The Importance of Chain-Length Dependent Kinetics in Free-Radical Polymerization: A Preliminary Guide

The effect of chain-length dependent propagation at short chain lengths on the observed kinetics in low-conversion free-radical polymerization (frp) is investigated. It is shown that although the values of individual propagation rate coefficients quickly converge to the high chain length value (at chain lengths, i, of about 10), its effect on the average propagation rate coefficients, 〈k_p〉, in conventional frp may be noticeable in systems with an average degree of polymerization (DP_n) of up to 100. Furthermore it is shown that, unless the system is significantly retarded, the chain-length dependence of the average termination rate coefficient, 〈k_t〉, is not affected by the presence of chain-length dependent propagation and that there exists a simple (fairly general) scaling law between 〈k_t〉 and DP_n. This latter scaling law is a good reflection of the dependence of the termination rate coefficient between two i-meric radicals, k, on i. Although simple expressions seem to exist to describe the dependence of 〈k_p〉 on DP_n, the limited data available to date does not allow the generalization of these expressions.     

New aspects of chain-length dependent termination

A survey is given on a selection of recently developed methods for the evaluation of the rate coefficient k_t of termination and its chain-length dependence. In particular these are the time-resolved single-pulse pulsed laser polymerization (TR-SP-PLP), the single pulse pulsed laser polymerization in combination with the analysis of the molecular weight distribution produced (SP-PLP-MWD), the methods yielding an average k_t either from the second moment of the chain-length distribution (CLD) or from the rate of polymerization, and a method focusing on the chain-length dependence of k_t consisting in an analysis of the CLD resulting from PLP experiments carried out at low pulse frequencies (LF-PLP). The results obtained by these methods are compared and discussed. The role of the shielding of the two radical chains by their appendant coils is emphasized.     

SP-PLP-EPR study of chain-length-dependent termination in free-radical polymerization of n-dodecyl methacrylate, cyclohexyl methacrylate, and benzyl methacrylate: evidence of "composite" behavior

The chain-length dependence of the termination rate coefficient in n-dodecyl methacrylate (DMA), cyclohexyl methacrylate (CHMA), and benzyl methacrylate (BzMA) bulk free-radical homopolymerizations at ambient pressure and at temperatures from -20 to 0 degrees C is deduced using the recently developed technique of SP-PLP-EPR: pulsed-laser polymerization (PLP) in which time-resolved EPR measurement of radical concentration, cR, is made following each single pulse (SP) of an excimer laser. The decay of cR results from termination of radicals of almost identical size. Their chain length, i, increases linearly with time, t, after applying a SP. The rate coefficient, kt(i,i), for termination of two radicals of size i is determined by fitting the experimental cR vs t data. This process demonstrates that (at least) two power-law exponents are necessary to describe kt(i,i) over the extended chain-length range of i = 1 to 1000. This is consistent with the so-called "composite model" , which uses power-law exponents alpha(S) and alpha(L) to describe termination of radicals either shorter or longer, respectively, than a crossover chain length, ic. The fourth parameter obtained from fitting the SP-PLP-EPR data with this model is kt(1,1), the termination rate coefficient for two radicals of degree of polymerization 1. Previous DMA experiments are reanalyzed while new experimental results are reported and analyzed for CHMA and BzMA. The parameter values for CHMA and BzMA termination at 0 degrees C are almost identical-kt(1,1) approximately 3 x 10(7) L mol(-1) s(-1), alpha(S) approximately 0.50, ic approximately 90, and alpha(L) approximately 0.21-and they are close to those for DMA at 0 degrees C: kt(1,1) approximately 1 x 10(7) L mol(-1) s(-1), alpha(S) approximately 0.64, ic approximately 50, and alpha(L) approximately 0.18. The results fully support the composite model in that the chain-length dependence is more pronounced for shorter than for longer radicals, i.e., alpha(S) > alpha(L). Moreover, the power-law exponent that characterizes termination of long-chain radicals is close to the theoretical value of alpha(L) = 0.16. In fact all parameter values-including the small differences between DMA and CHMA/BzMA-are more-or-less in accord with expectations based on polymer dynamics. Furthermore, our results suggest that termination of methacrylate radicals with large cyclic or long n-alkyl substituents may be affected by steric shielding of the radical functionality.     

The nature of the chain-length dependence of the propagation rate coefficient and its effect on the kinetics of free-radical polymerization. 1. Small-molecule studies

In this paper we summarize and analyze the currently available small-molecule data, both experimental and theoretical, that is relevant to chain-length-dependent propagation in free-radical polymerization (FRP). We do this in order to appreciate the nature of chain-length-dependent propagation, because workers are becoming increasingly cognizant of its necessity in reaching a complete understanding of FRP kinetics. We show that studies of addition in small-molecule (model) systems support a chain-length dependence (at short chain lengths i) which is described by the following functional form, which therefore can be said to be physically realistic: , where the values of C₁ and i_1/2 are of the order of 10 and 1, respectively. These results are supported by transition state theory, which predicts a very similar behavior for the Arrhenius frequency factor. We illustrate that in systems with low number-average degree of polymerization (DP_n), this chain-length dependence can dramatically affect the observed (chain-length-averaged) propagation rate coefficient 〈k_p〉, which can be significantly higher than the long chain value, k_p. However, this effect is only observed if the activation energy for the first radical addition is similar to that for propagation. In the case that the former is significantly higher (e.g., when choosing a less than optimal initiator or in the case of retardative chain transfer), the chain-length-dependent propagation predicted by our model will not be observed, and in fact a significant lowering of 〈k_p〉 can in cases be expected up to relatively high DP_n.     

Ab Initio Calculation of the Propagation Kinetics in Free Radical Polymerization: Chain Length and Penultimate Effects

Summary: In this work, Quantum Chemistry is applied to investigate the propagation kinetics in free radical polymerization. Energies, structures and transition state geometries are determined using density functional theory, which combines good accuracy with reasonable computational demand. In particular, B3LYP functional is used to evaluate the exchange and correlation energy with the 6-311+G(d,p) basis sets. The capabilities of the approach with respect to the prediction of the kinetic constants of elementary processes relevant to polymeric systems (propagation reactions) is first tested using literature experimental data as reference values. 1 Namely, two different monomers of industrial relevance have been selected, acrylonitrile and styrene. For such systems, the effect of chain-length on the propagation rate coefficient is examined. Finally, for the selected monomer pair, the relative reactivity (so-called reactivity ratios) is also analyzed, in particular considering the penultimate effect.     

The effects of chain length dependent propagation and termination on the kinetics of free-radical polymerization at low chain lengths

The kinetics of the free-radical polymerization of methyl methacrylate at 60 °C in the presence of large amounts of n-dodecanethiol (DDM) were investigated as a test at short chain lengths of our recently proposed composite termination model [Smith GB, Russell GT, Heuts JPA. Macromol Theory Simul 2003;12:299]. The experimental data were found to show an unexpected and therefore very interesting trend: at high concentrations of DDM, the rate actually increases as chain lengths become smaller. No termination model can explain this unusual behaviour. However it was found that these results are very successfully described when, in addition to our composite termination model, chain length dependent propagation is included in modelling of the kinetics. These findings have important ramifications for all kinetic studies involving short polymeric radicals, including in low conversion living radical polymerization systems and studies determining the chain length dependence of the termination rate coefficient.     

Mechanisms of propagation,transfer, and short-chain branching reactions in the free-radical polymerization of ethylene

The propagation, transfer, and short-chain branching reactions in the free-radical polymerization of ethylene were studied at temperatures of 20–80°C. under pressures of 160–400 kg. cm.² by means of two-stage polymerization with the use of a specially designed reaction vessel. In the first stage, the polymerization was carried out in the presence of AIBN as the initiator, and in the second stage, the propagation occurred with living radicals in the absence of the initiator. In the second stage the polymer yield is shown to increase with reaction temperature and pressure, and the molecular weight of the polymer reached constant values which were dependent upon the temperature when the contribution of the polymer formed in the first stage was very small. It is shown that in the second stage the rate of propagation, transfer, and short-chain branching are all proportional to the second power of ethylene fugacity, and that the activation energies of these reactions are 5.7, 23.4, and 10.9 kcal./mole, respectively. The polymer has no terminal vinyl group. The mechanism of these reactions is discussed on the basis of kinetic and energetic results.     

Monte Carlo simulation of chain length distribution in radical polymerization with transfer reaction

In this paper, the basic principle and a Monte Carlo method are described for numerically simulating the chain-length distribution in radical polymerization with transfer reaction to monomer. The agreement between the simulated and analytical results shows that our algorithm is suitable for systems with transfer reaction. With the simulation algorithm, we confirm that transfer reaction has a similar effect as disproportionation on the molecular weight distribution in radical polymerization with continuous initiation. In the pulsed laser (PL) initiated radical polymerization with transfer reaction, the ‘waves’ on the chain-length distribution profile become weaker as the ratio of transfer reaction rate constant, k_tr, to the propagation rate constant, k_p, is increased in the case with either combination-type or disproportionation-type termination. Moreover, it seems that the combination termination has a broadening effect on the waves. Therefore, k_p can also be determined by precisely locating the inflection point L_o on the chain-length distribution profile for radical polymerization with transfer reaction, unless k_tr is large enough to smear out the waves on the chain-length distribution.     

Modeling stable free-radical polymerization

A kinetic model has been developed for stable free-radical polymerization (SFRP) processes by using the method of moments. This model predicts monomer conversion, number-average molecular weight, and polydispersity of molecular weight distribution. The effects of the concentrations of initiator, stable radical, and monomer, as well as the rate constants of initiation, propagation, termination, transfer, and the equilibrium constant between active and dormant species, are systematically investigated by using this model. It is shown that the ideal living-radical polymerization having a linear relationship between number-average molecular weight and conversion and a polydispersity close to unity is the result of fast initiation, slow propagation, absence of radical termination, and a high level of dormant species. Increasing stable radical concentration helps to reduce polydispersity but also decreases polymerization rate. Thermal initiation significantly broadens molecular weight distribution. Without the formation of dormant species, the model predicts a conventional free-radical polymerization. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2692–2704, 1999     

Chain transfer in ethylene polymerization

Chain transfer constants in the homogeneous free-radical polymerization of ethylene at 1360 atm. and 130°C. have been determined for over 50 compounds, including nearly 300 hydrocarbons. The effects of substitution, unsaturation, and ring strain in the transfer agent molecule on the reactivity of its C? H bonds in chain-transfer reactions with a polyethylene growing chain are analyzed. Qualitatively, these trends parallel those found for simple radicals attacking simple molecules. However, the principle that the reactivity of a compound is the sum of the reactivities of all reactive bonds, which is well established for simple radicals and transfer agents, is found not to be true in ethylene polymerization. It is postulated that the deviations from this principle are due to steric factors which become very important when the free radical is bulky. The transfer constants measured in ethylene polymerization are also compared with transfer constants in other systems. A strong correlation is found between the transfer constants in ethylene and published data on rates of abstraction of hydrogen atoms by methyl radicals.     

Kinetics and mechanism of radical polymerization of weak unsaturated acids in aqueous solutions

The behaviour of weak unsaturated acids (such as acrylic and methacrylic) and their salts in radical polymerization in aqueous solutions was studied. A characteristic of these reactions was attributed to change of the effective reactivity of the propagating radicals with the nature of the reaction mixture. The data suggest that the formation of ion pairs may be responsible for a considerable increase in the propagation rate and, in consequence, in the overall polymerization rate. For alkaline values of pH, chain propagation involves only radicals having ion pairs at their ends; the participation of the ion pairs in the propagation can influence the microstructure of the polymer chains. Due to stereochemical control effected by the ion pairs, practically stereospecific polyacids may, in certain cases, be formed. Investigations on the temperature dependence of microtacticity have given values of activation enthalpy and entropy differences greatly exceeding those known up to now for isotactic and syndiotactic radical additions.     

Effect of pressure on free-radical copolymerization kinetics. I. A concept of additivity of partial molar volumes of activation

A short review of the effect of pressure on copolymerization kinetics shows the necessity of simple models for a better understanding of activation volumes. Therefore, a simple concept, possibly generally valid for free-radical polymerization, is proposed, based on the assumption that molar volumes of activation can be expressed as an addition of a characteristic radical and a monomer contribution, regardless of the combination involved. The scheme may facilitate the visualization of the transition state and contribute to the understanding of reaction mechanisms of radical polymerizations. Ethylene–vinyl acetate copolymerization at 62°C with tert-butyl alcohol as solvent agrees with the proposed scheme, appearing from the pressure independence of the product of reactivity ratios at the different levels (35,600, and 1200 kg/cm²). Implicitly it can be shown that an ethylene monomer contributes about 2 cm³/mole more to the activation volumes of the propagation reactions than does the vinyl acetate monomer, whereas for the radicals the difference of the respective contributions to the activation volumes is opposite in sign.     

聚甲基丙烯酸正烃酯的微观立构规整性

用碳13核磁共振谱(~(13)C NMR)测定了游离基聚合的聚甲基丙烯酸正烷基酯(PMA-1,-6,-7,-8,-10,-12,-14)的微观立构规整性。发现酯基的长短对规整性影响甚小, 聚合物以间规占多数。认为此现象与游离基聚合反应中链增长过程末端游离基的结构有关, 本文给予初步的解释.     

Polymerization of Acrylonitrile-Metal Haiide Complexes in the Frozen State. III. Relationship between Rate of Radiation-Induced Polymerization and Complex Concentration

Radiation-induced polymerization of acrylonitrile (AN) in the ZnCl₂-AN-H₂O ternary system was carried out at temperatures ranging from 30 to ?78°C, and correlation between the polymerization rate and the concentration of complexed AN with zinc atom was clarified. The selected systems were in the supercooled liquid state at ?78^CC with the molar composition ratio of ZnC12:AN:H₂O of 1:1:3. The polymerization is free-radical in character. The 0.5-power dependence of the polymerization rate on the dose rate at 30°C indicates bimolecular termination, while the 0.9-power dependence at ?78°C shows predominant unimolecular termination because of the high viscosity of the systems at Just above the glass transition temperature. The negative temperature dependence of the polymerization rate is indicative of the tendency of the complex concentration to increase with lower temperatures. The polymerization rate, therefore, is proportional to the 2 and 1.5 powers of the complex concentration at ?78 and 30°C, respectively. These results indicate participation of the complexed monomer both in generation of the initiating radical species on irradiation and in the propagation step. A kinetic scheme has been proposed on the basis of the results.     

Kinetic study of ethylene polymerization with chromium oxide catalysts by a radiotracer technique

The quenching of polymerization with a chromium oxide catalyst by radioactive methanol ¹⁴CH₃OH enables one to determine the concentration of propagation centers and then to calculate the rate constant of the propagation. The dependence of the concentration of propagation centers and the polymerization rate on reaction time, ethylene concentration, and temperature was investigated. The change of the concentration of propagation centers with the duration of polymerization was found to be responsible for the time dependence of the overall polymerization rate. The propagation reaction is of first order on ethylene concentration in the pressure range 2–25 kg/cm². For catalysts of different composition, the temperature dependence of the overall polymerization rate and the propagation rate constant were determined, and the overall activation energy E_ov and activation energy of the propagation state E_p were calculated. The difference between E_ov and E_p is due to the change of the number of propagation centers with temperature. The variation of catalyst composition and preliminary reduction of the catalyst influence the shape of the temperature dependence of the propagation center concentration and change E_ov.     

Synthesis,free-radical polymerization,and stereochemical configuration of methyl α-p-cyanobenzylacrylate

Methyl α-p-cyanobenzylacrylate was synthesized from dimethyl malonate following well-known organic reactions. The purified monomer was polymerized by a free-radical mechanism in benzene solution, using AIBN as initiator in the interval 50–90°C. The kinetic results seem to indicate an apparent ceiling temperature near 90°C. The analysis by ¹³C-NMR of polymers obtained indicates that the macromolecular chains are predominantly syndiotactic and the tacticity is independent of the polymerization temperature in the experimental interval studied. However, the determination of conditional probabilities for iso- and syndiotactic additions and the persistence ratios indicate that the propagation mechanism for the radical polymerization of methyl α-p-cyanobenzylacrylate does not follow a typical Bernoullian statistics.     

Initiation and propagation in γ-radiation-induced polymerization of ethylene

The initiation and propagation reaction in γ-ray-induced polymerization of ethylene was studied by the two-stage irradiation method, i.e., a first stage in which initiation and propagation occur at a high dose rate, and a second stage where only the growth of polymer radical occurs. The rate of initiation is calculated from the amount of polymerized monomer and the degree of polymerization as the rate of increase in the number of polymer chains. The initiation rate is shown to be proportional to the ethylene density in the reactor and dose rate. G_R of radical formation is found to be about 1.6 at 30°C. at a dose rate of 2.5 × 10⁴ rad/hr. and is almost independent of ethylene density but decreases slightly with increasing irradiation dose rate. The lifetime of the growing polymer chain radical is shown to be long at normal temperature. The absolute propagation rate is proportional to the square of ethylene fugacity and depends on dose rate to some extent. For chain growth, irradiation of low dose rate is necessary. The apparent activation energy for the propagation reaction is ?9 kcal./mole.     

Kinetic subtleties of nitroxide mediated polymerization

Due to the academic and industrial interest of Nitroxide Mediated Polymerization (NMP), a lot of investigations have focused on the kinetics of this process. During the last decade, although the simplified kinetic scheme--equilibrium reactions between dormant species (alkoxyamine) and active species (alkyl radicals and nitroxides), propagation reaction of the macro-alkyl radical, and termination reactions--was suitable to predict the main trends at the macromolecular level, it has become obvious that it was not sufficient to describe all the kinetic effects involved in the NMP process. Indeed, like the conventional radical polymerization, NMP should be described as a 3 stage process including initiation, propagation, and self- and cross-termination. These two types of radical polymerization differ by the occurrence during NMP of an activation/deactivation process involving the dormant species in both the initiation and propagation stages. Evidence is provided of the importance of the rate of homolysis of the initiator (alkoxyamines) and of the rate of the first alkyl radical addition onto the monomer for the success of NMP. Thus, the fundamental kinetics of the main reactions involved in NMP as well as side-reactions are also discussed in this tutorial review.     

乙烯和丙烯自由基共聚反应的多尺度模拟模型

结合量子化学和传统过渡态理论计算了乙烯和丙烯自由基聚合反应的速率常数.利用速率常数定义了聚合反应几率(Pijl),构造了乙烯和丙烯共聚合反应的粗粒化动力学模拟模型,并利用该模型研究了不同组成比的乙烯和丙烯的共聚合反应.发现反应速率常数和链端自由基周围的单体浓度都影响链上组分的序列分布.