Propagation Rate Coefficients for Homogeneous Phase VDF–HFP Copolymerization in Supercritical CO2

For the first time, propagation rate coefficients, k_p,COPO, for the copolymerizations of vinylidene fluoride and hexafluoropropene have been determined. The kinetic data was determined via pulsed‐laser polymerization in conjunction with polymer analysis via size‐exclusion chromatography, the PLP‐SEC technique. The experiments were carried out in homogeneous phase with supercritical CO₂ as solvent for temperatures ranging from 45 to 90 °C. Absolute polymer molecular weights were calculated on the basis of experimentally determined Mark–Houwink constants. The Arrhenius parameters of k_p,COPO vary significantly compared with ethene, which is explained by the high electronegativity of fluorine and less intra‐ and intermolecular interactions between the partially fluorinated macroradicals.     

Free Radical Bulk Polymerization of Styrene: Simulation of Molecular Weight Distributions to High Conversion Using Experimentally Obtained Rate Coefficients

Previously obtained experimental conversion‐dependences of the propagation rate coefficient (k_p), the termination rate coefficient (k_t) and the initiator efficiency (f) for the free‐radical bulk polymerization of styrene at 70 °C have been used to simulate the full molecular weight distributions (MWD) to high conversion using the software package PREDICI, providing a robust test of the kinetic model adopted. Satisfactory agreement with the experimental MWD's (GPC) was obtained up to approximately 70% conversion. Beyond 70% conversion, the high MW shoulder that appears was correctly predicted, although the amount of such polymer was somewhat underestimated. This discrepancy is believed to probably have its origin in experimental error in the conversion‐dependences of k_p, k_t and f, in particular k_t, that were employed in the simulations, rather than indicate a more fundamental short‐coming of the model employed.

     

Propagation Kinetics of Isoprene Radical Homopolymerization Derived from Pulsed Laser Initiated Polymerizations

The propagation kinetics of isoprene radical polymerizations in bulk and in solution are investigated via pulsed laser initiated polymerizations and subsequent polymer analyses via size‐exclusion chromatography, the PLP‐SEC method. Because of low polymerization rate and high volatility of isoprene, the polymerizations are carried out at elevated pressure ranging from 134 to 1320 bar. The temperatures are varied between 55 and 105 °C. PLP‐SEC yields activation parameters of k_p (Arrhenius parameters and activation volume) over a wide temperature and pressure range that allow for the calculation of k_p at technically relevant ambient pressure conditions. The k_p values determined are very low, e.g., 99 L mol^?1 s^?1 at 50 °C, which is even lower than the corresponding value for styrene polymerizations. The presence of a polar solvent results in a slight increase of k_p compared to the bulk system. The k_p values reported are important for determining rate coefficients of other elemental reactions from coupled parameters as well as for modeling isoprene free‐radical polymerizations and reversible deactivation radical polymerization with respect to tailored polymer properties and optimizing the polymerization processes.     

Free‐radical copolymerization of styrene with butyl acrylate. II. Elemental kinetic copolymerization step predictions from homopolymerization data

The free‐radical copolymerization of styrene and butyl acrylate has been carried out in benzene at 50 °C. The lumped k _p/k parameter (where k _p and k _t are the average copolymerization propagation and termination rate constants, respectively) has been determined. Applying the implicit penultimate unit model for the overall copolymerization propagation rate coefficient and the terminal unit effect for the overall copolymerization termination rate coefficient and using the homopolymerization kinetic coefficients, we have found good qualitative agreement between the experimental and theoretical k _p/k values. The variation of the copolymerization rate in solution with respect to the values previously found in bulk has been ascribed to a chain length effect on the copolymerization termination rate coefficient. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 130–136, 2004     

Intermolecular chain transfer to polymer with chain scission: general treatment and determination of kp/ktr in L,L-lactide polymerization

A general kinetic treatment of the system with intermolecular chain transfer followed by fast reinitiation is given. It leads to the broadening of the molecular weight distribution (MWD), the number of growing chains being invariable. Thus, this system can be considered as a special case of living polymerization. A general method has been elaborated allowing the determination of the ratio of the rate constant of propagation (k_p) to the rate constant of the bimolecular transfer (k⁽²⁾_tr) from the dependence of the MWD on monomer conversion. Numerical values of k_p/k⁽²⁾_tr equal to ≈ 10² and 25 were thus determined for the polymerization of L , L -lactide (L , L -dilactide) initiated with aluminium tris(isopropoxide) trimer ({Al(OⁱPr)₃}₃) and tributyltin ethoxide (ⁿBu₃SnOEt), respectively.     

Kinetic Analysis of Reversible Addition Fragmentation Chain Transfer (RAFT) Polymerizations: Conditions for Inhibition,Retardation, and Optimum Living Polymerization

Careful simulations of conversion vs. time plots and full molecular weight distributions have been performed using the PREDICI® program package in conjunction with the kinetic scheme suggested by the CSIRO group for the reversible addition fragmentation chain transfer (RAFT) process to probe RAFT agent mediated polymerizations. In particular, conditions leading to inhibition and rate retardation have been examined to act as a guide to optimum living polymerization behavior. It is demonstrated that an inhibition period of considerable length is induced by either slow fragmentation of the intermediate RAFT radicals appearing in the pre‐equilibrium or by slow re‐initiation of the leaving group radical of the initial RAFT agent. The absolute values of the rate coefficients governing the core equilibrium of the RAFT process – at a fixed value of the equilibrium constant – are confirmed to be crucial in controlling the polydispersity of the resulting molecular weight distributions: A higher interchange frequency effects narrower distributions. It is further demonstrated that the size of the rate coefficient controlling the addition reaction of propagating radicals to polyRAFT agent, k_β, is mainly responsible for optimizing the control of the polymerization. The fragmentation rate coefficient, k_–β, of the macroRAFT intermediate radical, on the other hand, may be varied over orders of magnitude without affecting the amount of control exerted over the polymerization. On the basis of the basic RAFT mechanism, its value mainly governs the extent of rate retardation in RAFT polymerizations.     

Ionic Liquids - New Solvents in the Free Radical Polymerization

Summary: The analysis of the influence of ionic liquids (ILs) in polymer synthesis as an alternative for common organic solvents is still an active field of research. 1 Using ILs as solvents for free radical polymerizations implies a significant increase in polymerization rates and molecular weights which can be observed. In this work we examined the copolymerization behaviour of styrene (S) and methyl methacrylate (MMA), glycidyl methacrylate (GMA) and 2-hydroxypropyl methacrylate (HPMA) with acrylonitrile (AN) in 1-etyhl-3-methylimidazolium ethylsulfate ([EMIM]EtSO₄). ILs are liquids with comparable high polarities and viscosities. These two characteristic properties are strongly correlated with the rate coefficients of propagation k_p and termination k_t. 2 - 4 The rate constant of termination k_t decreases when the IL concentration and therefore the viscosity of the reaction mixture is increased, whereas the propagation rate coefficient k_p increases with increasing IL content. The viscosity of the IL can be varied by either working with mixtures of IL with conventional organic solvents – here the IL [EMIM]EtSO₄ was mixed with DMF – or by variation of the temperature. The influence of the viscosity of the IL ([EMIM]EtSO₄) on polymerization kinetics of methyl methacrylate (MMA) and styrene/acrylonitrile (S/AN) was investigated.     

Kinetic model of reversible addition‐fragmentation chain transfer polymerization in microemulsions

A simplified kinetic model for RAFT microemulsion polymerization has been developed to facilitate the investigation of the effects of slow fragmentation of the intermediate macro‐RAFT radical, termination reactions, and diffusion rate of the chain transfer agent to the locus of polymerization on the control of the polymerization and the rate of monomer conversion. This simplified model captures the experimentally observed decrease in the rate of polymerization, and the shift of the rate maximum to conversions less than the 39% conversion predicted by the Morgan model for uncontrolled microemulsion polymerizations. The model shows that the short, but finite, lifetime of the intermediate macro‐RAFT radical (1.3 × 10^?4–1.3 × 10^?2 s) causes the observed rate retardation in RAFT microemulsion polymerizations of butyl acrylate with the chain transfer agent methyl‐2‐(O‐ethylxanthyl)propionate. The calculated magnitude of the fragmentation rate constant (k_f = 4.0 × 10¹–4.0 × 10³ s^?1) is greater than the literature values for bulk RAFT polymerizations that only consider slow fragmentation of the macro‐RAFT radical and not termination (k_f = 10^?2 s^?1). This is consistent with the finding that slow fragmentation promotes biradical termination in RAFT microemulsion polymerizations. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 604–613, 2010     

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.     

Effect of alkylaluminum on ethylene polymerization catalyzed by 2,6‐bis(imino)pyridyl complexes of Fe(II)

In the presence of tetraethylaluminoxane (TEAO), iron complexes were used to catalyze ethylene polymerizations with extremely high activities and generally produced polyethylene with a bimodal molecular weight distribution (MWD). This bimodal MWD of polyethylene was mainly derived from residual triethylaluminum in TEAO and was produced through a mechanism of chain transfer to aluminum. Ethylaluminoxane and tetraisobutylaluminoxane also were used to polymerize ethylene with high activities in the presence of iron complexes, and only polyethylene with a unimodal MWD was produced. The ratio of the rate constant of chain transfer to aluminum (k_trA) to the rate constant of chain propagation (k_p) was determined to be 0.12 for {[ArN?C(Me)]₂C₅H₃N}FeCl₂ when Ar was 2,6‐diisopropylphenyl ( 1 ) and 2.48 for {[ArN?C(Me)]₂C₅H₃N}FeCl₂ when Ar was 2,6‐dimethylphenyl ( 2 ); these values are far larger than those for metallocene‐based catalysts. This explains why an iron complex usually produces polyethylene with a broader MWD than metallocene‐based catalysts. Additionally, it can be concluded from the great difference between 1 and 2 with respect to k_trA/k_p that an iron complex with less congested aryl substituents is subjected to chain transfer to aluminum. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1599–1606, 2005     

Free‐radical copolymerization of styrene and m‐isopropenyl‐α,α′‐dimethylbenzyl isocyanate studied by 1H NMR kinetic experiments

The free‐radical copolymerization of m‐isopropenyl‐α,α′‐dimethylbenzyl isocyanate (TMI) and styrene was studied with ¹H NMR kinetic experiments at 70 °C. Monomer conversion vs time data were used to determine the ratio k_p × k_t^?0.5 for various comonomer mixture compositions (where k_p is the propagation rate coefficient and k_t is the termination rate coefficient). The ratio k_p × k_t^?0.5 varied from 25.9 × 10^?3 L^0.5 mol^?0.5 s^?0.5 for pure styrene to 2.03 × 10^?3 L^0.5 mol^?0.5 s^?0.5 for 73 mol % TMI, indicating a significant decrease in the rate of polymerization with increasing TMI content in the reaction mixture. Traces of the individual monomer conversion versus time were used to map out the comonomer mixture composition drift up to overall monomer conversions of 35%. Within this conversion range, a slight but significant depletion of styrene in the monomer feed was observed. This depletion became more pronounced at higher levels of TMI in the initial comonomer mixture. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1064–1074, 2002     

A simplified data treatment for dead-end and high conversion polymerization kinetics

A simplified approximation method for the treatment of dead-end and high conversion polymerization kinetics is presented. The method is based on the treatment of dead-end polymerization first described by Tobolsky. In appropriate circumstances, by contrast with Tobolsky's method, this method provides measurements of k_d and k_p/k_t^1/2 without recourse to the measurement of the monomer conversion at infinite time. Kinetic studies of free radical polymerizations are normally confined to measurements of initial rates. At low conversions the predictions of the general mechanism for chain-growth polymerization involving initiation, propagation, and termination steps are generally obeyed. Thus the polymerization rate should be first order in the vinyl monomer and half-order in the initiator concentrations. At high conversions, however, large deviations which can be ascribed to various effects can occur; for example, (1) the effect of the increasing viscosity of the polymerization medium on the termination rate constant k_t, and possibly also on the propagation rate constant k_p, which have been considered by North¹ and Cardenas and O'Driscoll,² or (2) depletion of the initiator as the polymerization progresses. This depletion will occur in all polymerizations but its significance will depend on the magnitude of the rate constant for initiator decomposition (k_d) and the period of polymerization. Appropriate conditions will lead to limiting monomer conversion even after infinite polymerization time; this phenomenon has been called dead-end polymerization by Tobolsky.³ Free radical polymerizations to high conversion are particularly important in the industrial context when initial kinetics are obviously inadequate. Suitable treatment of the conversion/time relationship is highly desirable. Senogles and Woolf⁴ have examined the polymerization of n-lauryl methacrylate at 60°C with 2-azobisisobutyronitrile as initiator under dead-end conditions. Here we propose a modification of Tobolsky's treatment of such polymerizations by using an approximation for the exponential decay in the initiator concentration. This method permits easy manipulation of the experimental data and the estimation of values for the kinetic parameters in favorable circumstances without recourse to the measurement of the conversion at infinite time or the evaluation of complicated functions of the monomer conversion. The method thus allows the duration of the laboratory experimentation to be significantly shortened and the complexity of the subsequent data analysis to be considerably reduced.     

Effect of the Intramolecular Chain Transfer to Polymer on PLP/SEC Experiments of Alkyl Acrylates

Pulsed‐laser polymerization (PLP) has been adopted by IUPAC as the method of choice for the determination of propagation rate constants (k_p). However, the method has failed in the polymerization of alkyl acrylates at temperatures above 30 °C. In this work, the PLP experiments were analyzed by simulation using a Monte Carlo algorithm. It was found that the experimental difficulties encountered to accurately determine k_p at temperatures above 30 °C were caused by extensive intramolecular chain transfer. This mechanism is not operative at lower temperatures because of its high activation energy.

Pulsed‐laser polymerization of BA in bulk at temperatures between −41 and +40 °C: Simulated MWD trace.     

Molecular weight distribution of a living polymer generated from a bifunctional initiator with non-equal initiation rate constants

This work deals with the kinetics of the living polymerization initiated by a bifunctional initiator with different rate constants of the first and the second step of initiation. The expressions of the molecular weight distribution (MWD) function, the number- and weight-average degrees of polymerization and the polydispersity index were derived rigorously. Numerical results show that the nonequal initiation rate constants often lead to a bimodal MWD except the ratio of k_i to k_i′ being very large (>500, for instance) or relatively small (<1, for example). The MWD of the resultant polymer is rather narrow even in the presence of double peaks. With decreasing initiator concentration, the MWD at full conversion becomes narrower, and the shoulder peak of the MWD curve declines.     

Determination of propagation‐rate constant of vinylidene chloride by emulsion polymerization

The propagation‐rate constant of vinylidene chloride (VDC) was determined at 40 and 50 °C, respectively, by applying the so‐called Ugelstad plot to the polymerization‐rate data of the seeded and unseeded emulsion polymerizations of VDC. The values of the propagation‐rate constant k_p thus determined are k_p = 64 dm³/mol · s at 50 °C and k_p = 52 dm³/mol · s at 40 °C, respectively. From these k_p values, the activation energy for propagation reaction was determined to be E_p = 4.2 kcal/mol, which is close to that of vinyl chloride (3.7 kcal/mol). © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1005–1015, 2001     

Kinetics and mechanism of metallocene‐catalyzed olefin polymerization: Comparison of ethylene,propylene homopolymerizations,and their copolymerization

A series of ethylene, propylene homopolymerizations, and ethylene/propylene copolymerization catalyzed with rac‐Et(Ind)₂ZrCl₂/modified methylaluminoxane (MMAO) were conducted under the same conditions for different duration ranging from 2.5 to 30 min, and quenched with 2‐thiophenecarbonyl chloride to label a 2‐thiophenecarbonyl on each propagation chain end. The change of active center ratio ([C^*]/[Zr]) with polymerization time in each polymerization system was determined. Changes of polymerization rate, molecular weight, isotacticity (for propylene homopolymerization) and copolymer composition with time were also studied. [C^*]/[Zr] strongly depended on type of monomer, with the propylene homopolymerization system presented much lower [C^*]/[Zr] (ca. 25%) than the ethylene homopolymerization and ethylene–propylene copolymerization systems. In the copolymerization system, [C^*]/[Zr] increased continuously in the reaction process until a maximum value of 98.7% was reached, which was much higher than the maximum [C^*]/[Zr] of ethylene homopolymerization (ca. 70%). The chain propagation rate constant (k_p) of propylene polymerization is very close to that of ethylene polymerization, but the propylene insertion rate constant is much smaller than the ethylene insertion rate constant in the copolymerization system, meaning that the active centers in the homopolymerization system are different from those in the copolymerization system. Ethylene insertion rate constant in the copolymerization system was much higher than that in the ethylene homopolymerization in the first 10 min of reaction. A mechanistic model was proposed to explain the observed activation of ethylene polymerization by propylene addition. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 867–875     

Thermal polymerization of styrene in the presence of some ferrocene derivatives. II. Low concentrations of vinylferrocene and ethylferrocene

Styrene has been polymerized thermally at 60°C in the presence of low concentrations of vinylferrocene and in the presence and absence of 2,2′-azobisisobutyronitrile (AIBN). The polymerizations were studied in bulk and also in benzene solution. The thermal polymerization of styrene in the presence of ethylferrocene, but without added AIBN or solvent, was also examined. The bulk polymerizations exhibited high initial rates of polymerization followed by a decrease in rate. Initial rates of polymerization for bulk polymerizations in the absence of AIBN have been interpreted by means of a kinetic scheme involving propagation with styrene participating in a specific interaction with the ferrocene derivative and some kinetic parameters associated with this scheme have been evaluated. The decrease in the rate of polymerization is due to the formation of a retarder. The benzene solution polymerizations fitted a simple kinetic scheme and the transfer constant for vinylferrocene with respect to polystyryl radicals C_s, has been evaluated as 1.98 × 10^?3.     

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     

Kinetic elucidation of comonomer‐induced chemical and physical activation in heterogeneous ziegler‐natta propylene polymerization

We have kinetically elucidated the origins of activity enhancement because of the addition of comonomer in Ziegler‐Natta propylene polymerization, using stopped‐flow and continuously purged polymerization. Stopped‐flow polymerization (with the polymerization time of 0.1–0.2 s) enabled us to neglect contributions of physical phenomena to the activity, such as catalyst fragmentation and reagent diffusion through produced polymer. The propagation rate constant k_p and active‐site concentration [C*] were compared between homopolymerization and copolymerization in the absence of physical effects. k_p for propylene was increased by 30% because of the addition of a small amount of ethylene, whereas [C*] was constant. On the contrary, both k_p (for propylene) and [C*] remained unchanged by the addition of 1‐hexene. Thus, only ethylene could chemically activate propylene polymerization. However, continuously purged polymerization for 30 s resulted in much more significant activation by the addition of comonomer, clearly indicating that the activation phenomenon mainly arises from the physical effects. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011