Molecular weight distribution in living polymerization proceeding with reshuffling of polymer segments due to chain transfer to polymer with chain scission, 1. Determination of kp/ktr ratio from DPw/DPn data. Ideal reproduction of polymer chain activities

The molecular weight distribution (MWD) curves for polymerization systems with chain transfer to polymer leading to reshuffling of polymer segments (and broadening of the MWD), but not changing chain functionalities, were simulated by the Monte Carlo method. The bimodality observed in some distributions was explained by different distribution functions of chains which did not undergo reshuffling and of those which underwent the chain transfer reaction. Using this observation, a numerical integration method for computing DP _w/DP _n (and the MWD curves) in the systems under consideration was devised. Plots relating DP _w/DP _n to monomer conversion and k_tr/k_p are presented and a method of determination of k_tr/k_p from the DP _w/DP _n data is proposed.     

Model Studies of Nitroxide‐Mediated Styrene Miniemulsion Polymerization – Opportunities for Process Improvement

Modeling studies were performed to investigate how persulfate‐initiated nitroxide‐mediated styrene miniemulsion polymerizations are influenced by changes to the polymerization recipe. By manipulating the initial concentrations of potassium persulfate and nitroxide, and the aqueous phase volume, trends in the predicted polymerization time, number average molecular weight, polydispersity and degree of polymer livingness were identified that indicate operating conditions for improved process performance. Specifically, our model predicts the existence of experimental conditions that simultaneously minimize polymer polydispersity and maximize the livingness of the polymer. The mechanisms responsible for the predicted trends were identified from the predicted molecular weight distributions of the living and dead polymer chains.

Predicted number MWDs at 20% monomer conversion for styrene NMMP systems employing various levels of [KPS]_aq,0. Dormant KPS‐initiated polymer radicals.     

Postpolymerization effect on molecular weight distribution generated by pulsed laser radical polymerization

The postpolymerization effect on molecular weight distribution (MWDs) and on the Pulsed Laser Polymerization (PLP) technique for evaluation of kinetic constants is investigated. General expressions for moments are derived for a polymerization scheme that contains the reactions of chain initiation, propagation, and termination by recombination or disproportionation, under polymerization initiation by an arbitrary sequence of radiation pulses. The results of calculation of MWDs and of the weight-average degree of polymerization (P _w) for methyl methacrylate are presented. It is shown that the P _w value strongly depends on postpolymerization. A new method for determining the rate constants of chain propagation and chain termination from a single experiment by polymerization with packets of laser pulses is presented.     

Molecular weight distribution in emulsion polymerizations

A mathematical formulation is given which describes the evolution of the number distribution of the molecular weight (MWD) of linear polymer chains that grow in emulsion polymerization systems. The resulting set of coupled ordinary differential equations takes into account the microscopic events of free radical entry, exit, chain annihilation, bimolecular termination (by combination and disproportionation), and chain transfer in a mono- or polydisperse system. Simple analytic solutions are presented for systems in which the number of particles, as well as the average number of free radicals per particle, is constant and in which the rate coefficients are size independent. These solutions indicate that compartmentalization of the free radicals in the latex particles results in a significant increase in the polydispersity of the polymer produced by emulsion polymerization, compared with that in bulk systems. The theory shows that significant mechanistic information may be obtained from experimental MWDs and that, in principle, experimental conditions may be prescribed to grow a desired MWD. The MWDs are presented in a novel manner that facilitates the comparison of theory with experiment.     

Pulsed Laser Polymerization at Low Conversions: Broadening and Chain Transfer Effects

Pulsed laser polymerization (PLP) is widely employed to measure propagation rate coefficients k_p in free radical polymerization. Various properties of PLP have been established in previous works, mainly using numerical methods. The objective of this paper is to obtain analytical results. We obtain the most general analytical solution for the dead chain molecular weight distribution (MWD) under low conversion conditions which has been hitherto obtained. Simultaneous disproportionation and combination termination processes are treated. The hallmarks of PLP are the dead MWD discontinuities located at integer multiples of n₀ = k_pt₀C_M, where t₀ is the laser period and C_M is the monomer concentration. We show that chain transfer reduces their amplitude by factors , consistent with numerical results obtained by other workers. Here c_tr is the chain transfer coefficient and Ln₀ (L = integer) are the discontinuity locations. Additionally, transfer generates a small amplitude continuous contribution to the MWD. These results generalize earlier analytical results which were obtained for the case of disproportionation only. We also considered two classes of broadening: (i) Poisson broadening of growing living chains and (ii) intrinsic broadening by the MWD measuring equipment (typically gel permeation chromatography, GPC). Broadening smoothes the MWD discontinuities. Under typical PLP experimental conditions, the associated inflection points are very close to the discontinuities of the unbroadened MWD. Previous numerical works have indicated that the optimal procedure is to use the inflection point to infer k_p. We prove that this is a correct procedure provided the GPC resolution σ is better than nequation/tex2gif-stack-1.gif. Otherwise this underestimates Ln₀ by an amount of order σ²/n₀.

Schematic of a chain transfer reaction with monomer as the transfer agent.     

Kinetic model of living radical polymerization

This work studies the kinetics of living radical polymerization by means of both the nonsteady state approach and the quasi-stationary state method. Expressions for the numberand weight-average degress of polymerization and the polydispersity index were derived. Numerical results show that the concentration of residual initiator seriously influences the polydispersity index of the resulting polymer. The calculated outcomes of the non-steady state approach are evidently different from those of the quasi-stationary state method when the magnitude of the rate constant of termination is comparable with that of the propagation rate constant, and the difference becomes negligible if the rate constant of the termination (k_t) is much larger than that of propagation (k_p). The polydispersity index of the resulting polymer increases with decreasing ratios of k_t to k_p or M_O to I_O (initial concentrations of monomer and initiator).     

The incorporation of side reactions into pseudostationary polymerization, 1. The closed solution of a kinetic scheme comprising chain-transfer to monomer or solvent

A procedure is developed that allows the calculation of chain length distributions of polymers prepared by periodic modulation of the initiation process, considering termination by disproportionation and chain transfer. For the case of a (pseudostationary) laserpulse initiated polymerization process a closed solution can be derived for the chain length distribution (cld) of dead polymer and its O^th, 1^st and 2^nd moments. By analysis of the detectability of the “extra-peaks” appearing in the cld (which represent the key for the determination of propagation constants) as a function of the parameters chosen the optimum conditions can be predicted for experiments.     

Gamma radiation-initiated polymerization of styrene at high pressure. II. Chain termination

The pressure dependence of the termination rate constant k_t for the free radical polymerization of monomers such as styrene is a function of polymer chain length, chain stiffness, and monomer viscosity, all of which influence the rate of segmental diffusion of an active radical chain end out of the coiled polymer chain to a position in which it can react with a proximate radical. Although k_t is not sensitive to changes in chain length, the large increase in molecular weight is responsible for a significant reduction in k_t at high pressures. For most of the common vinyl polymers, which exhibit some degree of chain stiffness, k_t is inversely proportional to a fractional power of the monomer viscosity because it depends in part on the resistance of chain segments to movement and in part on the influence of viscosity in controlling diffusion of the chain ends. The fractional exponent appears to increase with pressure and this is interpreted as evidence that the polymer chains become more flexible in a more viscous solvent. Because the fractional exponent is higher for more flexible chains, the value of the activation volume for chain termination is an indication of the degree of flexibility of the polymer chains, provided that the monomer is a good solvent for the polymer and that chain transfer is negligible.     

Simulation of pseudostationary radical polymerization, 1. Chain-length distributions for arbitrary initiation profiles

A procedure is developed which allows to treat arbitrary periodic initiation profiles (asymmetric and symmetric triangle profiles, sinusoidal profiles, Gaussian profiles etc.) in pseudostationary radical polymerization. Using an iterative method these profiles are transformed into the (likewise periodic) radical profiles and into the chain-length distributions of the resulting polymer in case of termination by disproportionation. These distributions are analysed for the position of their inflection points which may be used for experimental determination of the elementary rate constant of chain propagation k_p. It turned out that for all profiles that have at least one discontinuity (e.g. asymmetric triangle profiles) the position of the point of inflection is a correct measure of k_p for a conveniently wide range of experimental parameters. In case of profiles without discontinuity (symmetric triangle profiles, sinusoidal and Gaussian profiles) the position of the inflection point is shifted to lower values which means that the k_p values determined on this basis will be a little too small. In most cases, however, the error introduced by this fact will not exceed the overall error of the experiment so that in practice the method of determining k_p in pseudostationary polymerization is not restricted to those profiles which exhibit discontinuities.     

Effect of the Intramolecular Chain Transfer to Polymer on PLP/SEC Experiments of Alkyl Acrylates

Pulsed‐laser polymerization (PLP) has been adopted by IUPAC as the method of choice for the determination of propagation rate constants (k_p). However, the method has failed in the polymerization of alkyl acrylates at temperatures above 30 °C. In this work, the PLP experiments were analyzed by simulation using a Monte Carlo algorithm. It was found that the experimental difficulties encountered to accurately determine k_p at temperatures above 30 °C were caused by extensive intramolecular chain transfer. This mechanism is not operative at lower temperatures because of its high activation energy.

Pulsed‐laser polymerization of BA in bulk at temperatures between −41 and +40 °C: Simulated MWD trace.     

Simulation of Molecular Weight Distributions Obtained by Pulsed Laser Polymerization (PLP): New Analytical Expressions Including Intramolecular Chain Transfer to the Polymer

A new approach for the simulation of PLP (pulsed laser polymerization) is presented. This approach allows one to obtain new analytical solutions for different polymerization schemes, including either chain transfer to the monomer or intramolecular chain transfer to the polymer. The first results of the simulation of PLP experiments on n‐butyl acrylate at 20 °C and ambient pressure are presented.

MWDs simulated for PLP of n‐butyl acrylate, in bulk at 20 °C and ambient pressure using three models: the model with intramolecular chain transfer to the polymer (solid line), the model with chain transfer to monomer (dashed line), and the classical model (dotted line).     

The Influence of Chain Length‐Dependent Propagation on the Evaluation of the Chain Length Dependence of the Rate Coefficient of Bimolecular Termination, 1. PLP–SEC Methods

Chain length distributions have been calculated for polymers prepared by pulsed laser polymerization (PLP) under the condition that not only chain termination but also chain propagation is subject to chain length dependence. The interplay between these two features is analyzed with the chain length dependence of the rate coefficient of termination k_t introduced in the form of a power law and that of propagation k_p modeled by a Langmuir‐type decrease from an initial value for zero chain length to a constant value for infinite chain lengths. The rather complex situation is governed by two important factors: the first is the extent of the decay of radical concentration [R] during one period under pseudostationary conditions, while the second is that termination events are governed by [R]² while the propagation goes directly with [R]. As a consequence there is no general recommendation possible as to which experimental value of k_p is best taken as a substitute for the correct average of k_p characterizing a specific experiment. The second point, however, is apparently responsible for the pleasant effect that the methods used so far for the determination of k_t and its chain length dependence (i.e., plotting some average of k_t versus the mean chain‐length of terminating radicals on a double‐logarithmic scale) are only subtly wrong with regard to a realistic chain length dependence. This is especially so for the quantity k_t* (the average rate coefficient of termination derived from the rate of polymerization in a PLP system) and its chain length dependence.     

Antithetic function of alcohol in living cationic polymerization: From terminator/inhibitor to useful initiator

We employed alcohols as initiators for living cationic polymerization of vinyl ethers and p‐methoxystyrene, coupled with tolerant Lewis acid, borontrifluoride etherate (BF₃OEt₂), although they were known to be poisonous reagent to bring about chain‐breaking such as chain transfer/termination rather than such beneficial one for propagation and polymerization‐control. As well known, without assistance of additive, ill‐defined polymers with broad molecular weight distributions (MWDs) were produced. Even addition of conventional oxygen‐based bases, for example, ethyl acetate (AcOEt), 1,4‐dioxane (DO), tetrahydrofran (THF), and diethyl ether (Et₂O) was less efficient in this system to control molecular weights and MWDs (M_w/M_n > 2.0). In contrast, by addition of dimethyl sulfide (Me₂S), MWDs of the resultant polymers became much narrower (M_w/M_n < 1.23) and the number‐average molecular weight (M_n) increased in direct proportion to monomer conversion in agreement with the calculated values assuming that one alcohol molecule generates one polymer chain. Studying changed feed‐ratio of alcohol to monomer and structural analyses with NMR and MALDI‐TOF‐MS indicated that quantitative initiation from alcohol giving alkoxide counteranion. This system opens a new way to use a variety of alcohols as initiators, which would allow us to design variety of structures and functions of counteranion. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4194–4201, 2009     

Ab initio Emulsion Polymerization by RAFT (Reversible Addition–Fragmentation Chain Transfer) through the Addition of Cyclodextrins

A novel process to produce homo‐ and copolymers by RAFT polymerization in emulsion is presented. It is known that RAFT‐controlled radical polymerization can be conducted in emulsion polymerization without disturbing the radical segregation characteristic of this process, thus leading to polymerization rates identical to those encountered in the corresponding nonliving systems. However, RAFT agents are often characterized by very low water solubility and, therefore, they diffuse very slowly from the monomer droplets, where they are initially solubilized, to the reaction loci, i.e., the polymer particles. Accordingly, when used in emulsion polymerization, they are practically excluded from the reaction. In this work, we show that cyclodextrins, well‐known for their ability to form water‐soluble complexes with hydrophobic molecules, facilitate the transport across the H₂O phase of the RAFT agent to the polymer particles. Accordingly, chains grow through the entire process in a controlled way. This leads to the production of low‐polydispersity polymers with well‐defined structure and end functionalities as well as to the possibility of synthesizing block copolymers by a radical mechanism.     

Molecular weight distribution in random branching of polymer chains

Analytical expressions for the average molecular weights of randomly branched polymer molecules with any primary chain distribution are developed. A full molecular weight distribution (MWD) function is also derived for the case where primary chains conform to the most probable distribution. This MWD function can be separated into the fractional MWDs containing k branch points; therefore, very detailed information on the structure of randomly branched polymers can be obtained. The average molecular weights of the polymer fraction containing k branch points are linear functions of the number of branch points k, and the distribution becomes narrower as k increases. The heterogeneity in the distribution of branch points can make the weight-average degree of polymerization larger, although it is impossible to form a gel molecule only via branches (T-shaped junctions) without assistance of crosslinkages (H-shaped junctions).     

Synthesis and kinetic analysis of DPE controlled radical polymerization of MMA

The 1,1‐diphenylethene (DPE) controlled radical polymerization of methyl methacrylate was performed at 80 °C by using AIBN as an initiator and DPE as a control agent. It was found that the molecular weight of polymer remained constant with monomer conversion throughout the polymerization regardless of the amounts of DPE and initiator in formulation. To understand the result of constant molecular weight of living polymers in DPE controlled radical polymerization, a living kinetic model was established in this research to evaluate all the rate constants involved in the DPE mechanism. The rate constant k₂, corresponding to the reactivation reaction of the DPE capped dormant chains, was found to be very small at 80 °C (1 × 10^?5 s^?1), that accounted for the result of constant molecular weight of polymers throughout the polymerization, analogous to a traditional free radical polymerization system that polymer chains were terminated by chain transfer. The polydispersity index (PDI) of living polymers was well controlled <1.5. The low PDI of obtained living polymers was due to the fact that the rate of growing chains capped by DPE was comparable with the rate of propagation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2009     

Criteria for living systems with a special emphasis on living cationic polymerization of alkenes

A number of new living systems have been reported in recent years. Classic anionic polymerization of nonpolar monomers allows the synthesis of well-defined high molecular weight polymers (DP > 1000), block copolymers, chains with perfect terminal functionalities and behaves as a true living system. Some new systems abuse the term “living polymerization.” A relatively modest criterion for living systems is proposed “3 X 10,000,” i.e., k_p/k_t > 10⁴ mol^-1 L, k_p/k_tr > 10⁴, 1/k_t/tr > 10⁴ s (translated to < 10% of chains deactivated at t ≈ 1000 s), which is related to a typical limit of the polymeric chain dimensions (DP ≈ 100) and standard synthetic manipulations (≈ 15 min). New living cationic systems are discussed in detail with special emphasis on exchange phenomena. © 1993 John Wiley & Sons, Inc.     

Modeling molecular weight distribution in emulsion polymerization reactions with transfer to polymer

A mathematical model was developed for the computation of the dynamic evolution of molecular weight distributions (MWDs) during nonlinear emulsion polymerization reactions. To allow the direct computation of the whole MWD, an adaptive orthogonal collocation technique was applied. The model was validated with experimental methyl methacrylate/butylacrylate (BuA) semicontinuous and vinyl acrylate (VA)/Veova10 continuous emulsion polymerization results. Both systems considered introduce significant chain‐transfer reactions to polymer chains as a result of the presence of BuA and VA, respectively. The model developed was able to represent quite properly the kinetics and MWD of polymer samples during emulsion polymerizations. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3513–3528, 2001     

Modeling the reversible addition–fragmentation transfer polymerization process

A kinetic model has been developed for reversible addition–fragmentation transfer (RAFT) polymerization with the method of moments. The model predicts the monomer conversion, number‐average molecular weight, and polydispersity of the molecular weight distribution. It also provides detailed information about the development of various types of chain species during polymerization, including propagating radical chains, adduct radical chains, dormant chains, and three types of dead chains. The effects of the RAFT agent concentration and the rate constants of the initiator decomposition, radical addition, fragmentation, disproportionation, and recombination termination of propagating radicals and cross‐termination between propagating and adduct radicals on the kinetics and polymer chain properties are examined with the model. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1553–1566, 2003