Multiple rate-determining steps for nonideal and fractal kinetics

We show that the kinetic model of a single rate-determining step in a reaction mechanism can be extended to systems with multiple overall reactions for which the elementary reactions obey nonideal or fractal kinetics. The following assumptions are necessary: (1) The system studied is either closed or open, but no constraints exist preventing the evolution toward equilibrium. (2) Elementary reactions occur in pairs of forward and backward steps. (3) The kinetics of the elementary steps are either nonideal or fractal and are compatible with equilibrium thermodynamics. (4) The number of reaction routes is identical with the number of rate-determining steps. If these hypotheses are valid, then the overall reaction rates can be explicitly evaluated: they have a form similar to the kinetic equations for the elementary reactions and the apparent reaction orders and fractal coefficients can be expressed analytically in terms of the kinetic parameters of the elementary reactions. We derive a set of relationships which connect the equilibrium constants of the reaction routes, the corresponding overall rate coefficients, and the stoichiometric numbers of the rate-determining steps. We also derive a set of generalized Boreskov relations among the apparent activation energies of the forward and backward overall processes, the corresponding reaction enthalpies, and the stoichiometric coefficients of the rate-determining steps. If the elementary reactions obey fractal kinetics, the same is true for the rate-determining steps. The fractal exponents of the forward and backward overall reactions are linear combinations of the fractal exponents of the fractal elementary reactions. Similar to the theory of single rate-determining steps, our approach can be used for selecting suitable reaction mechanisms from experimental data.     

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.     

A simple model to explain the complex kinetic behavior of epoxy/anhydride systems

A survey of the literature dealing with the kinetics of epoxy/anhydride polymerizations initiated by tertiary amines, shows inconsistencies in results reported by several authors. Both first-order and autocatalytic expressions have been used to fit experimental results. In the former case, significantly different values of apparent activation energies were found in isothermal and nonisothermal experiments. A simple kinetic model is proposed to explain these inconsistencies, based on the following steps: (a) a reversible reaction transforming an inactive initiator species into an active one, (b) a propagation step, and (c) a chain transfer step regenerating the active initiator (step not relevant to the kinetic analysis). The simple model explains both the first-order and autocatalytic behaviors reported in the literature. It also leads to the experimental values of the apparent activation energies obtained under different conditions. It is also shown that isoconversional methods should not be applied to obtain fundamental kinetic parameters in systems where the reaction rate depends on the concentration of an active species that varies independently of the conversion of functional groups. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2799–2805, 1999     

Experimental microkinetic approach of the photocatalytic oxidation of isopropyl alcohol on TiO2. Part 1. Surface elementary steps involving gaseous and adsorbed C3H(x)O species

The present study concerns an experimental microkinetic approach of the photocatalytic oxidation (PCO) of isopropyl alcohol (IPA) into acetone on a pure anatase TiO2 solid according to a procedure previously developed. Mainly, the kinetic parameters of each surface elementary step of a plausible kinetic model of PCO of IPA are experimentally determined: natures and amounts of the adsorbed species and rate constants (preexponential factor and activation energy). The kinetics parameters are obtained by using experiments in the transient regime with either a FTIR or a mass spectrometer as a detector. The deep oxidation (CO2 and H2O formation) of low concentrations of organic pollutants in air is one of the interests of the PCO. For IPA, literature data strongly suggest that acetone is the single route to CO2 and H2O and this explains that the present study is dedicated to the elementary steps involving gaseous and adsorbed C3H(x)O species. The microkinetic study shows that strongly adsorbed IPA species (two species denoted nd-IPA(sads) and d-IPA(sads) due to non- and dissociative chemisorption of IPA, respectively) are involved in the PCO of IPA. A strong competitive chemisorption between IPA(sads) and a strongly adsorbed acetone species controls the high selectivity in acetone of the PCO at a high coverage of the surface by IPA(sads). The kinetic parameters of the elementary steps determined in the present study are used in part 2 to provide a modeling of macroscopic kinetic data such as the turnover frequency (TOF in s(-1)) of the PCO using IPA/O2 gas mixtures.     

On the performance of Au(111) for ethylene epoxidation: a density functional study

This work presents a periodic density functional study of the epoxidation mechanism of ethylene on Au(111). It is found that, once atomic oxygen is adsorbed on the surface, partial oxidation to ethylene oxide becomes possible. Calculated transition state theory rate constants for the elementary steps involved in the reaction predict that the selectivity of Au(111) toward epoxide is of approximately 40% in good agreement with recent experimental findings for styrene epoxidation on Au(111).     

Sensitive gas chromatographic methods for the determination of vinyl epoxide synthetase activity using trichloroethylene as a model substrate

Two specific and very sensitive methods for the determination of vinyl epoxide synthetase activity in liver microsomes are described. Trichloroethylene, which is used as a substrate, is converted into trichloroethylene oxide by a hepatic epoxide synthetase. Chloral hydrate, the final rearrangement product of trichloroethylene oxide, is determined by electron-capture gas chromatography, either after derivatization with pentafluorophenylhydrazine or after its conversion into chloroform under alkaline conditions. The kinetic parameters of the epoxidation reaction were determined on rat hepatic microsomal suspensions.     

Predicting catalysis: understanding ammonia synthesis from first-principles calculations

Here, we give a full account of a large collaborative effort toward an atomic-scale understanding of modern industrial ammonia production over ruthenium catalysts. We show that overall rates of ammonia production can be determined by applying various levels of theory (including transition state theory with or without tunneling corrections, and quantum dynamics) to a range of relevant elementary reaction steps, such as N(2) dissociation, H(2) dissociation, and hydrogenation of the intermediate reactants. A complete kinetic model based on the most relevant elementary steps can be established for any given point along an industrial reactor, and the kinetic results can be integrated over the catalyst bed to determine the industrial reactor yield. We find that, given the present uncertainties, the rate of ammonia production is well-determined directly from our atomic-scale calculations. Furthermore, our studies provide new insight into several related fields, for instance, gas-phase and electrochemical ammonia synthesis. The success of predicting the outcome of a catalytic reaction from first-principles calculations supports our point of view that, in the future, theory will be a fully integrated tool in the search for the next generation of catalysts.     

Dynamic Monte Carlo simulation of the NO + CO reaction on Rh(111)

The kinetics of the catalytic reduction of NO by CO on Rh(111) surfaces was investigated by using dynamic Monte Carlo simulations. Our model takes into account recent experimental findings and introduces relevant modifications to the classical reaction scheme, including an alternative pathway to produce N2 through an (N-NO)* intermediate, the formation of atomic nitrogen islands in the adsorbed phase, and the influence of coadsorbed species on the dissociation of NO. All elementary steps are expressed as activated processes with temperature-dependent rates and realistic values dictated by experiments. Calculated steady-state phase diagrams are presented for the NO + CO reaction showing the windows for the conditions under which the reaction is viable. The model predicts variations in both production rates and adsorbate coverages with temperature consistent with experimental data. The effect of varying the individual kinetic parameters and the importance of each step in the reaction scheme were probed.     

The thermal decomposition of hydrocarbons. Part 2. Alkylaromatic hydrocarbons: Alkylbenzenes

The pyrolysis of the n-alkylbenzenes is reviewed with emphasis on the radical chain mechanism and on the reactions of the intermediate radicals. The effects of the experimental conditions and conversion on the types and distribution of the final products are also evaluated. The Arrhenius rate parameters are summarized for both the elementary steps and the overall decomposition reactions.     

On the mechanism of low-temperature water gas shift reaction on copper

Periodic, self-consistent density functional theory (DFT-GGA) calculations are used to investigate the water gas shift reaction (WGSR) mechanism on Cu(111). The thermochemistry and activation energy barriers for all the elementary steps of the commonly accepted redox mechanism, involving complete water activation to atomic oxygen, are presented. Through our calculations, we identify carboxyl, a new reactive intermediate, which plays a central role in WGSR on Cu(111). The thermochemistry and activation energy barriers of the elementary steps of a new reaction path, involving carboxyl, are studied. A detailed DFT-based microkinetic model of experimental reaction rates, accounting for both the previous and the new WGSR mechanism show that, under relevant experimental conditions, (1) the carboxyl-mediated route is the dominant path, and (2) the initial hydrogen abstraction from water is the rate-limiting step. Formate is a stable "spectator" species, formed predominantly through CO2 hydrogenation. In addition, the microkinetic model allows for predictions of (i) surface coverage of intermediates, (ii) WGSR apparent activation energy, and (iii) reaction orders with respect to CO, H2O, CO2, and H2.     

Total Synthesis of the Polyoxygenated Sesquiterpenes Guignarderemophilanes C and D

The total syntheses of the neural anti‐inflammatory agents guignarderemophilanes C and D have been accomplished for the first time starting from γ‐hydroxy carvone in 15 and 14 steps, respectively. The presented synthetic route proceeds via a known intermediate, whose synthesis has been elaborated in our group in the course of the total synthesis of the sesquiterpenoid periconianone A. Key for the successful conversion of this intermediate into both targets was finding a suitable strategy to install the 1,2,3‐trihydroxylated A‐ring scaffold. For this purpose, we effectively employed a Mitsunobu inversion, epoxidation, and regioselective epoxide opening sequence, before the bicyclic ring system was constructed by an aldol condensation reaction on a sterically demanding substrate. Our reported synthesis set the stage for SAR studies to prepare even more potent compounds by modification and derivatization of the natural product's scaffold.     

An alternative stereoselective total synthesis of (-)-pyrenophorol

The total synthesis of 16-membered C₂–Symmetric dilactone (-)-Pyrenophorol was accomplished starting from commercially available (S)-epoxide prepared by hydrolytic kinetic resolution of (±) – epoxide with key steps of Grignard reaction, Swern oxidation, Wittig reaction and cyclization was achieved by intermolecular Mitsunobu cyclization. The synthesis of (-)-Pyrenophorol accomplished from cheaply available starting material, easily work-up procedures and reduction of cost in industrial process were major advantages of this route.     

Photopolymerization of bis-aromatic and alicyclic based solid urethane acrylate macromonomer in the presence of large excess of reactive diluent

A solid urethane acrylate macromonomer with bis-aromatic as well as alicyclic moieties was synthesized and the kinetics of photopolymerization reactions were studied in the presence of varying concentration of photoinitiator and large excess of reactive diluent using photo DSC. The studies show that the rate of maximum polymerization was found to increase with increase in concentration of photoinitiator while a decrease was observed by an increase in temperature. The final conversion showed a decrease at highest isothermal condition due to vitrification. Estimation of kinetic parameters including applicability of autocatalytic and modified autocatalytic models were investigated by nonlinear regression. It was observed that the modified models gave a better fit with the experimental data and kinetic parameters showed a decrease with increase in temperature and an increase with increase in concentration of photoinitiator.     

Influence of the chemorheology of toughened epoxy matrices on the processing behavior of high performance composites

The rheological and kinetic behavior of a new commercial toughened epoxy matrix is characterized through a complete experimental program. The kinetic behavior of the thermosetting resin is described by applying a new empirical model, accounting for autocatalytic and difussion control effects. The rheological model uses the kinetic information and describes the matrix viscosity as a function of temperature and degree of reaction using only three fitting parameters. The complete model is verified through calorimetric and rheological tests performed at different temperatures (isotherms) or heating rates (dynamic tests); or under more complex conditions simulating the processing conditions during autoclave lamination. Finally the chemo-rheological model is considered as a part of a master model describing the complete processing behavior of thermoset matrix composites. The use of the master model in control and optimization algorithms is also illustrated.     

Synthesis of hydrated furans: Analysis of the Prins reaction mechanism

Mechanistic analysis of hydrogenated furan synthesis by the Prins reaction was carried out using mathematical modeling. The direct and inverse chemical kinetic problems are solved for the rate constants of all elementary steps. A probable mechanism is derived from the obtained quantitative kinetic parameters and the kinetic patterns of the reaction. These include kinetic curves from the concentration changes of all species in the reaction.     

The thermal decomposition of hydro-carbons. Part 1. n-alkanes (C≥5)

The pyrolysis of the long (C≥5) chain n-alkanes is reviewed with emphasis on the radical chain mechanism and on the reactions of the intermediate alkyl radicals. The effects of the experimental conditions and conversion on the types and distributions of the final products are also evaluated. The Arrhenius rate parameters are summarized for both the elementary steps and the overall decomposition reactions.     

铁(III)卟啉催化β-胡萝卜素分解动力学研究

使用BeckmannDU-8B紫外可见分光光度计研究了以氯合四－间三甲苯基卟啉铁（Ⅲ）（FeTMPCl）为催化剂，间氯过氧化苯甲酸（mCPBA）为氧化剂，咪唑（I_m）、2－甲基咪唑（MeI_m）、2－乙基－4－甲基咪唑（EMI_m）为轴向配体，催化β-胡萝卜素（β－cte）氧化分解为维生素A的动力学规律，提出了反应机理，研究了温度、催化剂浓度、氧化剂浓度及轴向配体对反应速率的影响，应用Gauss－Newton－Marquardt方法求得各基元反应的有关动力学参数．