Copolymerization of ethylene and α‐olefins with combined metallocene catalysts. I. A formal criterion for molecular weight bimodality

Metallocene and other single‐site catalysts can be combined to produce polyolefins with broadened distributions of molecular weight, chemical composition, and long‐chain branching. These resins are finding increasing applications because of their enhanced properties compared to ones made with conventional Ziegler–Natta catalysts. Resins with bimodal molecular weight distributions (MWDs) have especially attractive mechanical and rheological properties. Although the use of these resins is expected to increase, there are very few studies available to quantify MWD bimodality or to decide a priori which combinations of metallocene catalysts will lead to the formation of polyolefins with bimodal MWDs. In this article, a necessary condition for the production of polymer with bimodal MWD using two single‐site‐type catalysts is derived. Additionally, a bimodality index is defined to quantify MWD bimodality. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1408–1416, 2000     

An experimental investigation on the evolution of the molecular weight distribution in styrene emulsion polymerization

Styrene ab initio emulsion polymerizations were conducted at 70°C in an automated reaction calorimeter. Two polymerizations were performed, one above and the other below the critical micelle concentration (CMC) of the surfactant, thus ensuring differing polymerization kinetics between the two: the system below the CMC gave large particles that were expected to follow pseudobulk kinetics, while that above the CMC gave small particles that were expected to follow zero-one kinetics. The evolutions of the molecular weight distributions (MWDs) were characterized by removing samples periodically during the course of the reactions and analyzing with gel permeation chromatography. Interpretation of the data used average molecular weights, the GPC MWDs, and the number MWDs, as functions of conversion. It was found that all of the number MWDs (plotted as ln (number of polymer chains) vs. molecular weight of polymer chains) were concave-up at low molecular weights and become nearly linear at molecular weights (≥3−4 × 10⁶); this linearity is expected from theory. The slope of the high molecular weight region was consistent with theory for the dominant mode for chain stoppage: termination and transfer for the pseudobulk system and (predominantly) chain transfer to monomer for the zero-one system. The most likely explanation for the concavity of the number MWDs is a heterogeneity of radicals: some surface anchored with sulfate end groups and others (with hydrogen end groups arising from transfer to monomer and/or reentry) being more mobile. Thus, two types of termination are proposed: slow reaction-diffusion for the less mobile surface anchored chains, and rapid short-long (center of mass) termination for the more mobile hydrogen-terminated chains. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 989–1006, 1997     

Evolution of the termination rate coefficient in styrene polymerization

Styrene bulk polymerization was conducted at 70 °C with a high initiator concentration, and this ensured that the dominant chain‐stopping mechanism was the combination of free radicals. The evolution of the molecular weight distribution (MWD) of the polymer was measured via the periodic removal of samples during the course of the reaction and their analysis with gel permeation chromatography. The overall termination rate coefficient was independent of the conversion in the dilute regime, as observed from cumulative MWDs. In the middle of the conversion range, the observed trend was compatible with a translational‐diffusion‐controlled mechanism for the termination step. A bimodal distribution of the molecular weights was also found at high conversions and could be explained in terms of an increase in the free‐radical concentration and a very low termination rate coefficient. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 178–187, 2005     

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.     

Monte Carlo simulation of size exclusion chromatography for randomly branched and crosslinked polymers

The elution curves of size exclusion chromatography for nonlinear polymers formed through random branching and crosslinking of long polymer chains were simulated with a Monte Carlo method. We considered two types of measured molecular weight distributions (MWDs): (1) the MWD calibrated relative to standard linear polymers and (2) the MWD obtained with a light scattering (LS) photometer in which the weight‐average molecular weight of polymers within the elution volume is determined directly. The calibrated MWDs clearly underestimate the molecular weights for both randomly branched and crosslinked polymers, and this technique can be used to assess the degree of deviation from the true MWD. When the primary chains conform to the most probable distribution, the calibrated MWD can be estimated reasonably well with the Zimm–Stockmayer equation for the g factor with the help of the relationship between the average number of branch points per molecule and the degree of polymerization. However, the LS method gives good estimates of the true MWD for both randomly branched and crosslinked polymers, although the agreement is better for the branched ones. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2009–2018, 2000     

Thermosensitive diblock copolymers with designed molecular weight distribution: Synthesis by continuous living cationic polymerization and micellization behavior

The synthesis of diblock copolymers with designed molecular weight distributions (MWDs) was successfully demonstrated in a continuous living cationic polymerization system using simple equipment. The control of MWDs was achieved by gradually feeding a polymerization reaction mixture into a terminating agent. As thermosensitive diblock copolymers, poly(vinyl ethers) containing a thermosensitive segment with oxyethylene side chains and a hydrophilic segment were prepared. The polymerization was carried out in a gas‐tight microsyringe, and the polymerization mixture was added continuously into methanol during the second‐stage polymerization. The self‐association behavior of the resulting diblock copolymers was evaluated by dynamic light scattering in water. MWD‐designed polymers with thermosensitive segments that varied continuously in length and hydrophilic segments of nearly uniform lengths formed micelles with a broad size distribution. Conversely, polymers with nearly uniform thermosensitive segments and hydrophilic segments of different lengths formed micelles with a narrow size distribution, as observed with conventional narrow MWD diblock copolymers. Thus, the MWD of the thermosensitive segment proved a decisive factor in achieving fine control of self‐association. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2212–2221, 2008     

Simulation of gel permeation chromatography measurement for long chain branched metallocene polyethylene

The research about the polymerization reaction mechanism of long chain branched polymer provides a method to simulate the generation of LCB mPE (long chain branched metallocene polyethylene).^[1-3] In this work, after simulating the generation of one million LCB mPE molecules, we calculate the sizes (i.e. radii of gyration) of molecules in good solvents to obtain the molecular size distributions. Then we simulate the fractionation in GPC (gel permeation chromatography) measurement and the different GPC detector responses to obtain simulated GPC MWDs (molecular weight distributions). The simulated MWDs are compared to the real GPC results provided by the Dow Chemical Company.     

Evolution of molecular weight distributions in the catalytic chain transfer polymerization of methyl methacrylate up to high monomer conversions

The evolution of molecular weight distributions (MWDs) with monomer conversion in the catalytic chain transfer (CCT) polymerization of methyl methacrylate at 60 °C is investigated by simulation (via the program package PREDICI®) and experiment. A Co(III)‐based complex is used as the precursor for the CCT agent, which is formed in situ by initiator‐derived (2,2′‐azobisisobutyronitrile) radicals to yield the catalytically active Co(II) species. The small shifts seen in the MWD toward lower molecular weights with increasing monomer conversion are shown to be of the same order of magnitude as the associated changes in the MWD in non‐CCT controlled free‐radical polymerization, indicating that no significant change in the MWD with monomer conversion is associated with the CCT process. These results are compared to the evolution of MWDs in conventional chain transfer polymerizations with thiols as transfer agents. A clear shift toward higher molecular weights is seen with increasing monomer conversion, indicating disparate rates of thiol and monomer consumption. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3303–3312, 2000     

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     

Effects of the structure and morphology of zinc glutarate on the fixation of carbon dioxide into polymer

Zinc glutarates were synthesized from zinc oxides with varying purities via different stirring routes. The particle size and structure of these zinc glutarates were determined by wide‐angle X‐ray diffraction, transmission electron microscopy, and the laser particle size analyzer technique. The results demonstrated that the crystallinity and crystalline perfectness of zinc glutarate are the crucial factors that affect the catalytic activity for the copolymerization of carbon dioxide (CO₂) and propylene oxide (PO). Additionally, the catalyst with a small particle size dramatically increased the yield of the copolymerization between CO₂ and PO. High‐molecular‐weight and regular molecular structure poly(propylene carbonate)s (PPC)s were obtained from CO₂ and PO with the synthesized zinc glutarates. Very high catalytic activity of 160.4 g polymer/g catalyst was afforded. The NMR technique revealed that the PPC copolymer exhibits an exact alternating copolymer structure. The relationships between the crystallinity and the particle size of catalyst with the catalytic activity are correlated and discussed. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3579–3591, 2002     

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     

Unimodal molecular weight distribution of commercial polymers from viscoelastic data

This article presents a method that provides the molecular weight distribution (MWD) of polymeric material from rheological data. The technique has been developed to deal with linear polymers with a log‐normal molecular weight distribution. The rheological data must include the shear storage modulus, G′(ω), and the shear loss modulus, G″ (ω), ranging from the terminal zone to the rubberlike zone. It was not necessary to achieve the relaxation spectrums via the extremely unstable problem of inverting integral equations. The method has been tested with different polymers (polydimethylsiloxane, polyisoprene, random copolymer of ethylene and propylene, and polystyrene) and the calculated MWDs were in good agreement with experimental data. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1539–1546, 2000     

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     

Cationic cyclopolymerization of new divinyl ethers: The effect of ether and ester neighboring functional groups on their cyclopolymerization tendency

The cationic polymerization of two new divinyl ethers, 1‐(2‐vinyloxyethoxy)‐2‐[(2‐vinyloxyethoxy)carbonyl]benzene ( 2 ) and 1,2‐bis[(2‐vinyloxyethoxy)carbonyl]benzene ( 3 ), as well as 1,2‐bis(2‐vinyloxyethoxy)benzene ( 1 ), with BF₃OEt₂ in CH₂Cl₂ at 0 °C at low initial monomer concentrations ([M]₀ = 0.15 and 0.075 M) gave soluble polymers with relatively high molecular weights and broad molecular weight distributions (MWDs), whereas reactions with the HCl/ZnCl₂ initiating system yielded soluble polymers with relatively narrow MWDs (weight‐average molecular weight/number‐average molecular weight ? 1.6) under similar reaction conditions. An NMR structural analysis of the HCl/ZnCl₂‐mediated polymers from the divinyl ethers showed that poly( 1 ) had virtually no unreacted vinyl ether groups throughout the polymerization (monomer conversion = 28–98%), whereas poly( 2 ) and poly( 3 ) possessed some amount of unreacted vinyl ether groups in the initial stage of the polymerization; the content of the vinyl groups of poly( 2 ) was 18 mol % at a 15% monomer conversion, and the content of the vinyl groups of poly( 3 ) was 31 mol % at an 18% monomer conversion. Therefore, divinyl ether 1 underwent cyclopolymerization exclusively to give almost completely cyclized polymers [degree of cyclization (DC) ～ 100%], whereas divinyl ethers 2 and 3 exhibited a lower cyclopolymerization tendency [DC for poly( 2 ) = 82%; DC for poly( 3 ) = 69%]. The differences in the cyclopolymerization tendencies among the divinyl ethers can be explained by the differences in the solvation powers of the neighboring functional groups adjacent to the vinyl ether moiety with the active center: the ether oxygen of the ether neighboring group solvates intramolecularly with the active center to accelerate the intramolecular propagation, but such an interaction is less effective with the more electron‐deficient oxygen attached to the carbonyl group of the ester neighboring group. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 281–292, 2003     

The effect of different catalytic chain transfer agents on particle nucleation and the course of the polymerization in ab initio batch emulsion polymerization of methyl methacrylate

The effect a Co(II) based catalytic chain transfer agent (CCTA) has on the course of the polymerization and the product properties of an emulsion polymerization is governed by the intrinsic activity and the partitioning behavior of the catalyst. The effect on the conversion time history, the molecular weight distribution and the particle size distribution is evaluated in batch emulsion polymerization of methyl methacrylate for three different CCTAs, which cover a range of intrinsic activities and partitioning behaviors. It was demonstrated that radical desorption from the particle phase to the aqueous phase preceded by chain transfer is the main kinetic event controlling the course of the polymerization and the product properties in terms of the particle size distribution. The experimental results show that the aqueous phase solubility of the CCTA is the key parameter controlling the course of the polymerization and the particle size distribution. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1038–1048, 2010     

The influence of surfactant coverage of the minidroplets on RAFT miniemulsion polymerization

The surfactant coverage of minidroplets was tuned by postaddition of more surfactants after preparation of the miniemulsion of styrene. The influence of surfactant coverage on reversible addition‐fragmentation chain transfer (RAFT) miniemulsion polymerization of styrene was investigated. When the surfactant (sodium dodecyl sulfate; SDS) coverage was as low as 40%, two kinds of particles, denoted as polymer and oligomer particles, were formed in the early stage of the polymerization. Polymer chains within two kinds of particles grew in a parallel way during the rest period of the polymerization. The oligomer particles contributed less than 10% to the final monomer conversion but consumed over one in third the original RAFT agent molecules. Oligomer particles were larger in size but much lower in molecular weight. Both the particle size and molecular weight distributions were bimodal. With increase of SDS coverage, the formation of oligomer particles was suppressed. As a result, the nucleation efficiency of the minidroplets was greatly enhanced and the molecular weight and particle size distributions were dramatically narrowed. The formation of the oligomer particles was ascribed to the superswelling occurring in the beginning stage of the polymerization. The experimental observations are in excellent accord to the superswelling theory. Postaddition of surfactant presents a novel method to narrow particle size and molecular weight distributions in RAFT miniemulsion polymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2293–2306, 2006     

Controlling molecular weight distributions of polyethylene by combining soluble metallocene/MAO catalysts

A critical look at the possibility of controlling the molecular weight distribution (MWD) of polyolefins by combining metallocene/methylalumoxane (MAO) catalysts is offered. Catalysts investigated were bis(cyclopentadienyl)zirconium dichloride (Cp₂ZrCl₂), its titanium and hafnium analogues (Cp₂TiCl₂ and Cp₂HfCl₂), as well as rac-ethylenebis(indenyl)zirconium dichloride (Et(Ind)₂ZrCl₂). As observed by other researchers, the MWD of polyethylene can be manipulated by combining soluble catalysts, which on their own produce polymer with narrow MWD but with different average molecular weights. Combined in slurry polymerization reactors, the catalysts in consideration produce ethylene homopolymer just as they would independently. Unimodal or bimodal MWDs can be obtained. This effect can be mimicked by blending polymers produced by the individual catalysts. We demonstrate how a variability in catalyst activity translates into a variability in MWD when mixing soluble catalysts in polymerization. Such a variability in MWD must be considered when setting goals for MWD control. We introduce a more quantitative approach to controlling the MWD using this method. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 831–840, 1998     

Tailored bimodal ultra‐high molecular weight polyethylene particles

A single molecular catalyst system supported on MgCl₂ has been developed and combined with a simple two‐stage fed‐batch polymerization process to produce tailored bimodal polyethylene reactor blend particles of UHMWPE. By varying and controlling the process conditions in the first stage and second stage, bimodal HMWPE:UHMWPE reactor particles are obtained with independent control over the individual molar masses, the mass ratio of the HMWPE and UHMWPE components, and the reactor powder particle size. This allows multidimensional control over the individual UHMWPE reactor particle properties. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 1645–1656     

Photon correlation spectroscopy of polymer solutions

A polynomial subdistribution method for analyzing the correlation profile in photon correlation spectroscopy of polymer solutions is described. This method generates a continuous distribution function from the measured photoelectron time-correlation function, which can be related to particle size or molecular weight distribution of solute. The method is tested using simulated data for unimodal and bimodal distributions and compared with cumulant and histogram methods, respectively. The polynomial subdistribution method has an advantage in that it not only generates a continuous distribution curve but also works well for bimodal distributions whose peaks are close together.     

Influence of a reversible addition–fragmentation chain transfer agent in the dispersion polymerization of styrene

Dispersion polymerization was applied to the controlled/living free‐radical polymerization of styrene with a reversible addition–fragmentation chain transfer (RAFT) polymerization agent in the presence of poly(N‐vinylpyrrolidone) and 2,2′‐azobisisobutyronitrile in an ethanol medium. The effects of the polymerization temperature and the postaddition of RAFT on the polymerization kinetics, molecular weight, polydispersity index (PDI), particle size, and particle size distribution were investigated. The polymerization was strongly dependent on both the temperature and postaddition of RAFT, and typical living behavior was observed when a low PDI was obtained with a linearly increased molecular weight. The rate of polymerization, molecular weight, and PDI, as well as the final particle size, decreased with an increased amount of the RAFT agent in comparison with those of traditional dispersion polymerization. Thus, the results suggest that the RAFT agent plays an important role in the dispersion polymerization of styrene, not only reducing the PDI from 3.34 to 1.28 but also producing monodisperse polystyrene microspheres. This appears to be the first instance in which a living character has been demonstrated in a RAFT‐mediated dispersion polymerization of styrene while the colloidal stability is maintained in comparison with conventional dispersion polymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 348–360, 2007