Effect of polyfunctional chain transfer agents on molecular weight distribution in free-radical polymerization, 1. The ideal case: C equals one

The theoretical approach to free-radical polymerization in the presence of polyfunctional transfer agents can be derived in a simple way if the effects of primary chains and termination reactions are neglected. Under these conditions, and for values of the chain transfer constant C = 1, the analytical expressions for the number- and weight-average degree of polymerization, dispersion index and weight distribution function were derived through the elementary probability theory and generating functions. Numerical examples are reported on the relationship between distribution parameters, functionality and monomer conversion.     

Molecular weight distribution formed during free‐radical polymerization in the presence of polyfunctional chain transfer agents

Free‐radical polymerization of styrene was carried out in the presence of chain transfer agents (CTAs) with functionality, f = 1–4. The size exclusion chromatography (SEC) with an ultraviolet absorption detector (UV) was used to measure the molecular weight distribution (MWD). A Monte Carlo simulation method proposed earlier was used to investigate the experimental results. In this simulation method, one can observe the structure of each polymer molecule directly, and very detailed information can be obtained in a straightforward manner, including the elution curve of SEC. It was found that up to the functionality f = 3, the equal reactivity model that assumes the reactivity of all functional groups in a CTA is equal agrees reasonably well with the experimental results. However, with f = 4, the reactivity of the fourth functional group seems to decrease and the substitution effects may need to be accounted for to fine control the formed branched structure. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1267–1275, 1999     

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.     

The molecular weight distribution for chain polymerization plus side reaction

The kinetics of chain polymerization is investigated for the case of a complicating side reaction. In addition to the polymerization reaction, A_i + M → A_i+1, there is a reversible side reaction, A_i + Q ↔ B_i. Initiation is assumed to be instantaneous. The monomer concentration M, and the concentration of the reacting species Q, are assumed to be constant. The reaction kinetics are solved exactly, yielding the distribution of living and dormant polymer, as well as the molecular weight distribution, as explicit functions of the reaction rate constants and the time. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1711–1725, 1997     

Statistical derivation of kinetic molecular weight development equations in nonlinear free-radical polymerization

We propose a statistical method to derive the differential equations that describe the weight-average molecular weight development during nonlinear free-radical polymerizations, by using the random sampling technique. We consider two types of nonlinear free-radical polymerization schemes, free-radical polymerization with chain transfer to polymer and free-radical crosslinking (co)polymerization. The obtained equations fully agree with those obtained through the kinetic approach using the method of moments. The physical meaning of each term in the differential equations as well as the implication of the functional form is discussed from the point of view of the statistical derivation.     

Effect of inititiator on the molecular weight distribution in dispersion polymerization of styrene

Dispersion polymerization of styrene in the particle size range of 10 μ with lauroyl peroxide as initiator results in a double-peak molecular weight (MW) distribution. The high-MW fraction was due to emulsion polymerization. The same phenomenon also exists in AIBN and benzoyl peroxide initiation, although it is less obvious. The kinetics of the reaction for dispersion polymerization was dependent on the concentration of the dispersing agent and the nature of the initiator.     

Molecular weight distribution in emulsion polymerization. II. The copolymer case

A model for evaluating instantaneous degree of polymerization distribution and the chain composition distribution of copolymers produced in emulsion is developed. The approach adopted is based on the mathematics of Markov processes and represents an extension of the one developed for homopolymers in Part I. As in the homopolymer case, the main aspect of the theoretical treatment is the definition of the proper one step transition probability matrix through the so called subprocess-main process procedure. The model accounts for monomolecular and bimolecular termination (both by combination and disproportionation) and, in principle, it can be applied to any number of reacting monomer species as well as to any number of active chains per particle. However, only the 0–1–2 and 0–1–2–3 emulsion copolymerization systems are discussed in detail. In the case of the chain composition distribution, the model allows the calculation of its moments only, through the method of the Generating Function associated with the probability density function. The expression obtained for the instantaneous probability density functions, as well as for the corresponding cumulative distributions, are all in explicit form and involve only algebraic operations among matrices. Efficient numerical procedure for their application are reported in the Appendix. Illustrative calculations are reported for a 0–1–2–3 copolymerization system, simulating the copolymer styrene–methylmethacrylate. The effect of the various termination mechanisms on the distribution of degrees of polymerization and on the first two moments of the chain composition distribution is discussed in detail. Finally, the three dimensional overall distribution function of both chain length and composition is shown under the assumption of Gaussian type chain composition distribution.     

Molecular weight distribution in emulsion polymerization. I. The homopolymer case

A model for evaluating the instantaneous degree of polymerization distribution of homopolymers produced in emulsion, based on the mathematics of the Markov chains, is developed. The model accounts for any number of active chains per particle, as well as for the two fundamental mechanisms of chain termination: mono- and bi-molecular, both by combination and by disproportionation. The core of the model is the so called subprocessmain process treatment, which allows us to correctly evaluate the degree of polymerization of the chains growing in the polymer particles, by distinguishing between the events experienced by the polymer chain which imply a change of its degree of polymerization (subject transitions) and those which imply only a change in the particle state (environment transitions). This is obtained by properly defining the one-step transition probability matrix of the relevant Markov process. Once this is done, the evaluation of the distribution of the degrees of polymerization reduces to a few simple operations among matrices. Explicit expressions for the instantaneous probability density functions and the relative cumulative distributions are obtained. The application of such relationships is facilitated by the numerical procedures reported in the Appendices. The results of the model developed in this work are in agreement with those of earlier models in the range of parameter values of practical interest. In the limit of very low molecular weights, only the model developed in this work provides the correct answer. Moreover, a much more significant result is its applicability to the case of emulsion copolymerization, as it is shown in Part II.     

Molecular weight distribution studies. I. Radiation-induced polymerization of liquid α-methylstyrene

The concentration of water in purified and BaO-dried α-methylstyrene was found to be 1.1 × 10^?4M. The radiation-induced bulk polymerization of the α-methylstyrene thus prepared was studied in the temperature range of ?20°C to 35°C. The polymerization rate varied as the 0.55 power of the dose rate. The theoretical molecular weights and molecular weight distribution were calculated from a proposed kinetic scheme and these values were then compared with those found experimentally. The agreement between these two was reasonably close, and therefore it was concluded that, from the molecular weight distribution point of view, the proposed kinetic scheme for the cationic polymerization of α-methylstyrene is an acceptable one. The rate constant for chain transfer to monomer k_f changed with temperature and was found to be responsible for the decrease in the molecular weight of the polymer with increase in temperature. k_f and k_p at 20°C were found to be 0.95 × 10⁴ l./mole-sec and 0.99 × 10⁶ l./mole-sec, respectively.     

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.     

The role of chain transfer agents in the emulsion polymerization of styrene

The effect of chain transfer agents on the nucleation and growth of polymer particles in the emulsion polymerization of styrene were examined extensively. The chain transfer agents used are carbon tetrachloride, carbon tetrabromide, and four primary mercaptans (C₂, n-C₄, n-C₇, and n-C₁₂). It is shown that with an increase in the amount of chain transfer agents charged the rate of polymerization per particle decreases progressively. The number of polymer particles formed, on the other hand, increases initially then decreases. These effects can be enhanced by using a chain transfer agent with higher values of chain transfer constant and solubility in water. It is also demonstrated that with increasing radical desorption from the particles, aided by chain transfer agents, the emulsifier dependence exponent for the number of polymer particles formed increases from 0.6 to 1.0 and the initiator dependence exponent decreases from 0.4 to 0. The effect of chain transfer agents on the nucleation and growth of polymer particles in the emulsion polymerization of styrene can be explained in terms of desorption of chain-transfered radicals from the polymer particles.     

Theoretical study of chain transfer in anionic polymerization, 2. Copolymerization accompanied by chain transfer to solvent

The main factors determining molar mass characteristics of copolymers formed in nonterminating copolymerization under the conditions of chain transfer to solvent are studied theoretically. The dependences of the mean polymerization degrees on conversion and monomer feed composition for various values of reactivity ratios are obtained. The results obtained greately differ from those for homopolymerization. This is explained by the contribution of cross-propagation reactions. In particular, it is shown that at ≪ and ≪ the azeotropic copolymerization proceeds like the living one even if homopolymerization of each monomer is accompained by extensive chain transfer to solvent.     

Modeling of molecular weight development in atom transfer radical polymerization

A kinetic model has been developed for atom transfer radical polymerization processes using the method of moments. This model predicts monomer conversion, number‐average molecular weight and polydispersity of molecular weight distribution. It takes into account the effects of side reactions including bimolecular radical termination and chain transfers. The determining parameters include the ratios of the initiator, catalyst and monomer concentrations, as well as the ratios of the rate constants of propagation, termination, transfer and the equilibrium constant between radicals and their dormant species. The effects of these parameters on polymer chain properties are systematically simulated. The results show that an ideal living radical polymerization exhibiting a linear relationship between number‐average molecular weight versus conversion and polydispersity approaching unity is only achievable under the limiting condition of slow monomer propagation and free of radical termination and transfers. Improving polymerization rate usually accompanies a loss of this linearity and small polydispersity. For polymerization systems having a slow initiation, the dormant species exercise a retention effect on chain growing and tend to narrow the molecular weight distribution. Increasing catalyst concentration accelerates the initiation rate and thus decreases the polydispersities. It is also shown that for a slow initiation system, delaying monomer addition helps to reduce the polydispersities. Radical termination and transfers not only slow down the monomer conversion rates but also broaden polymer molecular weight distributions. Under the limiting conditions of fast propagation and termination and slow initiation, the model predicts the conventional free radical polymerization behaviors.