Modelling free-radical copolymerization kinetics—evaluation of the pseudo-kinetic rate constant method, 1. Molecular weight calculations for linear copolymers

The moment equations for binary copolymerization in the context of the terminal model have been solved numerically for a batch reactor operating over a wide range of conditions. Calculated number- and weight-average molecular weights were compared with those found using pseudo-kinetic rate constants with the method of moments and with the instantaneous property method for homopolymerization. With the pseudo-kinetic rate constant method under polymerization conditions where number-average molecular weights (M̄_n) are below about 10³ the error in calculating M̄_n exceeds 5%. The error increases rapidly with decrease in molecular weight for M̄_n < 10³. M̄_n measured experimentally for polymer chains (homo- and copolymers) have error limits of greater than ±5% at the 95% confidence level. Therefore, for all practical purposes, the pseudo-kinetic rate constant method is valid for M̄_n greater than 10³. Errors in calculating weight-average molecular weights (M̄_w) or higher averages are always smaller than those for M̄_n when applying the pseudo-kinetic rate constant method. The assumptions involved in molecular weight modelling using the pseudo-kinetic rate constant approach are thus proven to be valid, and therefore it is recommended that the pseudo-kinetic rate constant method be employed with the instantaneous property method to calculate the full molecular weight distribution and averages for linear chains synthesized by multicomponent chain growth polymerization.     

Modelling free-radical copolymerization kinetics—evaluation of the pseudo-kinetic rate constant method, 2. Molecular weight calculations for copolymers with long chain branching

The full moment equations and equations using pseudo-kinetic rate constants for binary copolymerization with chain transfer to polymer in the context of the terminal model have been developed and solved numerically for a batch reactor operating over a wide range of conditions. Calculated number- and weight-average molecular weights (M̄_n and M̄_w) were compared with those found using the pseudo-kinetic rate constant method (PKRCM). The results show that the weight-average molecular weights calculated using PKRCM are in agreement with those found using the method of full moments for binary copolymerization when polymeric radical fractions φ₁^˙ and φ₂^˙ of type 1 and 2 (radical centers are on monomer types 1 and 2 for a binary copolymerization) are calculated accounting for chain transfer to small molecules and polymer reactions in addition to propagation reactions. Errors in calculating M̄_w using PKRCM are not always negligible when polymer radical fractions are calculated neglecting chain transfer to small molecules and polymer. In this case, the relative error in M̄_w by PKRCM increases with increase in monomer conversion, extent of copolymer compositional drift and chain transfer to polymer rates. The errors in calculating M̄_w, however, vanish over the entire monomer conversion range for all polymerization conditions when chain transfer reactions are properly taken into account. It is theoretically proven that the pseudo-kinetic rate constant for chain transfer to polymer is valid for copolymerizations. One can therefore conclude that the pseudo-kinetic rate constant method is a valid method for molecular weight modelling for binary and multicomponent polymerizations.     

Critical properties for gelation in free-radical crosslinking copolymerization

A kinetic model was used to predict the molecular weight developments and the critical properties in free-radical crosslinking copolymerization. The predictions of the model were compared to the experimental data reported previously. Agreement of the kinetic model with experiments is satisfactory for both low and high crosslinker contents. The model parameters indicate increasing extent of shielding of pendant vinyl groups as the reaction proceeds due to the increasing number of multiple crosslinkages. The calculation results indicate that the real critical exponents can only be observed in the region ε < 10⁻²–10⁻³ where experimental studies are very difficult. Outside of this region, the apparent critical exponent γ describing the divergence of the weight-average molecular weight was found to deviate from the classical value due to the conversion dependent kinetics of free-radical crosslinking copolymerization.     

Modelling of crosslinking and cyclization in free-radical copolymerization of vinyl/divinyl monomers

The Tobita-Hamielec kinetic model of the crosslink density distribution is further elaborated and extended to incorporate divinyl loop formation. Divinyl loop formation, primary and secondary cyclization, and their effects on the elastically effective crosslink density distribution are extensively examined as a function of cyclization parameters and double bond reactivities. Under conditions of equal double bond rectivity and negligible cyclization, primary chains born at different conversions have the same crosslink density. The variance of the crosslink density distribution is mainly due to unequal reactivities of double bonds and secondary cyclization. Divinyl loop formation and primary cyclization contribute neither to gelation nor to network elasticity and have an insignificant effect on the variance of the crosslink density distribution.     

Control of crosslinking free-radical copolymerization of ethylene glycol dimethacrylate with alkyl methacrylates of various structures and macromolecular design of copolymers

The possibility of controlling the crosslinking free-radical copolymerization of ethylene glycol dimethacrylate with alkyl methacrylates of various structures and of the macromolecular design of the resulting copolymers through the use of small additives of cobalt porphyrin, which terminates polymer chain growth via catalytic chain transfer, has been studied. It has been shown that steric hindrances to the interaction of a propagating radical R* with pendant C=C bonds that are created by bulky substituents of dodecyl methacrylate provide an additional factor that impedes intrachain cyclization and crosslinking reactions that give rise to network structures.     

Simulation model for network formation in free-radical crosslinking copolymerization: Pregelation period

A new simulation model for network formation in free-radical copolymerization of vinyl and divinyl monomers is proposed. This model is based on the crosslinking density distribution of the primary polymer molecules that results from a kinetically controlled network formation. The crosslinking density distribution provides information on how each chain is connected to other chains and therefore, a detailed analysis of the kinetics of network formation becomes possible by application of Monte Carlo simulations. In this method, not only averages but also various distributions, such as molecular weight distribution and distribution of crosslinked units as well as of unreacted pendant double bonds among various polymer molecules, can be calculated. The present theory is a direct solution for the Bethe lattice formed under nonequilibrium conditions, and therefore, it can be used to examine the applicability of the earlier theories of network formation to kinetically controlled systems. The present method is quite general and can be applied to various complex reactions systems that involve crosslinking, branching, cryclization and degradation in a nonequilibrium system.     

Synthesis of N-vinyl-2-pyrrolidone-based branched copolymers via crosslinking free-radical copolymerization in the presence of a chain-transfer agent

Branched copolymers are synthesized via the crosslinking free-radical copolymerization of N-vinyl-2-pyrrolidone and dimethacrylates of various st ructures that is conducted in the presence of the chain-transfer agent 1-decanethiol. The kinetics of this process and the composition of the products are studied by IR spectroscopy, and the content of pendant C=C bonds is estimated. Correlations between the content of dimethacrylate monomer units in the copolymer and the rate of discoloration of a photochromic probe (6-nitrospiropyran) incorporated into the product are established.     

Kinetic theory of anionic copolymerization with constant monomer ratio, 2 . Molecular weight distribution

The kinetic differential equations for the anionic copolymerization with constant monomer ratio are treated by Laplace transformation and a graphical technique. A theoretical method is established by which all molecular parameters of the copolymers, such as the molecular distribution (MWD), the average molecular weight and the polydispersity, can be calculated from reaction rate constants, initial conditions and polymerization time. Three-dimensional plots obtained by numerical computation are presented to illustrate the influence of the reaction conditions on the MWD's of the copolymers.     

Molecular weight relations for crosslinking of chains with length and site distribution

Many polymer networks are formed by crosslinked polymer chains through reactive sites distributed along the chains. How these sites are distributed as well as the chain length distribution can have a significant effect on properties like the gel conversion and molecular weight. Previous treatments have used simplifying approximations. In this paper we eliminate these approximations and derive computational formulae for weight average molecular weight and gel point for polymer chains of any length and reactive site distribution. Three types of crosslinking are considered: direct coupling of chains (homopolymerization), direct coupling through propagation, and coupling through copolymerization with small monomers.     

Molecular weight distribution in radiation-induced polymerization. I. γ-radiation-induced free-radical polymerization of liquid styrene

The kinetics of γ-radiation-induced free-radical polymerization of styrene were studied over the temperature range 0–50°C at radiation intensities of 9.5 × 10⁴, 3.1 × 10⁵, 4.0 × 10⁵, and 1.0 × 10⁶ rad/hr. The overall rate of polymerization was found to be proportional to the 0.44–0.49 power of radiation intensity, and the overall activation energy for the radiation-induced free-radical polymerization of styrene was 6.0–6.3 kcal/mole. Values of the kinetic constants, k_p²/k_t and k_trm/k_p, were calculated from the overall polymerization rates and the number-average molecular weights. Gelpermeation chromatography was used to determine the number-average molecular weight M?_n, the weight-average molecular weight M?_w, and the polydispersity ratio M?_w/M?_n, of the product polystyrene. The polydispersity ratios of the radiation-polymerized polystyrene were found to lie between 1.80 and 2.00. Significant differences were observed in the polydispersity ratios of chemically initiated and radiation-induced polystyrenes. The radiation chemical yield, G(styrene), was calculated to be 0.5–0.8.     

Solvent effects on free-radical polymerization, 4. Modelling of hompolymerization

A new so-called reactant-solvent complex model is proposed to describe the effect of solvent on chain propagation in homopolymerization. It takes into account complex formation of both monomer and radical with solvent by equilibria. Evaluation methods presented permit to estimate the complex equilibrium constant K which is assumed to be nearly the same for both monomer and radical complexation and the relative reactivity ratio r₁₁, for complexed monomer. Measured reaction rates as function of monomer concentration are needed for calculations.     

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.     

Effect of pressure on free-radical copolymerization kinetics. III. An improved method of measuring monomer reactivity ratios under high-pressure conditions

To investigate high-pressure copolymerizations a sampling technique has been developed enabling continual on-line GLC analysis of the reaction mixture. As a result more reliable kinetic data are obtained. This new “sequential sampling” method, allowing the use of gaseous monomers, has been tested for the copolymerization of ethylene with vinyl propionate at 118 MPa and 335 K with tert-butyl alcohol as solvent. The results are compared with those obtained with the “quenching” method used so far, which yields compositional data on the reaction mixture before and after the high-pressure stage, only. It is shown that the “sequential sampling” method is the most adequate method of determining high-pressure monomer reactivity ratios. Furthermore, it is an important safety feature that the present procedure can be easily remote controlled. The present experimental method is neither restricted to copolymerization nor to gas-chromatographic analysis of the reaction mixture.     

Quinone copolymerization. I. Reactions of p-chloranil,p-benzoquinone,and 2,5-dimethyl-p-benzoquinone with vinyl monomers under free-radical initiation

The free-radical copolymerization reactions of p-chloranil, p-benzoquinone, and 2,5-di-methyl-p-benzoquinone with vinyl monomers were studied. Reactions of p-chloranil with styrene yielded copolymers of approximately 1:1 composition under a variety of reaction conditions. A copolymer containing a block of 1:1 of styrene:p-chloranil and a block of polystyrene was prepared. Several styrene-like monomers copolymerized with p-chloranil to yield copolymrs possessing considerable amounts of incorporated quinone. p-Benzoquinone copolymerized with 1,3-butadiene and 2-vinyl-pyridine to yield copolymers of significant molecular weights. Reactions of 2,5-dimethyl-p-benzoquinone with vinyl monomers did not yield any isolable polymeric products.     

Proliferous polymerization under specified conditions in the free-radical crosslinking copolymerization of benzyl methacrylate with neopentyl glycol dimethacrylate in the presence of lauryl mercaptan

During our investigation concerned with the free-radical crosslinking copolymerization of benzyl methacrylate with neopentyl glycol dimethacrylate in the presence of lauryl mercaptan as a chain transfer agent with the intention to remove the obstacles between allyl and vinyl polymerizations, we observed, by chance, popcorn formation in spite of the presence of a large amount of chain transfer agent.     

Preparation,copolymerization kinetics,and viscoelastic behavior of copolymers of 1,3-butadiene and 1,4-diphenyl-1,3-butadiene

1,4-Diphenyl-1,3-butadiene reacts readily with sec-butyllithium in toluene to form adducts. Although this 1,4-substituted conjugated diene did not homopolymerize or copolymerize with styrene, with butadiene it formed copolymers having compositions varying from one end of the chain to the other. The monomer reactivity ratios found were r₁ = 8.2, r₂ = 0 in toluene and r₁ = 2.1, r₂ = 0 in toluene–tetrahydrofuran (0.2%) solution. The intramolecular composition distribution of these polymers varied from an initial butadiene-rich composition, dependent on the ratio of monomers charged, to the equimolar composition of the alternating copolymer. In spite of this compositional heterogeneity, the crosslinked polymers exhibited a single glass transition characteristic of the mean composition. A secondary, high-temperature dispersion observed in the dynamic viscoelastic properties of some of the products is shown to be attributable to network topological effects.     

Cationic copolymerization of indene with styrene derivatives: Synthesis of random copolymers of indene with high molecular weight

Random copolymers with high molecular weights of indene and p‐methylstyrene (pMeSt) were synthesized by cationic polymerization with trichloroacetic acid/tin tetrachloride in CH₂Cl₂ at low temperatures. When indene and pMeSt (1:1 v/v), for example, were polymerized at ?40 °C, both monomers were consumed at very similar rates to give a copolymer with high molecular weight [number‐average molecular weight (M_n): 8–9 × 10⁴]. This is indeed quite unexpected behavior for the combination of these two monomers because pMeSt polymerized over 1000 times faster than indene in the homopolymerization under the reaction conditions previously described. The product copolymer of indene and pMeSt had a random monomer sequence in it that was confirmed by NMR analyses and thermal‐property measurements. In sharp contrast with pMeSt, styrene and p‐chlorostyrene, which have no electron‐donating groups on the phenyl ring, led to low molecular weight polymers (M_n < 10,000) in the copolymerization with indene (1:1 v/v). © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2449–2457, 2002     

Cationic copolymerization of tetrahydrofuran with epoxides. III. Synthesis of block copolymers

Polymerization of various cyclic ethers by BF₃·O(C₂H₅)₂ in the presence of polymeric glycol leads to the formation of hydroxyl terminated block copolymers. Where poly(oxyethylene glycol) is used as the polymeric glycol, fission of the poly(oxyethylene glycol) chain occurs, and block copolymers, containing shorter ethylene oxide unit sequences are obtained. With poly(oxypropylene glycol), on the other hand, the polymer chain remains intact. This may be due to the steric influence of the pendant methyl groups. The cyclic oligomers formed as by-products in the polymerizations are easily removed.