Propagation Rate Constants Research Articles

Effects of initial composition and temperature on the kinetics of polymerizations of N,N′-bismaleimide-4,4′-diphenylmethane with barbituric acid

Kinetics of polymerizations of N,N′-bismaleimide-4,4′-diphenylmethane (BMI)/barbituric acid (BTA) with molar ratios of BMI to BTA equal to 1/1, 2/1 and 4/1 in the temperature range 373–403 K were studied. Both Michael addition polymerization and free radical polymerization mechanisms were operative in such reaction systems. With the knowledge of kinetic parameters of the Michael addition polymerization of BMI with BTA taken from the literature, optimized kinetic parameters for simultaneous free radical polymerization including the overall initiation rate constant and the combined propagation and termination rate constants were achieved. In addition, modeling results along with experimental gelation time data showed that contribution of free radical polymerization was promoted for the polymerization carried out at a higher reaction temperature and/or a larger molar ratio of BMI to BTA. By contrast, Michael addition polymerization was enhanced with a smaller molar ratio of BMI to BTA and/or a lower reaction temperature.

Kinetic study of styrene and methyl methacrylate emulsion polymerization induced by cumene hydroperoxide/tetraethylenepentamine

The redox initiator, cumene hydroperoxide/tetraethylenepentamine (CHPO/TEPA), was used to initiate the emulsion polymerizations of styrene and methyl methacrylate (MMA). The hydrophobic CHPO acting as oxidizer would interact with the hydrophilic TEPA employed as the reducer at the particle-water interface where the vinyl monomer is present. The kinetics of the styrene and MMA polymerizations were studied under a temperature range of 30–70 °C. The polymerization rate, the concentration of monomer in the particles, the average number of latex particles and the number of radicals per particle were investigated to evaluate the propagation rate constant during interval II of the polymerization. With increasing temperature, the number of latex particles increases while the monomer concentration in the particles slightly decreases. The observed number of radicals per particle, calculated from the number average volume of the particles and the relation between the entry rate coefficients of free radicals into the particles and the exit rate coefficients of free radicals from the particle, was found to be approximately 0.47 and 0.5 in case of styrene and MMA polymerization, respectively. The calculation shows that the propagation rate constant, kp = 6.84 × 107e−37.65/RT and kp = 3.4 × 107e−31.05/RT L/mol∙s for styrene and MMA polymerizations over the temperature range studied, respectively.

Modeling of diffusional limitations in styrene acrylonitrile random bulk copolymerization

Diffusional limitations (the gel, glass, and cage effects) are manifested in several bulk free radical homopolymerizations as well as in random copolymerizations. These are associated with decreases of several orders of magnitude of the rate constants of termination, propagation, and initiation (the initiator efficiency), respectively. These phenomena have been modeled earlier using the free volume theory for the diffusivities of primary radicals, macro-radicals, and monomer molecules, and have been applied to homopolymerizations. In this study, a similar model is developed for random bulk copolymerizations. The parameters of the model are fitted using isothermal data on styrene acrylonitrile random copolymerization carried out in small ampoules. Thereafter, best-fit global correlations have been developed for this system. This enables the model to be used for studying non-isothermal copolymerizations, as well as for carrying out optimization of industrial reactors, where non-isothermal conditions are a norm. POLYM. ENG. SCI., 55:2098–2110, 2015. © 2014 Society of Plastics Engineers

Kinetics and thermodynamics of l-lactide polymerization studied by differential scanning calorimetry

Kinetics of l-lactide polymerization was studied by differential scanning calorimetry in isothermal mode at various temperatures and catalyst concentrations. The enthalpy of l-lactide polymerization measured directly in DSC cell was found to be ΔH=−19±0.5kJmol−1. Kinetic curves of l-lactide polymerization and propagation rate constants were determined for polymerization with stannous octoate at concentrations 200–1100ppm at temperatures 180, 190, 200 and 220°C. Using model or reversible polymerization the following kinetic and thermodynamic parameters were calculated: activation energy Ea=50±5kJmol−1, preexponential constant lnA=18±1, entropy of polymerization ΔS=−12±1Jmol−1K−1.

Prediction of Fischer–Tropsch Synthesis Kinetic Parameters Using Neural Networks

Abstract The kinetic mechanism of the Fischer–Tropsch synthesis (FTS) is complex resembling a polymerization reaction. The kinetic rate constants for initiation, propagation and termination steps and the constants for the equilibrium reactions for methylene formation (in situ monomer) need to be estimated. A mathematical model for the FTS allows for simulating several operating conditions and determining the best operating conditions to produce a specific product distribution, so the kinetic parameters must be statistically valid. This work used neural networks (NNs) to estimate the FTS kinetic parameters, instead of using methods based on least squared error. The results show that NNs with three hidden layers were able to output good estimates of the kinetic parameters with less than 5% of deviation.

Parallel models for arborescent polyisobutylene synthesized in batch reactor

A mathematical model is developed for estimating kinetic parameters that influence the production of arborescent polyisobutylene via carbocationic copolymerization of inimer (IM) and isobutylene. Six different propagation rate constants arise due to the two types of vinyl groups and three types of carbocations. These six parameters are estimated using parallel simulation systems in PREDICI that track (1) functional groups, (2) internal and dangling segments in the polymer, and (3) concentrations of IM and polymer molecules. Parameter estimates obtained using the proposed model result in a better fit to literature data than was obtained using a previous model that neglected two types of propagations reactions. Predictions from the proposed model are consistent with Monte Carlo simulations for molecular weight distribution of the internal and dangling segments. © 2014 American Institute of Chemical Engineers AIChE J, 61: 253–265, 2015

Kinetic features of ethylene polymerization over titanium-magnesium Ziegler-Natta catalysts: Effect of monomer concentration on the number of active centers and propagation rate constant

It was found that the observed order of the polymerization rate with respect to ethylene concentration at ethylene polymerization over two titanium-magnesium catalysts of different compositions is significantly higher than 1 (1.6–2.1). The data on the effect of ethylene concentration on the number of active centers (CP) and the propagation rate constant (kP) at ethylene polymerization over these catalysts were obtained by method of polymerization quenching with 14CO. An increase in ethylene concentration was found to increase the number of active centers. In some cases the increase of ethylene concentration proceeds to the narrowing of the molecular weight distribution of the resulting polyethylene and an increase in the calculated value of propagation rate constant. These effects were shown to be most pronounced at low ethylene pressure and increased concentration of an activator (AlEt3). Based on the experimental data, we proposed a scheme of reactions to explain the effects of ethylene and AlR3 concentrations on the number of active centers, the average values of propagation rate constant and molecular weight distribution of polymers produced over these multi-site catalysts.

Comonomer effects in copolymerization of ethylene and 1‐hexene with MgCl2‐supported Ziegler‐Natta catalysts: New evidences from active center concentration and molecular weight distribution

ABSTRACTIn this article, comonomer effects in copolymerization of ethylene and 1‐hexene with four MgCl2‐supported Ziegler‐Natta catalysts using either ethylene or 1‐hexene as the main monomer were investigated. It was found that no matter which monomer was used as the main monomer, the polymerization activity was significantly enhanced by introducing small amount of comonomer. In copolymerization with ethylene as the main monomer, the strength of comonomer effects was much stronger in active centers producing low‐molecular‐weight polymer than those producing high‐molecular‐weight polymer. In copolymerization with 1‐hexene as the main monomer, the number of active centers ([C*]/[Ti]) was determined, and the propagation rate constants (kp) were calculated. Deconvolution of the polymer molecular weight distribution into Flory components were made to study the active center distribution. Introduction of small amount of ethylene caused marked increase in the number of active centers and decrease in average chain propagation rate constant. Introducing internal electron donor in the catalyst enhanced not only the number of active centers but also the chain propagation rate constant. In copolymerization of 1‐hexene with small amount of ethylene, the internal donor weakened the comonomer effects to some extent and changed the distribution of comonomer effects among different types of active centers. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 41264.

Influence of temperature and light intensity on the photocuring process and kinetics parameters of a pigmented UV curable system

The photopolymerization of pigmented coatings is a great challenge and hardly investigated in the literature. Therefore, in this work, the effect of photopolymerization temperature and light intensity on the curing behavior of a TiO2-pigmented UV curable epoxy acrylate system was investigated by using photo-differential scanning calorimetry (photo-DSC) analysis. The rate of conversion and ultimate conversion at four different temperatures (i.e., 25, 45, 65, and 85 °C) and four light intensities (i.e. 2, 20, 40 and 80 mW cm−2) for unpigmented and pigmented formulations were measured. The effect of photo-polymerization temperature and light intensity on the kinetics constants was also evaluated. It was observed that the rate of conversion and final conversion values were affected by the temperature and UV-light intensity. It was seen that the rate of conversion and ultimate conversion had their maximum values at 65 °C for unpigmented formulations. However, in pigmented formulations, these two parameters improved by increasing the temperature even up to 85 °C. Increasing the temperature caused an increase in the amount of propagation and termination rate constants in both pigmented and unpigmented formulations although the changes in the pigmented formulation were more pronounced. It was observed that the rate of polymerization and ultimate conversion for unpigmented formulations increased by increasing the light intensity up to 20 mW cm−2 and then decreased. On the other hand, it was found that these two parameters increased by increasing light intensity up to 40 mW cm−2 when pigmented formulations used. Finally, the dependence of termination and propagation kinetics constants on light intensity was established for both unpigmented and pigmented coatings.

Kinetic Features of Hexene-1 Polymerization over Supported Titanium-Magnesium Catalyst

The data on the effect of cocatalyst composition and polymerization conditions on activity and MWD of polyhexene (PH) produced over a high-activity titanium-magnesium catalyst are obtained. The cocatalyst has an extremely strong effect on the MWD of polyhexene. When triisobutylaluminum is used as a cocatalyst, PH with high Mw and narrow MWD is produced. The use of TEA decreases the Mw of PH and broadens the MWD. It is found the ratio between the rate constant of chain transfer to TEA (ktrAl) and the propagation rate constant (kp) is two orders of magnitude higher than the ktrAl/kp value calculated for polymerization of ethylene and propylene. We attributed this effect to formation of polyhexene in the solution, as opposed to polymerization of ethylene and propylene in slurry polymerization. The addition of hydrogen at polymerization of hexene-1 significantly increases activity and stereospecificity.

Understanding the Chemical and Physical Transformations of a Ziegler–Natta Catalyst at the Initial Stage of Polymerization Kinetics: The Key Role of Alkylaluminum in the Catalyst Activation Process

An improved stopped‐flow (SF) technique is employed to clarify the origin of kinetics in propylene polymerization with a Mg(OEt)2‐based Ziegler–Natta catalyst. Polymerization in the range of 0.1–5 s exhibits a kinetic transition from a linear development to a build‐up‐type development of the yield. It is found that a lower alkylaluminum concentration leads to a lower activity in the linear regime, whereas the extent of the activation becomes greater in the build‐up regime. The origin of these kinetic behaviors is studied using scanning electron microscopy (SEM) for catalyst/polymer particles and cross‐fractionation analyses for polymer structures. It is found that the kinetic transition mainly arises from the fragmentation of the catalyst particles and resultant increase in the active site concentration. The fragmentation manner strongly depends on the alkylaluminum concentration, which affects not only the amount, but also the placement of initial polymer formation. The nature of the active sites varies as a result of an aging effect with alkylaluminum: their stereospecificity, propagation rate constant, and tolerance for chain transfer reaction increase as the polymerization progresses. image

Kinetic Analysis of the Immortal Ring-Opening Polymerization of Cyclic Esters: A Case Study with Tin(II) Catalysts

A kinetic analysis of the metal-catalyzed immortal ring-opening polymerization (ROP) of cyclic esters is presented, based on a first-principles approach without making assumptions regarding the active species. The kinetics of all immortal ROP reactions performed with a metal catalyst and an exogenous chain transfer agent are characterized by the initiation, propagation and exchange rate constants (ki, kp, and ke, respectively). Curve fitting to this kinetic scheme in the initial stage of the polymerization allows the extraction of ki and kp from a single experiment. This has been illustrated for the ROP of l-lactide using tin(II) complexes of the type {LOi}Sn(X) ({LOi} = aminophenolate ancillary ligand, X = N(SiMe3)2 or methyl (S,S)-lactate), Sn(OiPr)2 or Sn(N(SiMe3)2)2 as precatalysts paired with excess iPrOH as a coactivator. Nonlinear regressions (R2 > 0.999) illustrate the three possible scenarios, ki < kp, ki = kp, and ki > kp. The kinetic model can be extended to any metal (pre)catalyst for the immortal ROP of any cyclic ester, as exemplified using trimethylene carbonate as a monomer or employing a germylene precatalyst. A kinetic treatment for the late phase of immortal ROP reactions is introduced, which also gives direct access to kp. In agreement with the ROP kinetic data for {LOi}Sn(N(SiMe3)2), Sn(OiPr)2, Sn(N(SiMe3)2)2, and the new Sn(OiPr)(N(SiMe3)2 recorded in the presence of various quantities of iPrOH, synthetic and 119Sn{1H} NMR data provide evidence for reversible production of tin(II) bis(alkoxide) when a small excess (1–3 equiv) of alcohol is used with tin(II) precatalysts. It is also shown that, regardless of the identity of the precatalyst, Sn(OiPr)2 and Sn(O-polymeryl)2 are, respectively, the actual initiating and propagating species when immortal ROP reactions are performed in the presence of a larger excess of alcohol (7 equiv or more vs Sn).

Vinyl acetate living radical polymerization mediated by cobalt porphyrins: kinetic–mechanistic studies

Radical polymerization of vinyl acetate (VAc) in the presence of cobalt(II) tetramesitylporphyrin, CoII(TMP), as a mediator was performed in a series of solvent environments. Cobalt porphyrin was observed to mediate an effective living radical polymerization reaction of vinyl acetate in bulk as shown by the linear increase in molecular weight with conversion, relatively narrow molecular weight distributions (Mw/Mn = 1.24–1.34), and molecular weights close to the theoretical value up to moderately high monomer conversions (∼70%). The levels of deviation for the observed PVAc molecular weights from the theoretical values varied with the choice of solvent medium, which suggests that the control of vinyl acetate radical polymerization was affected by chain transfer to the solvent. Non-coordinating solvents influence the polymerization rate primarily by different propagation rate constants (kp). Pyridine coordination with dormant organo-cobalt(III) increases the dissociation constant and changes the dominant polymerization process from degenerative transfer to reversible termination.

Solvent effect on the kinetics of the free-radical polymerization of styrene in the presence of fullerene C60

The induction period in the kinetic curves of styrene polymerization in the presence of fullerene C60 was found to increase significantly at a solvent (benzene, toluene, ortho-dichlorobenzene, CCl4) concentration of ≥50 mol %. The free-radical polymerization rates of styrene in the presence of fullerene C60 and solvents, the ratio of chain propagation and termination rate constants kp/k01/2, and the stoichiometric inhibition coefficient were determined.

Solvent effects on free-radical copolymerization of styrene and 2-hydroxyethyl methacrylate: a DFT study

The free-radical homopolymerization and copolymerization kinetics of styrene (ST) and 2-hydroxyethyl methacrylate (HEMA) in three different media (bulk, DMF, toluene) have been investigated by means of Density Functional Theory (DFT) calculations in combination with the Polarizable Continuum Model (PCM) and the Conductor-like Screening Model for Real Solvents (COSMO-RS). The conventional Transition State Theory (TST) is applied to calculate the rate parameters of polymerization. Calculated propagation rate constants are used to predict the monomer reactivity ratios, which are then used in the evaluation of the copolymer composition following the Mayo–Lewis equation. It is found that copolymerization reactions in bulk and toluene show similar transition geometries; whereas, DMF has a tendency to form H-bonding interactions with the polar HEMA molecules, thus decreasing the reactivity of this monomer during homopolymerization and towards ST during copolymerization. Calculations of copolymer composition further show that the amount of HEMA monomer in the ST–HEMA copolymer system decreases in the polar DMF solution. The calculated spin densities of the radical species are in agreement with the rate parameters and confirm that the copolymerization propagation rate of the ST–HEMA system is in the order: kp(bulk) ≈ kp(toluene) > kp(DMF).

EFFECTS OF HYDROGEN ON ACTIVE CENTERS IN PROPYLENE POLYMERIZATION WITH SUPPORTED ZIEGLER-NATTA CATALYST

The kinetics of propylene polymerization with a TiCl4/ Di / MgCl2( Di = internal donor) supported Ziegler-Natta catalyst was studied by measuring the number of active centers using 2-thiophenecarbonyl chloride as quenching agent. Influences of hydrogen and alkoxysilane type external donors on the number of active centers and chain propagation rate constant( k p) were investigated. The number and k p value of three groups of active centers that produce atactic,medium-isotactic and isotactic polypropylene( PP) fractions were determined. The catalyst activity was found to significantly increase with the addition of hydrogen,which was a result of simultaneous increases in the number of active centers and k p value. The three groups of active centers response to hydrogen differently. Hydrogen caused lower degree of increase in the number of active centers that produce atactic PP than the other two groups of active centers,and caused the highest degree of increase in the k p value of active centers that produce medium-isotactic PP. The hydrogen response of the active centers was also influenced by external donor. Increasing the bulkiness of alkyl groups in alkoxysilane donors leads to decreased hydrogen sensitivity,meanwhile the stereo- and regio-selectivities were evidently improved,implying that there are close relations between the hydrogen effect and the stereo-and regio-selectivities of the catalyst.A mechanistic model was proposed to explain the hydrogen effect.

Supported Ziegler–Natta catalyst for ethylene polymerization: Novel data on the effect of polymerization temperature on the number of active centers and propagation rate constant

The number of active centers at ethylene polymerization over highly active supported catalyst TiCl4/MgCl2+AlEt3 was determined at various polymerization temperatures. It was found that the increase in polymerization temperature in the range of 40–80°C increases the number of active centers. The data on reversible changes in the polymerization rate with temperature in a single experiment give grounds for supposing that alteration of the number of active centers with temperature is a reversible process. The propagation rate constants and the activation energy of the propagation reaction (4.0kcalmol−1) were calculated; the latter value being considerably lower than the effective activation energy of polymerization (16.5kcalmol−1) due to the increase in CP with rising temperature.

Modification effect of spherical zirconia with SiCl4 as a support of methylaluminoxane for heterogeneous single-site catalyst

Unmodified and SiCl4-modified spherical zirconia-supported methylaluminoxane were used as cocatalyst for propylene polymerization as well as ethylene/1-hexene copolymerization in combined with Me2Si(η3-C13H8)(η1-NtBu)TiMe2 (1) at 0°C. The modification with SiCl4 improved the catalytic activity. The improvement was clearer in ethylene/1-hexene copolymerization than in propylene polymerization. The number average molecular weight (Mn) of polypropylenes increased linearly against the polymerization time regardless the cocatalyst used to give polymers with narrow molecular weight distribution (Mw/Mn<1.32), indicating the living nature of the catalytic systems. Thus, propagation rate constant (kp) and the number of active centers (C*) were evaluated from Mn and the number of polymer-chains. When the zirconia was modified with SiCl4, the kp value decreased and the C* increased. The latter effect was more significant to enhance the catalytic activity.

Synthesis and Polymerization Kinetics of PMMA in [BMIM]BF&lt;sub&gt;6&lt;/sub&gt; Imidazolium Ionic Liquids

Polymerization of high molecular weight PMMA was achieved in [BMIPF6 by contrasted in cyclohexane, toluene solvent at reaction temperature 60 C, 65C and 70 C, reaction time 60min. The data including the yield, molecular weight and molecular weight distribution of PMMA were analysized in 3 kind of solvent. The results showed that the weight average molecular weight of PMMA in [BMIPF6 is up to 730000, respectively 7 and 10 times of molecular weight in cyclohexane and toluene. Secondly, the polymerization kinetics of PMMA in [BMIPF6 were tested, the apparent chain propagation rate constant of PMMA are 10.7×10412.9 ×104 and 19.9×104 in 60 C, 65C and 70 C. Compared with the growth rate constant in toluene, the polymerization rate constant PMMA in the ionic liquid increased by 5~10 times.

Synthesis and Polymerization Kinetics of PMMA in Imidazolium Ionic Liquids

Polymerization of high molecular weight PMMA was achieved in [BMIM]PF4at reaction temperature 60oC, 65°C and 70 °C, reaction time 60min. The data including the yield, molecular weight and molecular weight distribution of PMMA were analysized. The results showed that the weight average molecular weight of PMMA in [BMIM]PF4is up to 275867, respectively 4 and 7 times of molecular weight in cyclohexane and toluene. Secondly, the polymerization kinetics of PMMA in [BMIM]PF4were tested, the apparent chain propagation rate constant of PMMA are 0.93×104,1.11 ×104and 14.1×104in 60 °C, 65°C and 70 °C. Compared with the growth rate constant in toluene, the polymerization rate constant PMMA in the ionic liquid increased by 4~7 times.