Set Of Elementary Reactions Research Articles

Digital twins’ kinetics of virtual free-radical copolymerization of vinyl monomers with stable radicals. 1. Methyl methacrylate

The first experience of virtual free-radical polymerization of a set of vinyl monomers within the framework of the digital twins (DTs) concept (Polymers 2023, 15, 2999) is extended to methyl methacrylate, copolymerized with small additives of stable radicals such as fullerene C60 and TEMPO. A set of elementary reactions, covering the initial stage of the polymerization, is considered. The calculations, encompassing about 30 DTs, were carried out using a semi-empirical version of the unrestricted two-determinant Hartree-Fock approximation. The main energy and spin-density parameters of the ground state of DTs are determined. The barrier profiles of the decomposition of three DTs were calculated laying the foundation for determining the activation energy of the studied processes. The decisive role of spins in the formation of transition states is confirmed. A drastic difference in the copolymerization with fullerene C60 and TEMPO is established. The obtained virtual kinetic data are in a full consent with experimental reality.

Stochastic Modeling of Partially Stirred Reactor (PaSR) for the Investigation of the Turbulence-Chemistry Interaction for the Ammonia-Air Combustion

The Partially Stirred Reactor (PaSR) model is carried out for the ammonia-air combustion system by means of stochastic modeling, namely by solving the transport equation for the joint Probability Density Function (PDF). The turbulent mixing is accounted for by the Linear Mean-Square Estimation (LMSE) mixing model. Notwithstanding the simplified nature of the PaSR modeling, the transported-PDF method enables capturing the effect of mixing frequency on the combustion system, especially the NOx emission. Since the chemical source term is in a closed form in the transported-PDF method, it allows us to apply different chemical mechanisms to explore, whether the set of elementary reactions that are identified as important for the prediction of NOx in the PaSR model is sensitive to the choice of chemical mechanisms. Furthermore, the effect of the residence time in the PaSR model has also been studied, and compared with those in the Perfectly Stirred Reactor (PSR) model (infinite large mixing frequency). Moreover, since the ammonia under oxygen enrichment shows some similar combustion behaviors in terms of e.g. laminar burning velocity as the ammonia under hydrogen enrichment, how large the difference of thermo-kinetic states (e.g. temperature and NOx emission) predicted by PaSR models and in laminar premixed flame configuration is also investigated. A further discussion focuses on the effect of thermal radiation, where the radiative heat loss roles in the prediction of NOx for the turbulent simulation is examined. By using the optically thin approximation model, it is shown that the thermal radiation exhibits little effect on the considered combustion systems within a typical turbulent time-scale.

Automatic Generation of Microkinetic Mechanisms for Heterogeneous Catalysis

A novel approach is presented for generating microkinetic mechanisms in heterogeneous catalysis. The open-source software RMG-Cat automatically develops a detailed list of elementary surface reactions, including thermodynamic properties for the adsorbates and parametrized rate coefficients for the reactions. The software proposes numerous possible surface intermediates and reactions, but it only retains those species that have a sufficiently high rate of formation. RMG-Cat was tested on the dry reforming of methane on nickel. The software correctly found the same set of elementary reactions as in a previously compiled microkinetic mechanism, as well as a few missing reactions. These results demonstrate the potential of this approach for predicting the dominant pathways in heterogeneous catalysis.

A multipurpose reduced chemical-kinetic mechanism for methanol combustion

A multipurpose reduced chemical-kinetic mechanism for methanol combustion comprising 8 overall reactions and 11 reacting chemical species is presented. The development starts by investigating the minimum set of elementary reactions needed to describe methanol combustion with reasonable accuracy over a range of conditions of temperature, pressure, and composition of interest in combustion. Starting from a 27-step mechanism that has been previously tested and found to give accurate predictions of ignition processes for these conditions, it is determined that the addition of 11 elementary reactions taken from its basis (San Diego) mechanism extends the validity of the description to premixed-flame propagation, strain-induced extinction of non-premixed flames, and equilibrium composition and temperatures, giving results that compare favourably with experimental measurements and also with computations using the 247-step detailed San Diego mechanism involving 50 reactive species. Specifically, premixed-flame propagation velocities and extinction strain rates for non-premixed counterflow flames calculated with the 38-step mechanism show departures from experimental measurements and detailed-chemistry computations that are roughly on the order of 10%, comparable with expected experimental uncertainties. Similar accuracy is found in comparisons of autoignition times over the range considered, except at very high temperatures, under which conditions the computations tend to overpredict induction times for all of the chemistry descriptions tested. From this 38-step mechanism, the simplification is continued by introducing steady-state approximations for the intermediate species CH3, CH4, HCO, CH3O, CH2OH, and O, leading to an 8-step reduced mechanism that provides satisfactory accuracy for all conditions tested. The flame computations indicate that thermal diffusion has a negligible influence on methanol combustion in all cases considered and that a mixture-average species-transport model is sufficiently accurate for premixed and non-premixed flames, whereas for the former an even simpler constant-Lewis-number description gives equally satisfactory results.

The kinetics of disproportionation of hydrogen peroxide in the presence of palladium(II)porphyrins with regularly changing macroring structures

The kinetics and spectral manifestations of alkaline decomposition of H2O2 in a water-dimethylformamide medium catalyzed by PdIIP (P is the dianion of octaethylporphyrin and its monophenyl, 5,15-diphenyl,5,10-diphenyl, triphenyl, and tetraphenyl derivatives substituted at meso positions) was studied over a wide range of reagent concentrations under polythermal conditions. A complete kinetic description of the reacting systems was given, and the rates and set of elementary reactions, intermediate compounds, and kinetically significant equilibria were determined. The ion-molecular mechanism of hydrogen peroxide decomposition was substantiated. According to this mechanism, the only stable radicals involved in the reaction are the π radical cation forms of palladium(II)porphyhrin catalysts.

Linear Addition Polymers and Cyclic Oligomers ofN,N-Diglycidyl Aniline and Amines. Uncrosslinked Epoxide-Amine Addition Polymers, 46

The addition polymerization of N,N-diglycidyl aniline (DGA) and disecondary diamines leads to linear addition polymers with molecular weights ranging from 2 500 to 9 100 Da respectively. Their relatively broad molecular weight distribution (M w /M n = 5.5 to 17) is caused by the formation of small amounts of cyclic oligomers. Surprisingly, the addition polymerization of primary monoamines and DGA results in the formation of oligomers only. These oligomers have molecular weights between 684 and 1 165 g.mol -1 . 13 C NMR spectra proof that during addition reaction no side-reaction took place and that the epoxide end groups were completely consumed. Obviously, the addition products mainly consist of cyclic oligomers. In the MALDI-TOF mass spectra cyclic oligomers of repeat units between n = 1 and n = 7 were observed. The kinetics of the addition polymerization can be described by both a formal model and the smallest necessary set of elementary reactions. In order to find the optimum parameters, the set of differential equations was solved numerically by multivariate non-linear regression. The perfect agreement between model calculations and experimental curves allows reliable predictions of the reaction behavior for arbitrary temperature-time profiles.

Electrochemical Polymerization of 1,10-Decanedithiol in CH3CN at Constant Current

Full Paper: The addition polymerization of N,N-diglycidyl aniline (DGA) and disecondary diamines leads to linear addition polymers with molecular weights ranging from 2 500 to 9 100 Da respectively. Their relatively broadmolecular weight distribution (M w /M n = 5.5 to 17) is caused by the formation of small amounts of cyclic oligomers. Surprisingly, the addition polymerization of primary monoamines and DGA results in the formation of oligomers only. These oligomers have molecular weights between 684 and 1 165 g.mol - 1 . 1 3 C NMR spectra proof that during addition reaction no side-reaction took place and that the epoxide end groups were completely consumed. Obviously, the addition products mainly consist of cyclic oligomers. In the MALDI-TOF mass spectra cyclic oligomers of repeat units between n = 1 and n = 7 were observed. The kinetics of the addition polymerization can be described by both a formal model and the smallest necessary set of elementary reactions. In order to find the optimum parameters, the set of differential equations was solved numerically by multivariate non-linear regression. The perfect agreement between model calculations and experimental curves allows reliable predictions of the reaction behavior for arbitrary temperature-time profiles.

Enumeration and discrimination of mechanisms in heterogeneous catalysis based on response reactions and unity bond index–quadratic exponential potential (UBI–QEP) method

The problem of a complete enumeration of a unique set of overall reactions and the corresponding mechanisms from a given set of elementary reactions is discussed in terms of the recently introduced concept of response reactions. A simple algorithm for the systematic generation of direct overall reactions and direct mechanisms from the given set of elementary reactions is presented. Further, based on energetic characteristics of the surface elementary reactions, i.e. the enthalpy changes and activation energy barriers, calculated by using the unity bond index–quadratic exponential potential (UBI–QEP) method, a qualitative procedure for the selection of energetically the most favorable direct mechanisms is proposed. These theoretical considerations are illustrated by a detailed analysis of the mechanism of methanol synthesis on copper catalyst.

Dissolution and precipitation kinetics of gibbsite at 80°C and pH 3: The dependence on solution saturation state

Dissolution and precipitation rates of gibbsite were measured in dilute aqueous solutions at pH 3 and 80°C as a function of solution saturation state using stirred-flow reactors. Saturation state ( Q K eq = exp( ΔG RT ) ; where Q is the activity quotient, k eq , is the equilibrium activity quotient (or solubility), ΔG r is the deviation of the Gibbs free energy of the reaction (kcal mol −1) from the equilibrium value, R is the gas constant, and T is temperature in Kelvin) was determined with respect to the overall reaction Al(OH) 3(cr) + 3H + ⇔ A1 3+ + 3H 2O. The equilibrium solubility at 80°C for this reaction was tightly constrained using the solution saturation states from the experiments with the five slowest dissolution and precipitation rates. The calculated equilibrium solubility ( K eq = a Al 3+ A H+ 3 ) is 10 5.00±0.08, in excellent agreement with published values despite differences in thermodynamic models and the definition and measurement of pH. The variation in dissolution rate (mol m −2 sec −1) with ΔG r over the range −1.14 ≤ ΔG r ≤ 0 kcal mol −1 is given by Rate diss = −(4.72 ± 0.28) × 10 −10[1 − exp {(−8.12 ± 1.02) g (3.01±0.05)}] where g  ¦ΔG r¦ RT . The precipitation rate (mol m −2 sec −1) varies with ΔG r over the range 0 ≤ ΔG r ≤ +0.467 kcal mol −1 according to Rate ppt = −(2.07 ± 0.63) × 10 −10[1 − exp { g (1.20±0.31)}] or to Rate ppt = (1.94 ± 1.55) × 10 −10 g (1.10±0.11) The variation of the dissolution rate with ΔG r can be separated into three regions. Near equilibrium (0 ≥ ΔG r > −0.200 kcal mol −1), the rates increase gradually with increasing undersaturation according to an approximately linear function of ΔG r . Over the range −0.200 > ΔG r < −0.500 kcal mol −1, the rates increase sharply as ΔG r becomes more negative. Far from equilibrium, at ΔG r < −0.500 kcal mo −1, the dissolution rates are constant at their maximum value. On the other hand, precipitation rates are nearly linear with ΔG r for 0 ≤ ΔG r ≤ +0.467 kcal mol −1 (two times saturation). The complex functional dependence of dissolution rate on ΔG r indicates that the measured precipitation rates cannot be obtained from the far-from-equilibrium dissolution rate using transition state theory and the principle of detailed balancing. However, near equilibrium (−0.200 < ΔG r < +0.200 kcal mol −1), the approximate linear dependence of both dissolution and precipitation rates on ΔG r supports the application of transition state theory to the overall reaction and indicates that, only over this range of ΔG r , the same set of elementary reactions may control the overall rate. The sharp increase in dissolution rate from 0 ̄ .200 > ΔG r > −0.500 kcal mol −1 is suggestive of a surface phase change corresponding to a change in dissolution mechanism. A plausible dissolution mechanism over this range of ΔG r involves the opening of dislocation cores to form etch pits and is supported by theoretical calculations and SEM observations.

Kinetics of the multi-step catalytic degradation of a polymer to its constituent subunits

The stepwise catalytic degradation of a polymer to its constituent subunits results in many molecules of polymers of shorter chain length. Using the Law of Mass Action, ordinary differential equations for each species can be obtained from the set of elementary reactions and these can be integrated to obtain species concentrations as a function of time. A special case of catalytic degradation of polymers, in which one subunit is released at each step, is examined. A mathematical dissertation of the kinetics of the series of reactions involved is presented. The solution of the set of differential equations involve tedious computations and cannot be easily adapted to the analysis of experimental data. Two additional methods of analysis are described. The first one makes use of the property that for any intermediary polymer whose initial and final concentrations are zero, the integral of its concentration with respect to time is inversely proportional to the degradation rate constant. Stepwise calculation of the rate constants can thus be obtained by determining the area under the concentration-time trajectories while the degradation rate constant of the first polymer is known. The second method makes use of the property that the maximum concentration attained by any individual intermediary polymer is inversely proportional to its degradation constant. These methods have the advantage of being simple since the degradation constants can be obtained stepwise from experimental data.

Analysis of the structure and mechanisms of extinction of a counterflow methanol-air diffusion flame

Numerical calculations were performed to determine the structure and to clarify the extinction mechanisms of diffusion flames stabilized between counterflowing streams of methanol and air. The calculations were performed at a value of the thermodynamic pressure equal to 1 atmosphere, with different values for the rate of strain and with two different chemical kinetic mechanisms. We will refer to these two mechanisms as “mechanism a” and “mechanism b.” Mechanism a and mechanism b have the same set of elementary reactions, but the rate constants for these elementary reactions were obtained from two different references. Temperature profiles, concentration profiles of various species, rates of production and destruction of various species, and rates of various reactions were plotted as a function of the axial coordinate using mechanism a and mechanism b. Both chemical mechanisms show that the structure can be subdivided into three regions: the fuel consumption region where the reaction proceeds via the path CH 3OHCH 2OHCH 2OCO, H 2, the H 2CO oxidation region where the compounds H 2 and CO oxidize to form H 2O and CO 2, and the radical destruction region where radicals are destroyed by three body reactions. If mechanism a is used, we conclude that at low rates of strain the concentration of CH 2OH and HCO are in steady state and, if partial equilibrium is assumed for certain reactions, there exist algebraic relations among the concentrations of the radicals OH, H, and O. As the rate of strain is increased, HCO is no longer in steady state and no solution was obtained for a strain rate greater than 521 s −1. However, if mechanism b is used, the concentration of HCO alone is in steady state, and there also exist algebraic relations among the concentrations of the radicals OH, H, and O. As the rate of strain is increased, no solution was obtained for a strain rate greater than 168 s −1, and we speculate that extinction of the flame is due to a large value of the activation energy for a reaction controlling the pyrolysis of CH 2OH to CH 2O.

Reactions for chemical systems far from equilibrium

Reactions formulated for systems operating far from equilibrium may generate misleading conclusions if they contain an implied assumption of steady state. This assumption is introduced most commonly by eliminating an intermediate product from a pair of elementary reactions, condensing them into a single summary reaction. The consequences of using such inadequate reactions are illustrated through two well known model systems, the Lotka oscillator and the Brusselator. The Brusselator includes a termolecular reaction which could be generated by summarizing any of several sets of elementary reactions. When an elementary set is used in place of the termolecular reaction, the revised Brusselator fails to show its characteristic limit cycle. Both the Brusselator and the Lotka scheme have reactions in which the same substance appears both as reactant and as product, formed by eliminating some intermediate in a catalytic cycle. Including even short-lived intermediates alters the stability shown by the Lotka scheme, so that behaviour in the phase plane changes from a conservative cycle into an expanding spiral.

ChemInform Abstract: COMPUTER SIMULATION OF THE KINETICS OF COMPLICATED GAS PHASE REACTIONS

Modern digital methods and powerful computers make it possible to simulate the time behavior of chemical reactions. These calculations can be performed on systems containing an almost unlimited number of elementary reactions. Generally, however, the reaction models used should contain only those elementary reactions which describe the bulk of the conversion. Such a reaction model may be obtained by reduction of the complete set of elementary reactions. Another possibility is analysis of the chemical system starting from conditions ensuring a simple chemistry, which is generally the case at low temperatures and low conversions. The reaction model may then be extended into the range of the reaction variables (temperature, time) of interest. Mathematical simulations may be helpful during the development of the reaction model, and sometimes even decisive. These methods were applied to the pyrolysis of ethylbenzene and n-hexane, and to CO oxidation. They yield information on the reaction paths, the importance of particular elementary reactions, and reaction stability. Furthermore, quantitative data can be obtained concerning the influence of single elementary reactions on the product distribution. The sensitivity matrix shows, e.g., whether the determination of kinetic parameters of an elementary reaction from kinetic data of the overall reaction is possible in principle, and how high the accuracy of the rate constants should be for simulation of the reaction. Both results are important for modeling chemical reactions.