Toluene and benzyl decomposition mechanisms: elementary reactions and kinetic simulations

The high temperature decomposition kinetics of toluene and benzyl were investigated by combining a kinetic analysis with the ab initio/master equation study of new reaction channels. It was found that similarly to toluene, which decomposes to benzyl and phenyl losing atomic hydrogen and methyl, also benzyl decomposition proceeds through two channels with similar products. The first leads to the formation of fulvenallene and hydrogen and has already been investigated in detail in recent publications. In this work it is proposed that benzyl can decompose also through a second decomposition channel to form benzyne and methyl. The channel specific kinetic constants of benzyl decomposition were determined by integrating the RRKM/master equation over the C(7)H(7) potential energy surface. The energies of wells and saddle points were determined at the CCSD(T) level on B3LYP/6-31+G(d,p) structures. A kinetic mechanism was then formulated, which comprises the benzyl and toluene decomposition reactions together with a recently proposed fulvenallene decomposition mechanism, the decomposition kinetics of the fulvenallenyl radical, and some reactions describing the secondary chemistry originated by the decomposition products. The kinetic mechanism so obtained was used to simulate the production of H atoms measured in a wide pressure and temperature range using different experimental setups. The calculated and experimental data are in good agreement. Kinetic constants of the new reaction channels here examined are reported as a function of temperature at different pressures. The mechanism here proposed is not compatible with the assumption often used in literature kinetic mechanisms that benzyl decomposition can be effectively described through a lumped reaction whose products are the cyclopentadienyl radical and acetylene.     

Multifunctional polycondensation and gelation: A kinetic approach

The size distributions of a number of multifunctional polycondensation systems have been derived from kinetic reaction schemes. The size distribution obtained for a self-condensing multifunctional monomer is equivalent to the classic distributions derived by Flory and Stockmayer, and distribution expressions for mixtures of monomers of different functionalities have also been obtained. Molecular weight expressions have also been calculated for the same systems. In some case, these are exactly the same as those calculated by others, and in some cases the expressions differ from those by others only in the kind of average used for the mean functionality of the mixed monomer systems, but in other cases, the differences are more marked. In gelation, comparison with a number of actual gel point data shows that although the critical point P_crit for gel formation calculated from P_crit = 2/f was generally closer to actually measured gel points than when P_crit = 1(f –1), neither method of calculating P_crit can be regarded as completely reliable. The cause of the divergence from theory is interpreted in terms of intramolcular reaction, and the nature of this type of reaction is discussed and comparisons made with other gelling systems.     

Pyrolysis-gas-liquid-chromatography utilised for a kinetic study of the mechanisms of initiation and termination in the thermal degradation of polystyrene

Pyrolysis-gas-liquid-chromatography (“thermocouple feedback” technique) has been used to study the thermal degradation kinetics of ionically-initiated and free-radical-initiated samples of polystyrene. Although mass-spectrometric measurements confirm that the pyrolysis products from large samples (1 mg) contain oligomers up to at least hexamer in addition to monomer, only monomer is detected when small thin samples (0.1 μg, 10²–10⁵ Å) are used. This effect is not due to a sensitivity problem in detecting oligomers, nor to the incapacity of such compounds of limited volatility to elute from the GLC apparatus. In studying the kinetics of monomer evolution from thin films, initial work was concerned with the effect of film thickness and the limits of first-order behaviour. Then the specific rate of monomer evolution (k_obs) was measured as a function of molecular weight for both types of sample at 723 K and 753 K; the results indicate that the pyrolysis mechanism involves both initiation at the chain-ends and initiation by random scission. Kinetic schemes involving mixed initiation have been proposed, and on this basis the results have been analysed to yield activation energies for scission and end-initiation for both types of sample. Comparison of the activation energies obtained with the quoted value for scission of a CC bond has shown that the depolymerization chain termination process cannot be second order and must be first order in the concentration of long chain radicals. The experimental results also indicate that the ionically-initiated polystyrenes are more stable than free-radical-initiated samples of comparable molecular weight. Possible initiation sites have been discussed with reference to the samples examined and to previous published studies. Several mechanisms leading to first order termination have been proposed; it is suggested that the most probable process involves intramolecular transfer with subsequent scission to give an oligomer radical which is small enough to diffuse readily from the system without further reaction.     

Initiation and termination kinetics in fluid-phase free-radical polymerization up to high pressure

Rate coefficients of peroxyester decomposition in solution of n-heptane have been measured as a function of temperature and pressure. The data is used to determine initiator efficiencies for the ethene high-pressure polymerization. The efficiency strongly depends on the structure of the peroxyester. Free-radical termination rate coefficients of (meth)acrylate systems have been studied up to about 50% monomer conversion. The reaction is controlled by segmental diffusion in the early period and by reaction diffusion at later stages of the polymerization.     

Initiation,propagation and termination in fluid phase free‐radical polymerization

Free‐radical polymerizations are carried out in extended ranges of temperature, pressure, and conversion. The precise knowledge of individual rate coefficients of initiation, propagation, termination, and chain‐transfer is essential for the modelling and optimization of monomer conversion and of polymer microstructure in technical polymerizations. In addition to the application‐oriented interest, this data is of fundamental importance for the detailed understanding of reaction mechanisms of such free‐radical‐molecule, free‐radical‐free‐radical, and unimolecular decomposition processes. Even for the polymerization of rather common monomers at moderate temperatures and ambient pressure such information is scarce. The present paper illustrates some recent advances in measuring, within wide ranges of pressure and temperature, propagation and termination rate coefficients of free‐radical homo‐ and copolymerizations and also peroxyester decomposition rate coefficients.     

Studies on the mechanisms of gelation of kappa-carrageenan and agarose

It has been established that hydrogen bonds control both gelation and helix formation completely in the case of agarose and partially in the case of kappa-carrageenan, the major role belonging in the latter case to the interactions of a polysaccharide with metal ions. Na⁺ and K⁺ ions form contact ion pairs with sulphate groups of kappa-carrageenan. It is supposed that an increase in the number of contact ion pairs together with association of macromolecules having unordered conformation, a decrease in the second virial coefficient, and a decrease in the refraction index increment (i.e., an increase in the solvation degree of dissolved particles) is a necessary condition for forming the kappa-carrageenan gel netwórk. A sufficient condition of kappa-carrageenan gelation is the intermolecular coordination binding of ions such as K⁺ ions, promoting gelation. The coil-to-helix transition of the polysaccharide is controlled by shielding the charge of kappa-carrageenan-sulphate groups. Hydrophobic interactions proved to be unessential for gelation of either agarose or kappa-carrageenan.     

Chemical kinetic simulations behind reflected shock waves

Chemical kinetic simulations that more accurately consider reaction conditions behind reflected shock waves in a high pressure shock tube have been conducted by accounting for (1) time‐dependent temperature and pressure variations in contrast to assuming constant temperature and pressure, (2) the inclusion of reactions during quenching by cooling in contrast to the assumption of zero kinetic contributions, and (3) real gas behaviors in contrast to assuming ideal gas conditions. The primary objective of the current work is to assess the degree of uncertainty associated with assuming constant temperature and pressure and that no reactions occur during the finite time of quenching and prefect gas behavior. The assessment of the subsequent effect of the uncertainty on chemical kinetic modeling is evaluated by conducting extensive comparative studies. In order to achieve this purpose, available CHEMKIN II and CHEMKIN Real Gas codes were utilized and modified to adopt the proposed approaches. From our computational experiments, it is found: (1) For shock tube experiment with less than a 15% endwall pressure increase, the conventional assumptions lead to reasonable accuracy in predicting stable species; (2) during reaction quenching, the consumption of radical species occurs efficiently and is nearly complete once the pressure drops to 50% of its highest value, but concentrations of stable species are insignificantly perturbed by reactions occurring during quenching; and (3) at elevated pressures, the real gas effects, which are a combination of nonideal P–V–T (state variables), thermodynamic, and kinetic behaviors, affect kinetics by speeding the reaction progress up slightly and do not significantly influence the development or validation of a detailed kinetic model from shock tube data that are obtained in a wide temperature range. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 38: 75–97, 2006     

Multinomial tau-leaping method for stochastic kinetic simulations

We introduce the multinomial tau-leaping (MtauL) method for general reaction networks with multichannel reactant dependencies. The MtauL method is an extension of the binomial tau-leaping method where efficiency is improved in several ways. First, tau-leaping steps are determined simply and efficiently using a priori information and Poisson distribution-based estimates of expectation values for reaction numbers over a tentative tau-leaping step. Second, networks are partitioned into closed groups of reactions and corresponding reactants in which no group reactant set is found in any other group. Third, product formation is factored into upper-bound estimation of the number of times a particular reaction occurs. Together, these features allow larger time steps where the numbers of reactions occurring simultaneously in a multichannel manner are estimated accurately using a multinomial distribution. Furthermore, we develop a simple procedure that places a specific upper bound on the total reaction number to ensure non-negativity of species populations over a single multiple-reaction step. Using two disparate test case problems involving cellular processes--epidermal growth factor receptor signaling and a lactose operon model--we show that the tau-leaping based methods such as the MtauL algorithm can significantly reduce the number of simulation steps thus increasing the numerical efficiency over the exact stochastic simulation algorithm by orders of magnitude.     

Automatic sensitivity analysis of kinetic mechanisms

An algorithm for the automatic sensitivity analysis of kinetic mechanisms based on the Fourier amplitude sensitivity test (FAST) method of Shuler and co-workers is reported. The algorithm computes a measure of the relative sensitivity of each concentration to each parameter of interest, such as rate constants, Arrhenius parameters, stoichiometric coefficients, and initial concentrations. Arbitrary variations in the magnitude of the parameters are allowable. The algorithm is illustrated for the simple example of computing the sensitivity of the concentration of species A to variation of the two Arrhenius parameters for the hypothetical reaction A + A →.     

Relating kinetic rates and local energetic roughness by accelerated molecular-dynamics simulations

We show that our accelerated molecular-dynamics (MD) approach can extend the time scale in all-atom MD simulations of biopolymers. We also show that this technique allows for the kinetic rate information to be recaptured. In deducing the kinetic rates, the relationship between the local energetic roughness of the potential-energy landscape and the effective diffusion coefficient is established. These are demonstrated on a very slow but important biomolecular process: the dynamics of cis-trans-isomerization of Ser-Pro motifs. We do not only recapture the slow kinetic rates, which is difficult in traditional MD, but also obtain the underlying roughness of the energy landscape of proteins at atomistic resolution.     

Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles

We introduce a "virtual-move" Monte Carlo algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an important realization being self-assembling particles endowed with strong, short-ranged, and angularly specific ("patchy") attractions. Standard Monte Carlo techniques employ sequential updates of particles and can suffer from low acceptance rates when attractions are strong. In this event, collective motion can be strongly suppressed. Our algorithm avoids this problem by proposing simultaneous moves of collections (clusters) of particles according to gradients of interaction energies. One particle first executes a "virtual" trial move. We determine which of its neighbors move in a similar fashion by calculating individual bond energies before and after the proposed move. We iterate this procedure and update simultaneously the positions of all affected particles. Particles move according to an approximation of realistic dynamics without requiring the explicit computation of forces and without the step size restrictions required when integrating equations of motion. We employ a size- and shape-dependent damping of cluster movements, motivated by collective hydrodynamic effects neglected in simple implementations of Brownian dynamics. We discuss the virtual-move algorithm in the context of other Monte Carlo cluster-move schemes and demonstrate its utility by applying it to a model of biological self-assembly.     

Unsteady-state kinetic models for some typical catalytic mechanisms

A method of formulating thermodynamically correct expressions for the rates of elementary reactions is suggested for the unimolecular and bimolecular Eley-Rideal mechanisms. This method is based on the lattice gas model and transfer matrix method and provides means to calculate thermodynamic functions containing microlevel parameters, specifically, the energies of the body interactions between particles on the surface of a catalyst. Unsteady-state kinetic models have been constructed for mechanisms of reactions conducted in isothermal perfect- and imperfect-mixing reactors. A qualitative and numerical analysis of these models has been carried out.     

Primary radical termination and unimolecular termination in the heterogeneous polymerization of acrylamide initiated by a fluorinated azo‐derivative initiator: A kinetic study

Acrylamide was polymerized in acetonitrile at 82 °C with a perfluorinated azo‐derivative initiator. The polymerization proceeded heterogeneously. Varying amounts of initiator and monomer were used. The activation energy was deduced from three experiments carried out at 59, 71, and 82 °C. The following kinetic law, deviating a great deal from the classical law, was obtained: R ∼ [I₂][M](0.05% < [I₂]_o/[M]_o < 1.00%) and R ∼ [I₂][M](1% < [I₂]_o/[M]_o < 7%). These results can be interpreted in light of the contribution of primary radical termination and the emergence of occlusion. The development of a new kinetic relationship allowed us to confirm the existence of both of these termination reactions. The calculation of the k_prt /k_i · k_p ratio was also achieved. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1834–1843, 2000     

Initiation and termination mechanism in the cooligomerization of the styrene–methyl methacrylate–carbon tetrachloride system

The analysis of the endgroups of the oligomers produced in the styrene (A)–CCl₄(S) system (system I), the methyl methacrylate(B)–CCl₄ system (system II), and the styrene–methyl methacrylate–CCl₄ system (system III) was carried out in order to clarify the mechanism of the initiation, transfer, and termination. In system I, the number of Cl atoms per oligomer molecule N_Cl increases with the molar ratio of [S]/[A] when the molar ratio of [S]/[A] is below unity and is about four when the molar ratio of [S]/[A] is above unity, and the number of initiator fragments per oligomer molecule N_I decreases with the increase in the molar ratio of [S]/[A]. In system II, N_Cl is about 0.45 over a considerably wide range of the molar ratio of [S]/[B]. In system III, N_Cl increases and N_I decreases with the increase in the molar ratios of [S]/([A] + [B]) and [A]/[B]. From the data of N_Cl and N_I, the fraction I_CC14 of the initiation by the tri-chloromethyl radical in the overall initiation reactions and the fraction T_CC14 of the chain transfer reaction of the growing radical of styrene in all the reactions which produce the cooligomer in the system III were calculated. I_CCl3 and T_CC14 both increase with the molar ratios [S]/([A] + [B]) and [A]/[B].     

The use of Monte Carlo simulations to evaluate kinetic data and analytic approximations

Experimental kineticists are always faced with the problem of reducing kinetic data to extract physically meaningful information. A particularly vexing problem arises when different models reproduce the data but yield different values for the physical parameters. For over forty-five years Monte Carlo simulation techniques have been used to study the statistical behavior of parameters extracted from data. Not only do these simulations provide realistic uncertainties, correlation coefficients, and confidence envelopes, but they also provide insight into the nature of the model. These insights may be obtained by viewing two-dimensional scatter plots of the fractional changes of the parameters and one-dimensional histograms of the distributions of the changes in the parameters. Monte Carlo simulations are illustrated with examples from OH+CH₄ → CH₃+H₂O and the high-pressure rate coefficient for methyl-methyl association. A more complex problem involves models for pressure-dependent rate coefficients in the falloff region. We have modeled methyl-methyl association with five of the most current analytic approximations for behavior in the falloff region. All of these reproduce the data to within their uncertainties. However, when Monte Carlo techniques are applied the correlations between the parameters and the nonlinear nature of their behavior become evident. We postulate that the statistical behavior of the parameters of a model may be used to distinguish one model from another and, thereby, identify those analytic approximations that hold promise for further investigation and utilization. Finally, the recent advent of high-speed workstations implies that Monte Carlo simulations should become a routine part of the analysis of kinetic data. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 803–817, 1997     

Diffusion in confinement: kinetic simulations of self- and collective diffusion behavior of adsorbed gases

The self- and collective-diffusion behaviors of adsorbed methane, helium, and isobutane in zeolite frameworks LTA, MFI, AFI, and SAS were examined at various concentrations using a range of molecular simulation techniques including Molecular Dynamics (MD), Monte Carlo (MC), Bennett-Chandler (BC), and kinetic Monte Carlo (kMC). This paper has three main results. (1) A novel model for the process of adsorbate movement between two large cages was created, allowing the formulation of a mixing rule for the re-crossing coefficient between two cages of unequal loading. The predictions from this mixing rule were found to agree quantitatively with explicit simulations. (2) A new approach to the dynamically corrected Transition State Theory method to analytically calculate self-diffusion properties was developed, explicitly accounting for nanoscale fluctuations in concentration. This approach was demonstrated to quantitatively agree with previous methods, but is uniquely suited to be adapted to a kMC simulation that can simulate the collective-diffusion behavior. (3) While at low and moderate loadings the self- and collective-diffusion behaviors in LTA are observed to coincide, at higher concentrations they diverge. A change in the adsorbate packing scheme was shown to cause this divergence, a trait which is replicated in a kMC simulation that explicitly models this behavior. These phenomena were further investigated for isobutane in zeolite MFI, where MD results showed a separation in self- and collective- diffusion behavior that was reproduced with kMC simulations.     

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.     

Discrimination between catalyst deactivation mechanisms by kinetic measurements in open systems

Two competitive mechanisms of catalyst deactivation caused by either the starting substance or the reaction product are considered. The problem of the possible discrimination between these mechanisms according to kinetic measurements in open systems can be solved by a numerical experiment on a computer.

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