Comparing Long‐Chain Branching Mechanisms for Ethylene Polymerization with Metallocenes and Other Single‐Site Catalysts: What Simulated Microstructures Can Teach Us

Three different long‐chain branch (LCB) formation mechanisms for ethylene polymerization with metallocenes in solution polymerization semi‐batch and continuous stirred‐tank reactors are modeled to predict the microstructure of the resulting polymer. The three mechanisms are terminal branching, C–H bond activation, and intramolecular random incorporation. Selected polymerization parameters are varied to observe how each mechanism affects polymer microstructure. Increasing the ethylene concentration during semi‐batch polymerization reduces the LCB frequency of polymers made with the terminal branching and intramolecular mechanisms, but has no effect on those made with the C–H bond activation mechanism, which disagrees with most previous data published in the literature. The intramolecular mechanism predicts that LCB frequencies hardly depend on polymerization time or ethylene conversion, which also disagrees with the published experimental data for these systems. For continuous polymerization reactors, experimental data relating polydispersity to LCB frequency can be well described with the terminal branching mechanism, but both C–H bond activation and intramolecular models fail to describe this experimental relationship. Therefore, detailed simulations confirm that the terminal branching mechanism is indeed the most likely mechanism for LCB formation when ethylene is polymerized with single‐site coordination catalysts such as metallocenes in solution polymerization reactors.     

Modeling Kinetics and Structural Properties in High‐Pressure Fluid‐Phase Polymerization

The present contribution provides an overview of actual applications in modeling free‐radical polymerizations. Topics of interest are the simulation of pulsed laser polymerization experiments with subsequent analysis of the formed product by size exclusion chromatography (PLP‐SEC), single pulse laser experiments, experimental techniques for determining rate coefficients of elementary reactions that control polymer properties, and technical applications. Aspects being investigated are model validation and testing predictive potential in polymerization models using well‐defined experiments as well as developing and testing experimental strategies for deriving rate coefficients of elementary reactions that exist (especially when dealing with copolymerizations) within a network of complex coupled reactions. In any of these fields remarkable success in modeling can be achieved. This demonstrates the great potential that can grow from combining modern mathematical methods, computational power and detailed kinetic insights into the mechanism of polymerization. It is the wide scope of applications, e. g. ranging from modeling kinetics to the investigation of termination processes being dependent on the chain‐length of the macroradical (as an example of pure fundamental research) to modeling of technical reactors, that provides attractiveness and defines challenges. Especially, the success in transforming results directly from laboratory experiments into technical applications justifies laborious efforts in determining highly precise rate coefficients and proves the concept breaking down a complex process into elementary subparts. A necessary boundary condition for this is keeping in mind the demands along the whole scope of applications and avoiding simplifications that are only applicable for part of them. Although at a first glance this may appear to hinder fast progress in one discipline, it is the essential requirement for final success.     

A Semi‐Microscopic Modeling for Polymer Flow Reactors

Summary: A nonisothermal plug‐flow reactor for ethylene polymerization is reexamined so as to illustrate the principle and effect of a refined, semi‐microscopic modeling. The novel feature of the current simulation is the application of a Monte Carlo scheme to exactly solve the free‐radical polymerization involved, whereas a reptation‐based molecular theory is introduced in a self‐consistent manner to simulate more accurately the reactant fluid viscosity during polymerization. The simulation is shown to capture some in‐depth consequences of reaction‐transport coupling that cannot be revealed by a traditional, macroscopic type of modeling. The principle of a future extension for dealing with more complex flow reactors is briefly discussed.

Comparison of the predicted temperature profile between Monte Carlo‐based simulation and the ones using moment equations together with two different weight distributions is shown with experimental data for LDPE.     

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.     

Mixing Effects in Continuous Free‐Radical Solution Copolymerization Tank Reactors: II—Investigation of Micromixing Effects

The effect of micromixing on the dynamic behavior of continuous solution copolymerization tank reactors is evaluated both experimentally and theoretically. For this purpose, copolymerization reactions of styrene and divinylbenzene are carried out in a lab‐scale polymerization system, composed of two tank reactors in series, to provide experimental data of conversion and molar masses for analysis of micromixing effects. Besides, a detailed micromixing model, based on a dynamic population balance approach, is developed and solved with the method of characteristics, to investigate the micromixing effects on the dynamic behavior of conversion and molar masses in copolymerization reactions. Particularly, results show for the first time that micromixing effects can be important to explain the dynamic behavior of polymerization reactions performed in bulk, but are not sufficient to explain the whole set of available experimental data, which are much more sensitive to modification of residence time distributions and macromixing.     

Simulation of solid‐state polycondensation of nylon‐66

A new model of solid‐state polymerization of nylon‐6,6 has been developed. The polymer crystalline fraction is assumed to consist of only repeat units, leaving end‐groups and condensate in the amorphous fraction. Many effects neglected by previous models are considered, such as variable crystallinity, initial moisture and starting molecular weight. This model is compared to experimental data with good agreements. Differential scanning calorimetry graphs show that the crystalline structure phase tends to be increasingly perfect during heat treatment, indicative of the premelting temperature drawing near the melting point up to 14 °C after solid‐state polycondensation with little change of melting point. Copyright © 2000 John Wiley & Sons, Ltd.     

The Effect of Residence Time Distribution on the Slurry‐Phase Catalytic Ethylene Polymerization: An Experimental and Computational Study

This work is focused on the development and validation of a model accounting for the impact of the reactor residence time distribution in well‐stirred slurry‐phase catalytic polymerization of ethylene. Particle growth and morphology are described through the Multigrain model, adopting a two‐site model for the catalyst and a conventional kinetic scheme. Particle size distribution and polymer properties (average molecular weights and polydispersity) are computed as a function of particle size through a segregated model, assuming that neither breakage nor aggregation occur. Reactors are modeled by means of fundamental mass conservation equations. The model is applied to a system constituted by a series of two ideal continuous stirred tank reactors, where the synthesis of polyethylene with bimodal molecular weight distribution is performed, employing the initial catalyst size distribution as the only adjustable parameter. The model provides insights at the single particle scale for each specific size, thus highlighting the inhomogeneity which arises from the synergic effects of chemical kinetics and residence time distributions in both reactors. The satisfactory agreement between model results and experimental data, in terms of particle size distribution and average molecular weights, confirmed the suitability of the model and underlying assumptions.     

Synthesis of poly(chloromethylstyrene‐b‐styrene) block copolymers by controlled free‐radical polymerization

The controlled free‐radical polymerization of styrene and chloromethylstyrene monomers in the presence of 2,2,6,6‐tetramethyl‐1‐piperidinyloxyl (TEMPO) has been studied with the aim of synthesizing block copolymers with well‐defined structures. First, TEMPO‐capped poly(chloromethylstyrene) was prepared. Among several initiating systems [self‐initiation, dicumyl peroxide, and 2,2′‐azobis(isobutyronitrile)], the last offered the best compromise for obtaining a good control of the polymerization and a fast polymerization rate. The rate of the TEMPO‐mediated polymerization of chloromethylstyrene was independent of the initial concentration of TEMPO but unexpectedly higher than the rate of the thermal self‐initiated polymerization of chloromethylstyrene. Transfer reactions to the chloromethyl groups were thought to play an important role in the polymerization kinetics and the polydispersity index of the resulting poly(chloromethylstyrene). Second, this first block was used as a macroinitiator in the polymerization of styrene to obtain the desired poly(chloromethylstyrene‐b‐styrene) block copolymer. The kinetic modeling of the block copolymerization was in good agreement with experimental data. The block copolymers obtained in this work exhibited a low polydispersity index (weight‐average molecular weight/number‐average molecular weight < 1.5) and could be chemically modified with nucleophilic substitution reactions on the benzylic site, opening the way to a great variety of architectures. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3845–3854, 2000     

Side Reactions in Aqueous Phase Polymerization of N‐Vinyl‐Pyrrolidone as Possible Source for Fouling

An improved kinetic model for the radical polymerization of N‐vinyl‐pyrrolidone (NVP) in aqueous medium is developed. Quantum chemical simulations reveal that the transfer to polymer is of minor importance whereas the transfer to monomer by hydrogen abstraction in 3‐position of the pyrrolidone ring leads to a radical with a double bond which initiates a new chain bearing a terminal double bond (TDB). The resulting dead chains with one, two, or more TDB are the main source for a strong increase of molar mass in batch reactors at high conversion due to long chain branching and crosslinking. This can be a source for gel formation and fouling in continuous reactors.     

Investigations of thermal polymerization in the stable free‐radical polymerization of 2‐vinylnaphthalene

The feasibility of utilizing stable free‐radical polymerization (SFRP) in the synthesis of well‐defined poly(2‐vinylnaphthalene) homopolymers has been investigated. Efforts to control molecular weight by manipulating initiator concentration while maintaining a 2,2,6,6‐tetramethylpiperidinyl‐1‐oxy (TEMPO):benzoyl peroxide (BPO) molar ratio of 1.2:1 proved unsuccessful. In addition, systematic variations of the TEMPO: BPO molar ratio did not result in narrow molecular weight distributions. In situ Fourier transform infrared spectroscopy (FTIR) indicated that the rate of monomer disappearance under SFRP and thermal conditions were identical. This observation indicated a lack of control in the presence of the stable free radical, TEMPO. The similarities in chemical structure between styrene and 2‐vinylnaphthalene suggested thermally initiated polymerization occurred via the Mayo mechanism. A kinetic analysis of the thermal polymerization of styrene and 2‐vinylnaphthalene suggested that the additional fused ring in 2‐vinylnaphthalene increased the propensity for thermal polymerization. The observed rate constant for thermal polymerization of 2‐vinylnaphthalene was determined using in situ FTIR spectroscopy and was one order of magnitude greater than styrene, assuming pseudo‐first‐order kinetics. Also, an Arrhenius analysis indicated that the activation energy for the thermal polymerization of 2‐vinylnaphthalene was 30 kJ/mol less than styrene. © 2002 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 583–590, 2002; DOI 10.1002/pola.10131     

Numerical simulations of the polymerization reaction of deuterated diacetylene 2,4‐hexadiynylene bis(p‐toluenesulfonate) crystal

In this paper, we developed two types of programs in order to simulate the polymerization reaction of a fully deuterated crystal of diacetylene 2,4‐hexadiynylene bis(p‐toluenesulfonate) (pTS‐D). The first simulation is based on a modification of Baughman's model, a classical model for simulating the polymerization of diacetylene crystals. The agreement between the simulated and experimental results concerning the reaction kinetics is satisfactory. With this simulation algorithm, we take into account the experimental observation that the polymerization of pTS‐H and pTS‐D crystals is really a random process of formation of polymer chains along the crystallographic axis b . The second simulation is based on the Monte Carlo method, which permits not only to simulate the kinetics of the reaction, but also the chain‐length distribution in the hydrogenated and deuterated compounds. These two types of simulations were already developed for the hydrogenated crystal of diacetylene, named pTS‐H. Two main modifications are applied in the case of pTS‐D for taking into account experimental results: in the first the rate constants of chain‐terminating microscopic processes are different in pTS‐H and pTS‐D which must be considered. The second modification concerns the evolution of the lattice deformation during the course of polymerization. The experimental variation of the b parameter as a function of polymer content X in pTS‐D is different from that in pTS‐H; this result is important to consider when calculating the activation energy of the initiation and propagation microscopic processes.     

High‐molecular‐weight poly(1,5‐dioxepan‐2‐one) via enzyme‐catalyzed ring‐opening polymerization

To avoid organometallic catalysts in the synthesis of poly(1,5‐dioxepan‐2‐one), the enzymatic ring‐opening polymerization of 1,5‐dioxepan‐2‐one (DXO) was performed with lipase CA (derived from Candida antarctica) as a biocatalyst. A linear relationship between the number‐average molecular weight and monomer conversion was observed, and this suggested that the product molecular weight could be controlled by the stoichiometry of the reactants. The monomer consumption followed a first‐order rate law with respect to the monomer, and no chain termination occurred. Water acted as a chain initiator, but it could cause polymer hydrolysis when it exceeded an optimum level. An initial activation via the heating of the enzyme was sufficient to start the polymerization, as the monomer conversion occurred when samples were left at room temperature after an initial heating at 60 °C. A high lipase content led to a high monomer conversion as well as a high molecular weight. An increase in the monomer conversion and molecular weight was observed when the polymerization temperature was increased from 40 to 80 °C. A further increase in the polymerization temperature led to a decrease in the monomer conversion and molecular weight because of the denaturation of the enzyme at elevated temperatures. The polymerization behavior of DXO under lipase CA catalysis was compared with that of ε‐caprolactone (CL). The rate of monomer conversion of DXO was much faster than that of CL, and this may have been due to differences in their specificity toward lipase CA. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4206–4216, 2005     

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.     

Kinetics of hexene‐1 polymerization using [(N,N′‐diisopropylbenzene)‐2,3‐(1,8‐napthyl)‐1,4‐diazabutadiene] dibromonickel/methylaluminoxane catalyst system

Kinetics of hexene‐1 polymerization was investigated using [(N,N′‐diisopropylbenzene)2,3‐(1,8‐napthly)‐1,4‐diazabutadiene]dibromonickel/methylaluminoxane catalyst. Experiments were performed at varying catalyst and monomer concentrations in the temperature range of ?10 to 35 °C. First order time‐conversion plot shows a downward curvature at temperatures of 20 °C and 35 °C indicating the presence of finite termination reactions. A nonlinear plot of degree of polymerization (P_n) with respect to conversion indicates occurrence of transfer reactions and slow initiation. The experimental molar masses are higher than predicted, which implies that a fraction of catalyst species could not be activated or is deactivated at the early stages of the reactions. The efficiency of the catalyst (Cat_eff) varies from 0.77 to 0.89. The observed polydispersity of the poly(hexene‐1) s is in the range of 1.18–1.48. The reaction order was found to be 1.11 with respect to catalyst. The Arrhenius plot obtained using the overall propagation rate constant, k_p, at five different temperatures (?10, 0, 10, 20, and 35 °C) was found to be linear with an activation energy, E_a = 4.3 kcal/mol. Based on the results presented it is concluded that the polymerization of hexene‐1 under the above‐mentioned conditions shows significant deviation from ideal “living” behavior. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1093–1100, 2007     

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     

Atom transfer radical polymerization of n‐butyl acrylate catalyzed by CuBr/N‐(n‐hexyl)‐2‐pyridylmethanimine

The homogeneous atom transfer radical polymerization (ATRP) of n‐butyl acrylate with CuBr/N‐(n‐hexyl)‐2‐pyridylmethanimine as a catalyst and ethyl 2‐bromoisobutyrate as an initiator was investigated. The kinetic plots of ln([M]₀/[M]) versus the reaction time for the ATRP systems in different solvents such as toluene, anisole, N,N‐dimethylformamide, and 1‐butanol were linear throughout the reactions, and the experimental molecular weights increased linearly with increasing monomer conversion and were very close to the theoretical values. These, together with the relatively narrow molecular weight distributions (polydispersity index ～ 1.40 in most cases with monomer conversion > 50%), indicated that the polymerization was living and controlled. Toluene appeared to be the best solvent for the studied ATRP system in terms of the polymerization rate and molecular weight distribution among the solvents used. The polymerization showed zero order with respect to both the initiator and the catalyst, probably because of the presence of a self‐regulation process at the beginning of the reaction. The reaction temperature had a positive effect on the polymerization rate, and the optimum reaction temperature was found to be 100 °C. An apparent enthalpy of activation of 81.2 kJ/mol was determined for the ATRP of n‐butyl acrylate, corresponding to an enthalpy of equilibrium of 63.6 kJ/mol. An apparent enthalpy of activation of 52.8 kJ/mol was also obtained for the ATRP of methyl methacrylate under similar reaction conditions. Moreover, the CuBr/N‐(n‐hexyl)‐2‐pyridylmethanimine‐based system was proven to be applicable to living block copolymerization and living random copolymerization of n‐butyl acrylate with methyl methacrylate. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3549–3561, 2002     

R‐RAFT approach for the polymerization of N‐isopropylacrylamide with a star poly(ε‐caprolactone) core

Reversible addition‐fragmentation chain transfer (RAFT) polymerization is a more robust and versatile approach than other living free radical polymerization methods, providing a reactive thiocarbonylthio end group. A series of well‐defined star diblock [poly(ε‐caprolactone)‐b‐poly(N‐isopropylacrylamide)]₄ (SPCLNIP) copolymers were synthesized by R‐RAFT polymerization of N‐isopropylacrylamide (NIPAAm) using [PCL‐DDAT]₄ (SPCL‐DDAT) as a star macro‐RAFT agent (DDAT: S‐1‐dodecyl‐S′‐(α, α′‐dimethyl‐α″‐acetic acid) trithiocarbonate). The R‐RAFT polymerization showed a controlled/“living” character, proceeding with pseudo‐first‐order kinetics. All these star polymers with different molecular weights exhibited narrow molecular weight distributions of less than 1.2. The effect of polymerization temperature and molecular weight of the star macro‐RAFT agent on the polymerization kinetics of NIPAAm monomers was also addressed. Hardly any radical–radical coupling by‐products were detected, while linear side products were kept to a minimum by careful control over polymerization conditions. The trithiocarbonate groups were transferred to polymer chain ends by R‐RAFT polymerization, providing potential possibility of further modification by thiocarbonylthio chemistry. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Atom transfer radical polymerization of ionic liquid 2‐(1‐butylimidazolium‐3‐yl)ethyl methacrylate tetrafluoroborate

Polymeric forms of ionic liquids may have many potential applications because of their high thermal stability and ionic nature. They are generally synthesized by conventional free‐radical polymerization. Here we report a living/controlled free‐radical polymerization of an ionic liquid monomer, 2‐(1‐butylimidazolium‐3‐yl)ethyl methacrylate tetrafluoroborate (BIMT), via atom transfer radical polymerization. Copper bromide/bromide based initiator systems polymerized BIMT very quickly with little control because of fast activation but slow deactivation. With copper chloride as the catalyst and trichloroacetate, CCl₄, or ethyl α‐chlorophenylacetate as the initiator, BIMT was polymerized at 60 °C in acetonitrile with first‐order kinetics with respect to the monomer concentration. The molecular weight was linearly dependent on the conversion. The monomer concentration strongly affected the polymerization: a low monomer concentration caused the polymerization to be incomplete, probably because of catalyst disproportionation in polar solvents. The addition of a small amount of pyridine suppressed such disproportionation, but a further increase in the amount of pyridine greatly slowed the polymerization. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5794–5801, 2004     

Role of sodium dodecylbenzenesulfonate in 2,2,6,6‐tetramethy‐1‐piperidinyloxy‐mediated styrene miniemulsion polymerization

In studying 2,2,6,6‐tetramethy‐1‐piperidinyloxy (TEMPO)‐mediated styrene miniemulsions, we have observed that the surfactant sodium dodecylbenzenesulfonate (SDBS) not only provides colloidal stability but also influences the rate of polymerization. Increasing the SDBS concentration results in higher polymerization rates, although the molecular weight distribution and particle size distribution are not significantly impacted. We have also examined another common sulfonate surfactant, DOWFAX 8390. In contrast to SDBS, DOWFAX 8390 does not affect the polymerization rate. Furthermore, DOWFAX‐stabilized polymerizations are slower than SDBS‐stabilized polymerizations. TEMPO‐mediated bulk styrene polymerizations are also accelerated significantly in the presence of SDBS. Although the mechanism for the rate acceleration is unknown, the experimental evidence suggests that SDBS is participating in the generation of radicals capable of propagating, thereby reducing the TEMPO concentration within the particles. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5974–5986, 2006