Simplified treatment of cooligomerization kinetics

Equations for the degree of polymerization and the cooligomer composition in the styrene (A)–methyl methacrylate (B)–CCl₄(S) system were derived from the assumed reaction scheme by the use of some assumptions for simplification, and their appropriateness was examined. The chain transfer constants of the growing radicals of styrene (C_SA) and methyl methacrylate (C_SB) to CCl₄, which were estimated from the apparent chain transfer constants C_SAB in the cooligomerization system, agreed with the homooligomerization values. This means that the degree of the polymerization of the cooligomer can be expressed by the equation: where P_n is the degree of polymerization of the cooligomer and P_nO is that when no chain transfer agent (CCl₄) is added; r_A and r_B are the monomer reactivity ratios of monomers A and B in this system. The cooligomer composition deviated from the statistical steady-state composition on the low molecular weight side, and this deviation was explained by the equation:      

Statistical nonstationarity of the composition of styrene with methyl methacrylate in the cooligomer

It was found that the composition of cooligomer produced in the styrene(A)–methyl methacrylate(B)–CCl₄(S) system deviates from the statistical steady-state composition predicted from the Mayo-Lewis equation on the low molecular weight side when the molar ratio of [A]/[B] is large. When the molar ratio of [A]/[B] is small, however, it is not obvious whether or not this phenomenon is observed, because the cooligomer of low molecular weight cannot be obtained easily since the chain transfer constant of the poly(methyl methacrylate) radical to CCl₄ is very small in comparison, with that of the polystyryl radical. This behavior is shown to be attributable mainly to the preferential consumption of styrene monomer in the initiation step, based on the structure of the cooligomer, as inferred from the mechanism of the initiation, transfer, and termination, and the stochastic approach in which the cooligomerization process is regarded as a Markov process.     

Mechanism and thermochemistry of oxidation of HCl and HBr at high temperatures. The heat of formation of HO2

Using currently available thermochemical and kinetic data and estimation methods to analyze the thermochemistry and the kinetic parameters of the elementary reactions involved in the oxidation of HCl and HBr, reaction mechanisms are proposed which account for the previously reported reaction products, the rate law, and the kinetic data. For oxidation of HCl, two competitive pathways, the radical initiation by hydrogen abstraction and the fourcenter reaction pathway, were invoked to account for the observations. In the oxidation of HBr one must invoke a fast surface reaction of the type to account for the reaction.     

The self-inhibited pyrolysis of isobutane

The pyrolysis of isobutane was investigated in the ranges of 770° to 855°K and 20 to 150 Torr at up to 4% decomposition. The reaction is homogeneous and strongly self-inhibited. A simple Rice-Herzfeld chain terminated by the recombination of methyl radicals is proposed for the initial, uninhibited reaction. Self-inhibition is due to abstraction of hydrogen atoms from product isobutene giving resonance-stabilized 2-methylallyl radicals which participate in termination reactions. The reaction chains are shown to be long. It is suggested that a previously published rate constant for the initiation reaction (1) is incorrect and the value k₁ = 10^16.8 exp (?81700 cal mol^?1/RT)s^?1 is recommended. The values of the rate constants for the reactions (4i) (4t) (8) are estimated to be and From a recalculation of previously published data on the pyrolysis of isobutane at lower temperatures and higher pressures, the value k_11c, = 10^9.6 cm³ mol^?1 s^?1 is obtained for the rate constant of recombination of t-butyl. A calculation which is independent of any assumed rate constants or thermochemistry shows that the predominant chain termination reaction is the recombination of two methyl radicals in the conditions of the present work and the recombination of two t-butyl radicals in those of our previous study at lower temperatures and higher pressures.     

Donor-Acceptor Complexes in Copolymerization. IX. Kinetic Features of Copolymerization of Styrene and Methyl Methacrylate… Al(C2H5))1.5Cl1.5

The kinetic features of the copolymerization of styrene and methyl methacrylate in the presence of ethylaluminum sesquichloride in toluene do not unequivocally distinguish between first- and second-order reactions. The reaction does not attain steady-state conditions. The course of the reaction is apparently influenced by many factors including the dissociation of the polymerizable complex into unreactive monomeric species and physical phenomena such as diffusion and dilution effects as well as matrix formation. The use of azobisisobutyronitrile as an initiator indicates apparent bimolecu-lar termination but the kinetic curves show deviation from linearity.     

Modeling of Nitroxide‐Mediated Semibatch Radical Polymerization

A mechanistic model is developed for high‐temperature (138 °C) styrene semibatch thermally and conventionally initiated FRP, as well as NMP with a two‐component initiating system (tert‐butyl peroxyacetate, 4‐hydroxy‐TEMPO). The model, using kinetic coefficients from literature, provides a good representation of the FRP experimental results. Implementation of a gel effect correlation to represent the change in the diffusion‐controlled termination rate coefficient with conversion improves the fit to the thermally initiated system, but is not required to represent the production of low molecular weight material ( Dalton) by conventionally initiated FRP or NMP. The low initiator efficiency found in NMP is well explained by a reaction network involving combination of free nitroxide with methyl radicals formed from initiator decomposition.

     

The pyrolysis of acetylene-styrene mixtures between 450 and 550°C

The pyrolysis of acetylene-styrene mixtures has been studied from 450–550°C in a quartz reaction vessel in the absence and presence of O₂ or NO. The rates of disappearance of reactants and formation of adducts are first-order in each reactant. The major product is polymer, with the adducts accounting for about 2.5% and 6.2% of the styrene removed at 450 and 550°C, respectively. The acetylene-to-styrene removal ratio is about 27 independent of temperature. The adducts formed are methyl indene and 1,2-dihydronaphthalene. These are about half-suppressed in the presence of O₂ or NO. The rate coefficients for reactant removal and adduct formation are: where the activation energies are in kJ/mol and the uncertainties are one standard deviation. As the reaction proceeds, the methyl indene and 1,2-dihydronaphthalene decompose, and indene and naphthalene are formed. In addition, an unidentified isomer of naphthalene is produced as an initial minor product, and it also decomposes as the reaction proceeds.     

Minor products and initiation rate in the chain pyrolysis of propane

With a continuous jet-stirred tank reactor operating at small space time (0.05–1.2 s) the kinetics of the formation of six minor products (ethane, isobutane, butene-1, 2,3-dimethyl-butane, 4-methylpentene-1, and 1,5-hexadiene) are studied during the pyrolysis of propane, at small extents of reaction and over the temperature range of 600–780°C. The experimental results are in agreement with the free radical mechanism proposed by Jezequel, Baronnet, and Niclause for this reaction. They show that the two most important termination processes are The measured rates of formation of the minor products are consistent with the quasi-identical values estimated by Jezequel and co-workers (between 475 and 505°C) and by Allara and Edelson (between 510 and 560°C) for kinetic parameters (A₁ ? 10^16.65 s^?1 and E₁ ? 84.7 kcal/mole) of the chain initiation process      

Initiation Kinetics in Free‐Radical Polymerization: Prediction of Thermodynamic and Kinetic Parameters Based on ab initio Calculations

Initiation kinetics in free radical polymerization is investigated using density functional theory. Thermodynamic and kinetic parameters of the initiation reactions are predicted, and the role of the initiators in the polymerization process is evaluated. Methyl acrylate, methyl methacrylate, acrylonitrile, and styrene homo‐polymerizations with different initiators are studied. Reaction enthalpy and activation energy for each reaction between monomer and the radical fragments arising from the initiators have been determined. The initiation kinetic constants for all of these initiation reactions are evaluated and compared with both computational and experimental propagation kinetic constants of each monomer.

     

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 mechanism and rate parameters for the pyrolysis of n-hexane in the range 723–823 K

The pyrolysis of n-hexane has been investigated in the ranges 723–823 K and 10–100 Torr at up to 3% decomposition. The reaction is homogeneous and free from the self-inhibition by olefin products observed for several other alkanes. The products of the reaction are hydrogen, methane, ethane, ethene, propene, but-1-ene, and pent-1-ene, with smaller amounts of propane. It is shown that the results are in quantitative agreement with a conventional Rice-Herzfeld chain mechanism terminated by the combination and disproportionation of ethyl radicals, but with the mechanism extended so as to include the unimolecular isomerizations via a six-membered cyclic transition state between 1-hexyl and 2-hexyl (1-methylpentyl) radicals. The overall rate constant of initiation is estimated to be given by The rate constant for the reaction is given by which when combined with published data gives an Arrhenius plot curved upwards at low values of 1/T as has been observed for several other hydrogen abstraction reactions of methyl and of ethyl. Estimates are made of rate constants and ratios of rate constants for several reactions of the free radicals involved in the reaction. It is suggested that the minor product propane arises mainly from a hydrogen abstraction by 1-propyl from hexane with a contribution from a minor termination process involving ethyl and methyl.     

Induced heterogeneity,a novel technique for the study of gas-phase reactions. Part I. Determination of the arrhenius parameters for C?C bond scission in propane

It is shown that, by deliberate activation of the reaction vessel, heterogeneous reaction at the wall can be made to dominate chain termination in a complex gas-phase reaction. For a homogeneous process, characterized, as is often the case, by multiple terminations, this has the effect of simplifying the mechanism and allowing explicit solution of the relevant steady-state equations so that the rate constants of some individual steps can be evaluated without assumption as to the values of those of others. The pyrolysis of propane, in the vicinity of 500°C, has been used as an example of this approach. Enhancement of the wall activity leads to the reaction (1) providing, almost exclusively, chain termination. As a result, rate constants for the initiation step (2) can be directly determined. The results of this study provide the Arrhenius equation In combination with current thermochemical values this result gives k_?1 = 10^13.40 cm³/mol·s which, in turn, implies, via the geometric mean rule, k_Et-Et = 10^12.9 cm³/mol·s for ethyl–ethyl recombination, in good accord with the most recent determinations and compatible with the newly proposed value of the enthalpy of formation of ethyl. The first-order wall constant k₈ has been evaluated as k₈<10^4.2 s^?1. This appears to be the first occasion on which a wall constant has been evaluated from data for a high-temperature complex gas reaction.     

Thermal Polymerization of Styrene,Part 1 – Bulk Polymerization

The thermal bulk polymerization of styrene is critically reviewed. There is still no generally accepted kinetic model for the thermal radical formation process, but ideal second‐ or third‐order models are widely used for modeling bulk systems. Since initiation and chain transfer reactions cannot be treated independently from one another as long as the same species is considered to be involved, it is concluded that non‐ideal kinetics, possibly in form of a (micro‐)viscosity dependency of the Mayo mechanism, are likely to be present. A mathematical model is presented that keeps the predictive capabilities of the Hui‐Hamielec model, but allows facile implementation of reaction specific modifications. Part 2 of this paper will focus on the effect of compartmentalization on the thermal polymerization of styrene.

     

Absolute rate constants for the reactions O(3P) atoms with HCl and HBr

A flow tube method has been used to determine rate constants for the elementary reactions: Oxygen atoms were produced by adding a small excess of NO to a stream of partially dissociated nitrogen, and their reaction with hydrogen halide was monitored by observing the intensity of the NO + O afterglow. Experiments were carried out at temperatures from 293 to 440°K with HCl, and from 267 to 430°K with HBr. The role of secondary reactions was minimised and the residual effects were allowed for. The rate constants for the primary reactions could be matched by Arrhenius expressions: where the units are cm³/molec·sec and the errors correspond to a standard deviation.     

Effects of olefins on the thermal decomposition of propane part III. Some remarks on the kinetics of decomposition

Conditions of applicability of quasi-steady-state kinetic treatment have been investigated with respect to the explanation of the decomposition of propane and the influence of ethylene on this. From the measured rate of accumulation of ethane and from the relations between the kinetic equations describing product formation, the rate parameters of the initiation reactions were determined, for which the temperature-dependences and were found. In the decomposition of propane under the examined conditions, the chain length exceeds 500. In response to ethylene the chain length significantly decreases, but even in this case the decomposition chains are long enough for it to be assumed that the ratios of radical concentrations are governed by the propagation steps. Calculations demonstrated that the actual radical concentration during a sufficiently short induction period approximates to the stationary concentration, so that it does not seriously affect the accuracy of the kinetic treatment.     

Nitroxide‐Mediated Radical Polymerization in Miniemulsion at Stationary State: Rationale for Independence of Polymerization Rate on Nitroxide Partitioning Using Oil‐Phase Initiation

Summary: Simulations based on the kinetics and mechanism of nitroxide‐mediated free radical polymerization (NMP) have been carried out in order to understand the hitherto largely unexplained effects (or lack thereof) of nitroxide partitioning in aqueous miniemulsion NMP. The focus has been on the miniemulsion NMP of styrene mediated by TEMPO and 4‐hydroxy‐TEMPO, two nitroxides with very similar activation‐deactivation equilibria, but very different organic phase‐aqueous phase partition coefficients. The general conclusion is that the organic phase propagating radical and nitroxide concentrations are unaffected by the partition coefficient in the stationary state, but the rate of polymerization and the extent of bimolecular termination increase with increasing nitroxide water solubility in the pre‐stationary state region. Specific NMP systems are, therefore, affected differently by nitroxide partitioning depending on whether polymerization predominantly occurs in the stationary state or not, which in turn is governed mainly by the activation‐deactivation equilibrium constant and the rate of thermal initiation.

Simulated organic‐phase propagating radical concentrations in the presence of thermal initiation for TEMPO‐mediated miniemulsion free radical polymerization of styrene for different nitroxide partitioning coefficients at 125 °C.     

Kinetics of polymerization reactions with reversible-chain termination

General kinetic features of radical and ionic polymerization processes accompanied by reversible chain termination reactions are considered. Special attention is paid to the conditions of applicability of the steady-state approximation usually employed to analyze the kinetics of radical polymerization. It is shown that the steady-state concentration of radicals is attained at practically the very beginning of the reaction, while the steady-state concentration of a reversible termination agent is reached with a certain delay. A kinetic explanation of the reversible termination reaction effect on the pattern of the molecular-mass distribution is suggested. Conditions providing the obtainment of a polymer with a narrow molecular-mass distribution in processes with reversible termination are formulated.     

Kinetics of UV-laser induced dehydrochlorination of 1-chloro-1,1-difluoroethane

The decomposition of 1-chloro-1,1-difluoroethane by a radical chain reaction has been studied in a flow reactor in the temperature range from 503 to 773 K. For the initiation of the chain small amounts of added chlorine were photolyzed with a XeCl laser (λ = 308 nm). The formation of the dehydrochlorination and chlorination products, vinylidene fluoride, and 1,2-dichloro-1,1-difluoroethane respectively, is described by a kinetic model. Arrhenius parameters for the two abstraction reactions and were determined by a competition method: Experimental and modeling results are discussed with respect to former studies on the thermal reaction of 1-chloro-1,1-difluoroethane.     

Mechanism of pyrolysis of C2Cl6

Using published data on the kinetics of pyrolysis of C₂Cl₆ and estimated rate parameters for all the involved radical reactions, a mechanism is proposed which accounts quantitatively for all the observations: The steady-state rate law valid for after about 0.1% reaction is and the reaction is verified to proceed through the two parallel stages suggested earlier whose net reaction is A reported induction period obtained from pressure measurements used to follow the rate is shown to be compatible with the endothermicity of reaction A, giving rise to a self-cooling of the gaseous mixture and thus an overall pressure decrease. From the analysis, the bond dissociation energy DH⁰(C₂Cl₅? Cl) is found to be 70.3 ± 1 kcal/mol and ΔH_f300⁰(·C₂Cl₅) = 7.7 ± 1 kcal/mol. The resulting π? bond energy in C₂Cl₄ is 52.5 ± 1 kcal/mol.     

Recent Advances in the Study of High‐Temperature Free Radical Acrylic Solution Copolymerization

Semibatch starved‐feed solution copolymerization is used to produce acrylic resins for coatings formulations. Mechanisms and rate coefficients for polymerization of methacrylates, acrylates, and styrene (ST) under these high‐temperature conditions are reviewed. An extended set of experimental results at 138 °C is used to refine a model describing the solution copolymerization of ST and methacrylates. The data suggest that both changing initiator efficiency and transfer reactions of oxygen‐centered radicals to polymer affect the development of polymer molecular weight. A penultimate model is used to describe the variation in termination rate coefficient with copolymer composition. Significant progress has been made to develop an extended model capable of representing multicomponent high‐temperature acrylic polymerizations.