Molecular weight distribution in free radical polymerization with long-chain branching

A new theory to predict the molecular weight distribution in free radical polymerization that includes chain transfer to polymer is proposed. This theory is based on the branching density distribution of the primary polymer molecules. The branching density distribution provides the information on how each chain is connected to other chains, and therefore, a full molecular weight distribution can be calculated by application of the Monte Carlo simulation. The present theory accounts for the history of the generated branched structure and can be applied to various reaction systems that involve branching and crosslinking regardless of the reactor types used. The present simulation confirmed the validity of the method of moments in a batch polymerization proposed earlier. It was shown clearly why gelation never occurs by chain transfer to polymer without the assistance of other interlinking reaction such as bimolecular termination by combination. © 1993 John Wiley & Sons, Inc.     

Long-chain branching in free-radical polymerization due to chain transfer to polymer

The Monte Carlo sampling technique is used to investigate the branched structure formation during free-radical polymerization that involves chain transfer to polymer. This method accounts for the history of the generated branched structure and can provide virtually any structural information, because one can observe each polymer molecule directly. In this paper, we investigate the whole molecular weight distribution (MWD) for both pre- and postgelation periods, the MWDs for polymer molecules containing 0, 1, 2, 3, … branch points, the branching density of polymer molecules as functions of both size and the number of branch points, the spatial distribution of the branched chains at the theta state, etc. Contrary to the term ‘long-chain’ branching, many branch chains are relatively small, and the branched structures formed are significantly different from those usually depicted to introduce ‘branched polymers’ in many introductory textbooks. The radii of gyration at the theta state can be approximated by the Zimm-Stockmayer equation for random branching, in spite of various violations against the assumptions used in deriving the equation © 1995 John Wiley & Sons, Inc.     

Branched structure formation in free radical polymerization of vinyl acetate

The branched structure formation during free radical polymerization of vinyl acetate is investigated in detail by application of the computer simulations on the basis of the Monte Carlo sampling technique. Simulations are made for the whole molecular weight distribution (MWD), the MWDs for polymer molecules containing 0, 1, 2, 3, etc., branch points, the branching density as functions of both size and the number of branch points, the spatial distribution of the branched chains, etc. It was found that the effect of polyradicals on the formed MWD could be neglected for batch polymerizations of the present reaction system. A large number of relatively small branch chains are formed due to both chain transfer to polymer (CTP) and the terminal double-bond polymerization (TDBP). The radius of gyration at a Θ state is found to agree satisfactorily with the Zimm-Stockmayer equation for random branching in spite of the heterogeneous branched structure formed in the polymerization. The present investigation reveals important characteristics of the complex molecular structure formation during free radical polymerization that involves both CTP and TDBP. © 1996 John Wiley & Sons, Inc.     

Markovian approach to nonlinear polymer formation: Free-radical polymerization with chain transfer to polymer

A Markovian model is proposed for nonrandom branching reactions, by using free-radical polymerization that involves chain transfer to polymer as an example. Free-radical polymerizations are kinetically controlled; therefore, each primary polymer molecule experiences different history of branched structure formation. By assuming that the primary chains with the identical birth time conform to the same chain connection probabilities, the nonlinear structural development can be viewed as a system in which the primary chains formed at different birth times are combined into nonlinear polymers in accordance with the first-order Markov chain statistics. An explicit formula for the weight-average chain length is derived in a matrix form. The onset of gelation is simply stated as a point at which the largest eigenvalue of the transition matrix X reaches unity, i.e., det(X − I) = 0. This criterion for the onset of gelation can be considered as an extension of the Flory/Stockmayer theory to a nonequilibrium reaction system. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 357–371, 1998     

Molecular weight distribution in nonlinear emulsion polymerization

A modelistic study of the molecular weight distribution (MWD) formed in emulsion polymerization that involves chain transfer to polymer is conducted, by focusing our attention to the effect of very small reaction volume on the formed MWD. In emulsion polymerization, a polymer radical that causes polymer transfer reaction must choose the partner only within the same particle, which makes the expected size of the polymer molecule to be chosen smaller compared with the corresponding polymerization system that involves an infinitely large number of polymeric species. The usual assumption for homogeneous polymerization that the rate of chain transfer to a particular polymer molecule is proportional to its chain length cannot be used, except when branching frequency is low and particle size is large enough. This fact invalidates the direct use of models developed for homogeneous nonlinear polymerizations to emulsion polymerizations. Model equations that could be used to assess the significance of the limited space effects on the MWD under a given polymerization condition are also proposed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1515–1532, 1997     

Simulation model for the molecular weight distribution in emulsion polymerization

A Monte Carlo simulation model for the kinetics of emulsion polymerization is proposed. In the present model, the formation of each polymer molecule is simulated by the use of only a couple of probability functions; therefore, the calculation can be handled well even on personal computers. It is straightforward to account for virtually any kinetic event, such as the desorption of oligomeric radicals and chain length dependence of kinetic parameters, and as a consequence very detailed information such as the full distributions of the dead polymer molecular weights and the macroradicals among various polymer particles can be obtained. When bimolecular terminations are the dominant chain stoppage mechanism, the instantaneous molecular weight distribution (produced in a very small time interval) becomes broader than that for homogeneous polymerizations due to a higher possibility that short and long polymer radicals react with each other if bimolecular reactions are fast enough. The increase in the polydispersity of the MWD is fairly large, especially when bimolecular termination by disproportionation is significant; however, the gel permeation chromatography (GPC) may not be a suitable analytical technique to detect such broadening since oligomeric peaks may not be observed in the elution curve. The present simulation method provides greater insight into the complicated phenomena of emulsion polymerizations. © 1995 John Wiley & Sons, Inc.     

Molecular weight distribution of metallocene polymerization with long chain branching using a binary catalyst system

In metallocene polymerization, termination by β-hydride elimination generates polymer chains containing unsaturated vinyl groups at their chain ends. Further polymerization of these macromonomers produces branched polymers. Material properties of the branched polymers not only depend on molecular weight and branching density, but also on chain structure. This work presents analytical expressions to predict the bivariate distribution of molecular weight and branching density for polymer chains having dendritic and comb structures. It is shown that when a single metallocene catalyst is used the formation of dendritic polymers is favored with only a very small fraction of highly branched chains assuming comb structure. The use of a binary catalyst system is therefore proposed to obtain high content of comb polymers. One catalyst generates macromonomers and the other yields in-situ branching. It is found that the comb polymers give much narrower molecular weight distributions than dendritic polymers with same branching densities.     

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.     

Importance of active-site reactivity and reaction conditions in the preparation of hyperbranched polymers by self-condensing vinyl polymerization: Highly branched vs. linear poly[4-(chloromethyl)styrene] by metal-catalyzed “living” radical polymerization

The self-condensing vinyl polymerization of 4-(chloromethyl)styrene using metal-catalyzed living radical polymerization catalyzed by the complex CuCl/2,2′-bipyridyl has been attempted. Given the unequal reactivity of the two potential propagating species in this system, a variety of polymerization conditions were tested to optimize the extent of branching in the products. Typical reaction conditions included polymerization in the bulk, or preferably in chlorobenzene solution, with catalyst to monomer ratios in the range 0.01–0.30, temperatures of 100–130°C, and reaction times from 0.1 to 32 h. Polymers with weight average molecular weights between 3 × 10³ and 1.6 × 10⁵ and different extents of branching are formed as evidenced by size-exclusion chromatography, light scattering, and NMR analysis of the reaction products. The influence of reaction conditions on the molecular weight and branching of the resulting polymers is discussed in detail. In sharp contrast to an earlier report, the weight of evidence suggests that, at a catalyst to monomer ratio of 0.01, an almost linear polymer is obtained, while a high catalyst to monomer ratio favors the formation of a branched structure. As a result of the unequal reactivity of the primary and secondary benzylic halide reactive sites, growth occurs by a modified self-condensing vinyl polymerization mechanism that involves incorporation of the largely linear vinyl-terminated fragments formed early on in the polymerization into the vinyl polymer, to afford an irregularly branched structure. Chemical transformations involving the numerous benzylic halide functionalities of the highly branched polymer have been investigated. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 955–970, 1998     

Evolution of Molecular Weight and Long Chain Branch Distributions in Olefin–Diene Copolymerization

A model for olefin–diene copolymerization and long chain branch formation was developed. The model shows that the number‐average molecular weight and branching density increases linearly with time in a semi‐batch polymerization, while the polydispersity depends on the diene content in the polymer and on the polymerization time. For low diene fractions or low polymerization times, the polydispersity increases linearly with time. For higher diene contents, the polydispersity increases exponentially with polymerization time after a critical polymer concentration is reached. The calculated distributions of branched species indicate that diene content influences the amount of highly branched chains produced in the polymerization, markedly broadening the distribution of molecular weight and leading to gel formation.

Weight distribution of branched species after 30 min of polymerization.     

Architectural control of polystyrene physical properties using branched anionic polymerization initiated at ambient temperature

Ambient temperature-initiated anionic polymerization has generated branched polystyrenes of varying molecular weights and architectures by inclusion of a distyryl branching comonomer into a conventional sec-Butylithium-initiated polymerization of styrene. Primary chain length control within the branched polymers, and restriction of the branching points to varying segments of the primary chains, led to variations of glass transition temperature with no direct correlation to the branched polymer molecular weight but a strong relationship to the length of individual chains comprising the branched macromolecules.     

Particle formation under monomer‐starved conditions in the semibatch emulsion polymerization of styrene. I. Experimental

Particle formation and particle growth compete in the course of an emulsion polymerization reaction. Any variation in the rate of particle growth, therefore, will result in an opposite effect on the rate of particle formation. The particle formation in a semibatch emulsion polymerization of styrene under monomer‐starved conditions was studied. The semibatch emulsion polymerization reactions were started by the monomer being fed at a low rate to a reaction vessel containing deionized water, an emulsifier, and an initiator. The number of polymer particles increased with a decreasing monomer feed rate. A much larger number of particles (within 1–2 orders of magnitude) than that generally expected from a conventional batch emulsion polymerization was obtained. The results showed a higher dependence of the number of polymer particles on the emulsifier and initiator concentrations compared with that for a batch emulsion polymerization. The size distribution of the particles was characterized by a positive skewness due to the declining rate of the growth of particles during the nucleation stage. A routine for monomer partitioning among the polymer phase, the aqueous phase, and micelles was developed. The results showed that particle formation most likely occurred under monomer‐starved conditions. A small average radical number was obtained because of the formation of a large number of polymer particles, so the kinetics of the system could be explained by a zero–one system. The particle size distribution of the latexes broadened with time as a result of stochastic broadening associated with zero–one systems. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3940–3952, 2001     

Bimodal molecular weight distribution formed in the emulsion polymerization of ethylene

It is known that the molecular weight distribution (MWD) formed in an emulsion polymerization of ethylene can be bimodal. However, the origin of the bimodality has not been elucidated. In this article, a Monte Carlo simulation is conducted, mostly with parameters reported in the literature. The simulated MWDs are bimodal because of the limited volume effect; that is, the high molecular weight profiles are distorted by the small particle size, which is comparable to the size of the largest branched polymer molecule in a particle. The simulated MWDs agree reasonably well with the experimentally obtained MWDs. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3426–3433, 2002     

由可控聚合反应直接制备不同形貌的聚集体

由可控聚合,包括活性阴离子和自由基聚合直接制备不同形貌纳米材料,是近几年来合成化学领域的一个重要研究成果.与两亲性嵌段共聚物在选择性溶剂中自组装方法不同,在选择性溶剂中进行的分散聚合,首先生成两亲性嵌段共聚物,并逐渐增加第二段聚合物的链长,以实现相分离,形成球形胶束;聚合物链继续增长,实现形貌转变,从而制备预期的聚合物形貌,包括球形胶束、纳米棒、纳米线、囊泡和复合囊泡等.本文综述了乳液聚合法制备球形胶束等形貌;描述了不同聚合体系形成的形貌以及它们的性质和应用,讨论了形貌的形成机理和控制方法,同时指出了存在的问题.     

Calculation of the molecular-mass distribution for hyperbranched macromolecules synthesized by living three-dimensional radical polymerization

Kinetic analysis of the scheme underlying the formation of branched and hyperbranched macro- molecules formed by living three-dimensional radical po lymerization in the pregel period makes it possible to derive some theoretical dependences relating the conditions of polymerization and the molecular-mass distribution of polymers. In this case, a polymer product constitutes a mixture of macromolecules with different degrees of branching, and the fractional weight of macromolecules with hyperbranched structure is no more than one-third with respect to the overall polymer product.     

Microgel formation in emulsion copolymerization: II. Seeded polymerization

Microgel formation in seeded emulsion copolymerization of methyl methacrylate and ethylene glycol dimethacrylate is investigated both experimentally and theoretically. By introducing seed latex, the network structure development can be changed significantly. Even when the crosslinking density development takes a similar pattern as the crosslinking copolymerization in homogeneous media, the molecular weight development shows both types of behavior that is characteristic of emulsion polymerization without seed latex and of homogeneous polymerization, depending on the primary polymer chain length and the mole fraction of the divinyl monomer used. Once the microgels are formed, the weight-average molecular weight increases just linearly with conversion due to a very small locus of polymerization. The present investigation reveals important characteristics of gelation phenomena in a limited space. © 1996 John Wiley & Sons, Inc.     

Free‐Radical Polymerization with Long‐Chain Branching and Scission in a Continuous Stirred‐Tank Reactor

Free‐radical polymerization that involves the polymer transfer reactions leading to both long‐chain branching and scission, as in the cases of high‐pressure olefin polymerization, is considered. In CSTR, the residence time distribution is broad and the primary polymer chain, whose residence time is large, is subjected to polymer transfer reaction for a longer time, leading to a larger number of branching and scission points. The distributions of both branching and scission density are much broader in a CSTR than in a batch, or equivalently, a PFR. The radius of gyration for larger sized polymers formed in a CSTR tends to be much smaller than that for randomly branched polymers.

     

Branching and crosslinking in emulsion polymerization

The seeded semibatch emulsion polymerization of butyl acrylate (BA) with allyl methacrylate (AMA) and butanediol diacrylate (BDA) was used to study the influence of the crosslinkers on the kinetics, branching and crosslinking density, gel fraction and sol MWD produced during the experiments carried out at 80°C using potassium persulfate as initiator. Surprisingly, the most reactive crosslinker, BDA, produced the less crosslinked, branched and gel containing polymer. These results were explained with the help of a mathematical model in terms of cyclization reactions and diffusion controlled propagation and termination reactions.     

Simultaneous long‐chain branching and random scission: I. Monte Carlo simulation

In free‐radical olefin polymerizations, the polymer transfer reactions could lead to chain scission as well as forming long‐chain branches. For the random scission of branched polymers, it is virtually impossible to apply usual differential population balance equations because the number of possible scission points is dependent on the complex molecular architecture. On the other hand, the present problem can be solved on the basis of the probability theory by considering the history of each primary polymer molecule in a straightforward manner. The random sampling technique is used to solve this problem and a Monte Carlo simulation method is proposed. In this simulation method, one can observe the structure of each polymer molecule formed in this complex reaction system, and virtually any structural information can be obtained. In the illustrative calculations, the full molecular weight distribution development, the gel point determination, and examples of two‐ and three‐dimensional polymer structure are shown. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 391–403, 2001