Controlled Bimodal Molecular‐Weight‐Distribution Polymers: Facile Synthesis by RAFT Polymerization

The RAFT agents RAFT‐1 and RAFT‐2 were used for RAFT polymerization to synthesize well‐defined bimodal molecular‐weight‐distribution (MWD) polymers. The system showed excellent controllability and “living” characteristics toward both the higher‐ and lower‐molecular‐weight fractions. It is important that bimodal higher‐molecular‐weight (HMW) polymers and block copolymers with both well‐controlled molecular weight (MW) and MWD could be prepared easily due to the “living” features of RAFT polymerization. The strategy realized a mixture of higher/lower‐molecular‐weight polymers at the molecular level but also preserved the features of living radical polymerization (LRP) of the RAFT polymerization.     

Monte Carlo simulation of size exclusion chromatography for branched polymers formed through free‐radical polymerization with chain transfer to polymer

The elution curves of size exclusion chromatography (SEC) for branched polymers formed through free‐radical polymerization that involves chain transfer to polymer were theoretically investigated by using a Monte Carlo method. We considered two types of measured molecular weight distribution (MWD), (1) the calibrated MWD relative to standard linear polymers, and (2) the MWD obtained by using a light scattering photometer (LS) in which the weight‐average molecular weight of polymers within the elution volume is determined directly. It was found that the calibrated MWD clearly underestimates the high molecular weight tail, and the measured distributions are narrower than the true MWD. On the other hand, the present simulation results showed that the LS method gives reasonable estimates of the true MWDs. The mean square radius of gyration of the polymer molecules having the same molecular weight was also investigated. The radii of gyration showed clear deviation from the Zimm‐Stockmayer equation^[1] because of the non‐random nature of branched structure and the difference in the primary chain length distribution.     

Dimensions of branched polymers formed in simultaneous long‐chain branching and random scission

In free‐radical olefin polymerizations, the polymer‐transfer reactions could lead to chain scission as well as the formation of long‐chain branches. The Monte Carlo simulation for free‐radical polymerization that involves simultaneous long‐chain branching and random scission is used to investigate detailed branched structure. The relationship between the mean‐square radius of gyration 〈s²〉 and degree of polymerization P as well as that between the branching density and P is the same for both with and without random scission reactions—at least for smaller frequencies of scission reactions. The 〈s²〉 values were larger than those calculated from the Zimm–Stockmayer (Z‐S) equation in which random distribution of branch points is assumed, and therefore, the Z‐S equation may not be applied for low‐density polyethylenes. The elution curves of size exclusion chromatography were also simulated. The molecular weight distribution (MWD) calibrated relative to standard linear polymers is much narrower than the true MWD, and high molecular weight tails are clearly underestimated. A simplified method to estimate the true MWD from the calibrated MWD data is proposed. The MWD obtained with a light scattering photometer in which the absolute weight‐average molecular weight of polymers at each retention volume is determined directly is considered a reasonable estimate of the true MWD. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2960–2968, 2001     

Simulation of Molecular‐Weight Distribution Using a New Kinetic Model of Ethene Polymerization Catalyzed by Cp2ZrCl2‐MAO

The kinetics of ethene polymerization catalyzed by Cp₂ZrCl₂‐methylaluminoxane (MAO) is studied by applying a new kinetic model. Important kinetic parameters of polymerization were estimated. In addition a method of calculating the molecular‐weight distribution (MWD) of the resultant polyethene was established by developing this new model. The final product is expected to comprise three components, which are produced by different active‐site types, and the MWD of one of the components is less than 2. Good agreement between the estimated value and the variation of polydispersity was achieved.     

Molecular Weight Distribution Simulation in Equilibrium Ring‐Opening Polymerization: A New Macroscopic Model

Compared with other types of polymerization, the molecular weight and its distribution (MWD) of equilibrium ring‐opening polymerization (EROP) are complicated and have not been extensively studied. By using statistic method, a series of equations based on polymerization mechanism is established to describe numbers of rings, chains, and active centers. Using this new model, the predicted results of polydimethylsiloxane synthesized by EROP agree well with experimental results. This model has advantages in molecule number, calculation speed, and stability when compared with the Monte Carlo simulation. It also has the potential to replace Monte Carlo simulation in MWD prediction.     

Deconvolution of Molecular Weight Distributions Using Dynamic Flory‐Schulz Distributions

Summary: The deconvolution of molecular weight distributions (MWDs) may be useful for obtaining information about the polymerization kinetics and properties of catalytic systems. However, deconvolution techniques are normally based on steady‐state assumptions and very little has been reported about the use of non‐stationary approaches for the deconvolution of MWDs. In spite of this, polymerization reactions are often performed in batch or semi‐batch modes. For this reason, dynamic solutions are proposed here for simple kinetic models and are then used for deconvolution of actual MWD data. Deconvolution results obtained with dynamic models are compared to deconvolution results obtained with the standard stationary Flory‐Schulz distributions. For coordination polymerizations, results show that dynamic MWD models are able to describe experimental data with fewer catalytic sites, which indicates that the proper interpretation of the reaction dynamics may be of fundamental importance for kinetic characterization. On the other hand, reaction dynamics induced by modification of chain transfer agent concentration seem to play a minor role in the shape of the MWD in free‐radical polymerizations.

This Figure illustrates that MWDs obtained at unsteady conditions should not be deconvoluted with standard steady‐state Flory‐Schulz distributions.     

Round‐robin experiment in high‐temperature gel permeation chromatography

The results of an interlaboratory or round‐robin experiment in high‐temperature gel permeation chromatography (HT‐GPC) analysis are presented. The intention was to determine and raise awareness of interlaboratory reproducibility of HT‐GPC techniques. Fifteen laboratories performed analyses of five polyethylene samples and standards SRM 1475 and 1476. Reproducibility, as measured by the interlaboratory standard deviation (s_LAB), was greatly influenced by the breadth of the molecular weight distribution (MWD) and branching. The s_LAB values for the weight‐average molecular weight (M_w) of linear polyethylenes of narrow and broad MWDs were 4 and 14%, respectively. For branched polymers, GPC viscometry methods are shown to measure significantly higher molecular weights than the noncoupled GPC method, with higher variance. For branched polyethylenes measured with GPC viscometry, the reproducibility of M_w was characterized by s_LAB = 18%. Reproducibility of the SRM 1475 standard was better than for unknowns. The results for branched standard SRM 1476 emphasize the important role of the detection method in GPC but call into question the use of this material as a molecular weight standard. For single‐site polyethylene, only a handful of labs measured an MWD that closely matched the Flory distribution. Qualitatively, the responses indicate that many variations in instrument and analytical methods exist among laboratories; this is partly a reflection of the development and refinements that this technique must yet undergo before a truly standard method is widely accepted and practiced. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 905–921, 2002     

Kinetics of the styrene emulsion polymerization using n‐dodecyl mercaptan as chain‐transfer agent

The kinetics of the styrene emulsion polymerization using n‐dodecyl mercaptan as chain‐transfer agent was studied. It was found that the chain‐transfer agent (CTA) had no effect on polymerization rate but substantially affected the molecular weight distribution (MWD). The efficiency of the CTA in reducing the MWD was lowered by the mass‐transfer limitations. The process variables affecting CTA mass transfer were investigated. A mathematical model for the process was developed. The outputs of the model include monomer conversion, particle diameter, number of polymer particles, and number‐average and weight‐average molecular weights. The model was validated by fitting the experimental data. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4490–4505, 2000     

Reconstruction of the Chain Length Distribution for Vinyl‐Divinyl Copolymerization Using the Numerical Fractionation Technique

A proposed theory for evaluating the chain length distribution (CLD) using the numerical fractionation (NF) technique was extended to the vinyl‐divinyl (VDV) copolymerization. The CLD is reconstructed for this system, in which pendant double bond propagation leads to crosslinking and gel formation. The method was earlier developed for a non‐linear free‐radical polymerization scheme where chain transfer to polymer and termination by combination resulted in gel formation. The VDV study presented indicates that the proposed method of weighted summation (WS) accurately predicts the resulting CLDs evaluated using NF.

Comparison of the overall polymer NF and the direct solution CLDs near the gel point.     

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.     

Synthesis of polyethylene with bimodal molecular weight distribution by supported iron‐based catalyst

Through immobilization of two iron‐based complexes, [((2,6‐MePh)N = C(Me))₂C₅H₃N]FeCl₂ ( 1 ) and [((2,6‐iPrPh)N = C(Me))₂C₅H₃N]FeCl₂ ( 2 ), on SiO₂ pretreated with tetraethylaluminoxane (TEAO), two supported iron‐based catalysts, 1 /TEAO/SiO₂ ( 3 ) and 2 /TEAO/SiO₂ ( 4 ), were prepared. These two supported catalysts 3 and 4 could be used to catalyze ethylene polymerization with moderate polymerization activity and prepare linear high‐density polyethylene with bimodal molecular weight distribution (MWD). It was demonstrated that immobilization of catalyst could significantly improve molecular weight (MW) of high‐MW fraction of the resultant polyethylene, as well as maintain bimodal MWD of polyethylene produced by the corresponding homogeneous catalysts. Such bimodal MWD of polyethylene produced by supported iron‐based catalysts could be well tailored by varying polymerization conditions, such as ethylene pressure and molar ratio of Al to Fe. It has been proven that TEAO is an efficient activator for both homogeneous and heterogeneous iron‐based catalysts for producing polyethylene with bimodal MWD. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5662–5669, 2004     

Ring‐Opening Polymerization of Propylene Oxide by Double Metal Complex in Micro‐Reactor

The ring‐opening polymerization of propylene oxide catalyzed by double metal complex (DMC) is carried out in continuous micro‐reactor (C‐MR). It is found that the monomer conversion at the C‐MR outlet is usually 100% within 2 min of average residence time, which means that the polymerization rate in the C‐MR is faster than that in a traditional semi‐continuous tank reactor. However, the induction period still exists in the polymerization in C‐MR, but can be shortened by increasing the reaction temperature or the micro‐reactor length. The mechanism of monomer coordination and ring opening on DMC during the induction period is confirmed by the ¹H NMR analysis of the samples obtained under very short average residence time. The molecular weight distribution (MWD) of product from C‐MR is generally narrow, which indicates that the process still maintain the characteristics of the “living” polymerization. That is, there is a very high rate ratio of chain transfer to chain propagation provided by the DMC catalyst. However, with the same average residence time, the MWD of product from the longer C‐MR is broader, which can be attributed to the increase of the chain propagation rate caused by rise of pressure.     

Molecular‐Weight Multimodality of Multiple Flory Distributions

It is well‐known that the final end‐use properties of polymer resins depend on the shape of the molecular‐weight distribution (MWD) very strongly. Particularly, polymer resins with bimodal MWDs are required for certain special applications, as they may simultaneously present enhanced mechanical and flow properties. A theoretical framework for the characterization of bimodality (or multimodality) of MWDs of polymers produced through linear polymerizations at steady‐state or quasi‐steady‐state conditions is developed and presented here. Conditions for the development of bimodality in generalized NS‐Schulz–Flory distributions are characterized for different forms of presentation of the MWDs. It is shown that the bimodal character of the MWD depends on the particular form used to represent it, which can then be used to generate an index of bimodality of the MWD. The theoretical results are finally used to compute the index of bimodality of actual polymer materials obtained at plant site.     

Producing bimodal molecular weight distribution polymers through facile one‐pot/one‐step RAFT polymerization

Well‐defined bimodal molecular weight distribution (MWD) polystyrene and polystyrene‐b‐poly(acrylonitrile) were successfully synthesized using a pair of mono/difunctional trithiocarbonate RAFT agents 1 and 2 via one‐pot RAFT polymerization. The kinetics of RAFT polymerization for styrene in bulk with a molar ratio of [St]₀:[AIBN]₀:[ 1 ]₀:[ 2 ]₀ = 1200:1:2.5:2.5 was studied at 75°C. The results indicated that the system showed excellent controllability and “living” characteristics to both higher and lower molecular weight fractions, providing an efficient and facile way to producing bimodal MWD (co)polymers with both controlled molecular weight (MW) and MWD in molecular level, and the plausible mechanism was discussed in this work. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Emulsifier‐free,organotellurium‐mediated living radical emulsion polymerization (emulsion TERP): Effect of monomer hydrophilicity

Emulsifier‐free, organotellurium‐mediated living radical emulsion polymerizations (emulsion TERPs) of methyl methacrylate (MMA) and n‐butyl methacrylate (BMA) with dimethyl ditelluride were carried out at two different stirring rates (220 rpm and 1000 rpm). In the emulsion TERP of MMA as a hydrophilic monomer, the molecular weight distribution (MWD) controls with both stirring rates were good with high polymerization rate (100% conversion at 1.5 h). On the other hand, in the emulsion TERP of BMA as a hydrophobic monomer, at 220 rpm the polymerization rate was much slow (～50% conversion at 22 h) and the MWD control was bad, but at 1000 rpm the polymerization was completed within 7 h and MWD control was good. These results suggest that monomer transportation from droplets to polymerizing particles via aqueous medium is important for good MWD control and steady polymerization in the emulsion TERP. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Copolymerization of ethylene and α‐olefins with combined metallocene catalysts. II. Mathematical modeling of polymerization with single metallocene catalysts

The relation between the polymerization conditions and the distributions of molecular weight (MWD) and chemical composition (CCD) of poly(ethylene‐co‐1‐hexene) made with single supported metallocene catalysts was investigated. Understanding the behavior of each metallocene under different polymerization conditions is necessary for designing combined metallocene catalysts to produce tailor‐made polyolefins. In this article, a simple mathematical model based on experimental results is developed and combined with the bimodality criterion developed in Part I of this series to predict polymerization conditions and metallocene combinations that will produce polymers with desired MWDs and CCDs. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1417–1426, 2000     

Copolymerization of ethylene with 1‐hexene promoted by novel multi‐chelated non‐metallocene complexes with imine bridged imidazole ligand

A series of novel bridged multi‐chelated non‐metallocene catalysts is synthesized by the treatment of N,N‐imidazole, N,N‐dimethylimidazole, and N,N‐benzimidazole with n‐BuLi, 2,6‐dimethylaniline, and MCl₄ (M = Ti, Zr) in THF. These catalysts are used for copolymerization of ethylene with 1‐hexene after activated by methylaluminoxane (MAO). The effects of polymerization temperature, Al/M molar ratio, and pressure of monomer on ethylene copolymerization behaviors are investigated in detail. These results reveal that these catalysts are favorable for copolymerization of ethylene with 1‐hexene featured high catalytic activity and high comonomer incorporation. The copolymer is characterized by ¹³C NMR, WAXD, GPC, and DSC. The results confirm that the obtained copolymer features broad molecular weight distribution (MWD) about 33–35 and high 1‐hexene incorporation up to 9.2 mol %, melting temperature of the copolymer depends on the content of 1‐hexene incorporation within the copolymer chain and 1‐hexene unit in the copolymer chain isolates by ethylene units. The homopolymer of ethylene has broader MWD with 42–46. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 417–424, 2010     

Addition‐Fragmentation Chain Transfer to Polymer in the Free Radical Ring‐Opening Polymerization of an Eight‐membered Cyclic Allylic Sulfide Monomer

Summary: A detailed investigation of chain transfer to polymer during free radical ring‐opening polymerization of the eight‐membered disulfide monomer 2‐methyl‐7‐methylene‐1,5‐dithiacyclooctane (MDTO) is presented. It has been shown that extensive chain transfer to polymer occurs involving both poly(MDTO) radicals and cyanoisopropyl radicals. Significant decreases in molecular weight were observed when cyanoisopropyl radicals were generated in the presence of poly(MDTO) in the absence of monomer. The molecular weight distribution (MWD) obtained from polymerization of MDTO in the presence of pre‐added poly(MDTO) was markedly different from that obtained without pre‐added polymer. A kinetic model was constructed in an attempt to quantitatively describe the chain transfer to polymer process based on the addition fragmentation chain transfer mechanism. It was found however that the simulated MWDs were considerably broader than the experimental MWDs, which were similar to the Schulz‐Flory distribution.

Mechanism for chain transfer to polymer.     

Influence of n‐dodecyl mercaptan as chain transfer agent in dispersion polymerization of styrene

Dispersion polymerization of styrene with n‐dodecyl mercaptans (DDM) as the chain transfer agent was investigated. PS particles with various molecular weight, molecular weight distribution (MWD), and particle diameter were prepared by varying the concentration of DDM and also the addition time of DDM before and after the particle nucleation. The average particle diameter was increased, whereas polymerization rate, molecular weight, and MWD were decreased with increasing DDM concentrations from 0 to 10 wt %. The effect of addition of DDM before and after particle nucleation was studied at 0.4, 0.8, and 1.0 wt % DDM. The addition of DDM before particle nucleation produced PS particles of relatively large particle diameter and low molecular weight when compared with the addition of DDM after particle nucleation. This study shows that particle nucleation occurs in about 5–6 min, which corresponds to the 15–16% conversion, 372–378 nm in D_n , and provides a facile way to control the particle size and interesting information about the particle formation using the delayed addition of DDM. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6612–6620, 2008