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.     

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.     

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     

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     

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.     

Radical polymerization of vinyl thiocyanatoacetate: Participation of group‐transfer mechanism

Vinyl thiocyanatoacetate (VTCA) was synthesized, and its radical polymerization behavior was studied in acetone with dimethyl 2,2′‐azobisisobutyrate (MAIB) as an initiator. The initial polymerization rate (R_p) at 60 °C was expressed by R_p = k[MAIB]^0.6±0.1 [VTCA]^1.0±0.1 where k is a rate constant. The overall activation energy of the polymerization was 112 kJ/mol. The number‐average molecular weights of the resulting poly (VTCA)s (1.4–1.6 × 10⁴) were almost independent of the concentrations of the initiator and monomer, indicating chain transfer to the monomer. The chain‐transfer constant to the monomer was estimated to be 9.6 × 10^?3 at 60 °C. According to the ¹H and ¹³C NMR spectra of poly (VTCA), the radical polymerization of VTCA proceeded through normal vinyl addition and intramolecular transfer of the cyano group. The cyano group transfer became progressively more important with decreasing monomer concentration. © 2002 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 573–582, 2002; DOI 10.1002/pola.10137     

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.     

From metal‐catalyzed radical telomerization to metal‐catalyzed radical polymerization of vinyl chloride: Toward living radical polymerization of vinyl chloride

The metal‐catalyzed radical polymerization of vinyl chloride (VC) in ortho‐dichlorobenzene initiated with various activated halides, such as α,α‐dihaloalkanes, α,α,α‐trihaloalkanes, perfloroalkyl halides, benzyl halides, pseudohalides, allyl halides, sulfonyl halides, α‐haloesters, α‐halonitriles, and imidyl halides, in the presence of Cu(0)/2,2′‐bipyridine, Fe(0)/o‐phenantroline, TiCp₂Cl₂, and other metal catalysts is reported. The formation of the monoadduct between the initiator and VC was achieved with all catalysts. However, propagation was observed only for metals in their zero oxidation state because they were able to reinitiate from geminal dihalo or allylic chloride structures. Poly(vinyl chloride) with molecular weights larger then the theoretical limit allowed by chain transfer to VC were obtained even at 130 °C. In addition, the most elemental features of a living radical polymerization, such as a linear dependence of the molecular weight and a decrease of polydispersity with conversion, were observed for the most promising systems based on iodine‐containing initiators and Cu(0), that is, I? CH₂? Ph? CH₂? I/Cu(0)/bpy (where bpy = 2,2′‐bipyridyl), at 130 °C. However, because of the formation of inactive species via chain transfer to VC and other side reactions, the observed conversions were in most cases lower than 40%. A mechanistic interpretation of the chain transfer to monomer in the presence of Cu species is proposed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3392–3418, 2001     

Synthesis of poly(vinyl acetate)‐graft‐polystyrene by a combination of cobalt‐mediated radical polymerization and atom transfer radical polymerization

Vinyl acetate and vinyl chloroacetate were copolymerized in the presence of a bis(trifluoro‐2,4‐pentanedionato)cobalt(II) complex and 2,2′‐azobis(4‐methoxy‐2,4‐dimethylvaleronitrile) at 30 °C, forming a cobalt‐capped poly(vinyl acetate‐co‐vinyl chloroacetate). The addition of 2,2,6,6‐tetramethyl‐1‐piperidinyloxy after a certain degree of copolymerization was reached afforded 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐terminated poly(vinyl acetate‐co‐vinyl chloroacetate) (PVOAc–MI; number‐average molecular weight = 31,000, weight‐average molecular weight/number‐average molecular weight = 1.24). A ¹H NMR study of the resulting PVOAc–MI revealed quantitative terminal 2,2,6,6‐tetramethyl‐1‐piperidinyloxy functionality and the presence of 5.5 mol % vinyl chloroacetate in the copolymer. The atom transfer radical polymerization (ATRP) of styrene (St) was studied with ethyl chloroacetate as a model initiator and five different Cu‐based catalysts. Catalysts with bis(2‐pyridylmethyl)octadecylamine (BPMODA) or tris(2‐pyridylmethyl)amine (TPMA) ligands provided the highest initiation efficiency and best control over the polymerization of St. The grafting‐from ATRP of St from PVOAc–MI catalyzed by copper complexes with BPMODA or TPMA ligands provided poly(vinyl acetate)‐graft‐polystyrene copolymers with relatively high polydispersity (>1.5) because of intermolecular coupling between growing polystyrene (PSt) grafts. After the hydrolysis of the graft copolymers, the cleaved PSt side chains had a monomodal molecular weight distribution with some tailing toward the lower number‐average molecular weight region because of termination. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 447–459, 2007     

A cyclic selenium‐based reversible addition‐fragmentation chain transfer agent mediated polymerization of vinyl acetate

A cyclic selenium‐based reversible addition‐fragmentation chain transfer (RAFT) agent, 5,5‐dimethyl‐3‐phenyl‐2‐selenoxo‐1,3‐selenazolidin‐4‐one (RAFT‐Se), was synthesized and utilized in the RAFT polymerizations of vinyl acetate (VAc). Its analog, 5,5‐dimethyl‐3‐phenyl‐2‐thioxothiazolidin‐4‐one (RAFT‐S), was also used in RAFT polymerizations for comparison under identical conditions. The RAFT polymerizations of VAc with RAFT‐Se were moderately controlled evidenced by the increase of molecular weights with conversion, despite the slightly high M_w/M_n (less than 1.90), whereas the molecular weights were poorly controlled in the presence of RAFT‐S (2.00 < M_w/M_n < 2.30). Thanks to its unusual cyclic structure of RAFT‐Se, one or more RAFT‐Se species was incorporated into the resultant poly(VAc) as revealed by the results of cleavage of polymer and atomic absorption spectroscopy. Considering the biorelated functions of both poly(VAc) and Se element, this work undoubtedly provided a successful methodology of how to incorporate high content of Se into a molecular weight controlled poly(VAc). © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Heterochain model for simultaneous long‐chain branching and crosslinking. III. Multicomponent polymerization

The matrix formula developed in the context of heterochain theory, M?_w = M?_wp + WF ( I ? M )^?1 S , was applied to describe the molecular weight development during free‐radical multicomponent polymerization. All of the required probabilistic parameters are expressed in terms of the kinetic‐rate constants and the various concentrations associated with them. In free‐radical polymerization, the number of heterochain types, N, needs to be extrapolated to infinity, and such extrapolation is conducted with only three different N values. This matrix formula can be used as a benchmark test if other approximate approaches can give reasonable estimates of the weight‐average molecular weights. The moment equations with the average pseudo‐kinetic‐rate constants for branching and crosslinking reactions may provide poor estimates when the copolymer composition drift during polymerization is very significant. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2801–2812, 2004     

Prediction of Chain Length Distribution of Polystyrene Made in Batch Reactors with Bifunctional Free‐Radical Initiators Using Dynamic Monte Carlo Simulation

The objective of this paper is to present a dynamic Monte Carlo model that is able to simulate the polymerization of styrene with bifunctional free‐radical initiators in a batch reactor. The model can predict the dynamic evolution of the chain length distribution of polystyrene in the reactor. The model includes all relevant polymerization mechanistic steps, including chemical and thermal radical generation, and diffusion‐controlled termination. The model was applied to styrene polymerization and the Monte Carlo estimates for chain length averages were compared to those obtained with the method of moments. Excellent agreement was obtained between the two methods. Although styrene polymerization was used as a case study, the proposed methodology can be easily extended to any other polymer type made by free‐radical polymerization.

     

Molecular‐Weight‐Distribution Modelling of Radical Polymerization in Batch and Continuous Reactors with Transfer to Polymer Leading to Gel Formation

Full chain‐length distribution (CLD) modelling applying the Galerkin finite‐element method^[1] (FEM) to polymerization reactors featuring a certain degree of gel formation is confronted with extremely long computation times. The paper describes a new method to predict CLDs for systems where gel formation may occur. The new concept is to model a part of the CLD up to a cut‐off length L, while satisfying the full set of population balances. With transfer to polymer as the mechanism responsible for gelation, this gives rise to a closure problem, which has been solved by assuming the dead CLD beyond L to be represented by a part of a Flory distribution. The method could be proved to work by performing simulations and comparing cut‐off CLDs to full CLDs for non‐gelling systems and comparing results for different L for systems with gelation. The model is demonstrated for polymerization reactors, the batch reactor and the continuous stirred‐tank reactor (CSTR), with either disproportionation or recombination termination. Reliable results are obtained for systems with moderate gel formation. Comparing these results to those from moment models including balance equations up to the fourth moment, a number of interesting differences have been found.     

Cobalt(II) phenoxy-imine complexes in radical polymerization of vinyl acetate: The interplay of catalytic chain transfer and controlled/living radical polymerization

A series of cobalt(II) phenoxy-imine complexes (Co^II(FI)₂) have been synthesized to mediate the radical polymerization of vinyl acetate (VAc) and methyl acrylate (MA) to evaluate the influence of chelating atoms and configuration to the control of polymerization. The VAc polymerizations showed the properties of controlled/living radical polymerization (C/LRP) with complexes 1a and 3a , but the catalytic chain transfer (CCT) behaviors with complexes 2a , 1b , 2b , and 3b . The control of VAc polymerization mediated by complex 1a could be improved by decreasing the reaction temperature to approach the molecular weights that not only linearly increased with conversions but also matched the theoretical values and relatively narrow molecular weight distributions. The catalytic chain transfer polymerizations (CCTP) mediated by complexes 2a , 1b , 2b , and 3b were characterized by Mayo plots and the polymer chain end double bonds were observed by ¹H NMR spectra. The tendency toward C/LRP or CCTP in VAc polymerization mediated by Co^II(FI)₂ could be determined by the ligand structure. Cobalt complex coordinated by the ligand with more steric hindered and less electron-donating substituents favored the controlled/living radical polymerization. In contrast, the efficiency of CCT process could be enhanced by less steric hindered, more electron-donating ligands. The controlled/living radical polymerization of MA, however, could not be achieved by the mediation of these cobalt(II) phenoxy-imine complexes. Associated with the results of polymerization mediated by other cobalt complexes, this study implied that the configuration and spin state of cobalt complexes were more critical than the chelating atoms to the control behavior of radical polymerization. © 2019 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 101–113     

Dynamic Monte Carlo Simulation of ATRP in a Batch Reactor

A dynamic MC model was developed to simulate the polymerization kinetics and the detailed microstructure of copolymers made with ATRP in a batch reactor. The model was used to predict monomer conversion, average molecular weight, polydispersity index, and copolymer composition as a function of polymerization time. The model can also predict the distribution of molecular weight, chemical composition, and comonomer sequence length at any polymerization time or comonomer conversion. The simulation was used to explore the effects of rate constants and reactant stoichiometry on the microstructure of chains. Two copolymerization systems were chosen to demonstrate the effect of reactivity ratios and comonomer feed compositions on the final chemical composition distribution.

     

Cobalt‐Mediated Radical Polymerization of Vinyl Acetate in Miniemulsion: Very Fast Formation of Stable Poly(vinyl acetate) Latexes at Low Temperature

Summary: Poly(vinyl acetate) macroinitiators end‐capped by a Co(acac)₂ complex (PVAc–Co(acac)₂), prepared in bulk by cobalt‐mediated radical polymerization (CMRP), are used for the controlled radical polymerization of vinyl acetate in miniemulsion to give high‐molecular‐weight polymers and high monomer conversion. Stable poly(vinyl acetate) latexes with solid contents ranging from 25 to 30 wt.‐% are prepared within unusually short reaction times (∼1 h) at low temperatures (0–30 °C).

SEC chromatograms for the PVAc–Co(acac)₂ macroinitiator and PVAc latex obtained under ultrasonication for 6 min at 0 °C (79% monomer conversion).