioxide in NaX zeolite pellets and the change of the diffusion coefficient and of the isosteric heat of adsorption when the adsorbent is not fully dehydrated.     

离子交换吸附平衡及其动力学兼论海水提铀机理

本文通过质量作用定律导出的离子交换吸附等温式, 可概括经验的、半经验的Gapon公式、Sips公式、Langmuir公式和Freundlich公式。采用交换吸附是动力学的控制步骤, 可导出交换动力学公式。该式得到海水提铀实验的验证; 且可解释用于证明“颗粒内扩散或液膜扩散机理”的实验数据; 也可解释“颗粒内扩散和液膜扩散联合控制”的实验数据。此外, 本文还讨论了钛胶海水提铀的机理, 为平衡吸铀量的计算提供了理论和方法。     

Laser flash photolysis of benzophenone in polymer films

With a nanosecond laser we studied flash photolysis of benzophenone (BP) dissolved in four different polymer films. We measured kinetics of decay of a triplet state of benzophenone (3)BP as well as kinetics of decay of benzophenone ketyl free radicals BPH(?). Polymer matrices have plenty of reactive C-H bonds, and the hydrogen abstraction by (3)BP leads to a formation of geminate pair which either recombines into molecular products or dissociates. Decay kinetics of (3)BP is well described by dispersive kinetics and in particular by the kinetic law suggested in Albery, W. J.; et al. J. Am. Chem. Soc. 1985, 107, 1854. We observed a broader distribution of rate constants in hard films. It was observed that the decay kinetics of transients radicals in the "hard" polymers is quite satisfactory described by the same law for dispersive kinetics. Kinetics of radicals decay in "soft" polymers is satisfactorily described as a diffusion-enhanced reaction. Effect of a hardness of polymer matrix on the measured kinetic parameters is discussed.