Average termination rate coefficients in emulsion polymerization: Effect of compartmentalization on free‐radical lifetimes

A method is presented by which the time‐dependent average termination rate coefficient in an emulsion polymerization may be calculated as an appropriate average of the chain‐length‐dependent termination rate coefficients. The method takes advantage of the fact that the overall termination rate is dominated by terminations between rapidly moving short radicals and much slower long ones. This termination rate coefficient is suitable for use in the Smith–Ewart equations describing the compartmentalization of radicals in an emulsion polymerization. Rate data in emulsion polymerizations can be quantitatively interpreted if the kinetics fall into one of two categories: zero–one (showing compartmentalization; intraparticle termination is not rate‐determining) or pseudo‐bulk (no compartmentalization; intraparticle termination is rate‐determining). The new method can be used to interpret rate data for systems falling between these categories and also can be used to find termination rate coefficients from Monte Carlo simulations of termination kinetics. The latter is especially useful for predicting and understanding kinetics in controlled radical polymerizations in disperse media. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1076–1089, 2005     

The Influence of Chain Length‐Dependent Propagation on the Evaluation of the Chain Length Dependence of the Rate Coefficient of Bimolecular Termination, 1. PLP–SEC Methods

Chain length distributions have been calculated for polymers prepared by pulsed laser polymerization (PLP) under the condition that not only chain termination but also chain propagation is subject to chain length dependence. The interplay between these two features is analyzed with the chain length dependence of the rate coefficient of termination k_t introduced in the form of a power law and that of propagation k_p modeled by a Langmuir‐type decrease from an initial value for zero chain length to a constant value for infinite chain lengths. The rather complex situation is governed by two important factors: the first is the extent of the decay of radical concentration [R] during one period under pseudostationary conditions, while the second is that termination events are governed by [R]² while the propagation goes directly with [R]. As a consequence there is no general recommendation possible as to which experimental value of k_p is best taken as a substitute for the correct average of k_p characterizing a specific experiment. The second point, however, is apparently responsible for the pleasant effect that the methods used so far for the determination of k_t and its chain length dependence (i.e., plotting some average of k_t versus the mean chain‐length of terminating radicals on a double‐logarithmic scale) are only subtly wrong with regard to a realistic chain length dependence. This is especially so for the quantity k_t* (the average rate coefficient of termination derived from the rate of polymerization in a PLP system) and its chain length dependence.     

Determination of the cumulative degree of polymerization for the dead‐end polymerization of styrene

This article explores the use of a new relation correcting theoretical (DPn ) with experimental values obtained in the dead‐end polymerization of styrene with azocompound. The syntheses were realized for several starting initiator‐to‐monomer ratios (C₀'s); values comprised between 10 and 0.1%, and the experimental (DPn ) were obtained by size exclusion chromatography. Concerning the theoretical (DPn ), a new relation is proposed considering the loss of initiating radicals [I · ] used in primary termination and both stationary states of I · and M · (macromolecular radicals) introduced as Bamford. Finally, (DPn )_cum, previously defined by us, is introduced to consider the monomer conversion during oligomerization. Our relation fit very well in a large range of C₀'s, contrary to the application of the usual Mayo rule, and a discussion of validity is proposed. Our model also allows the prediction of (DPn )_cum in a large range of telechelic oligomers from 10 to 150. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 236–247, 2003     

Chain-length dependent termination in pulsed-laser polymerization, 5. The evaluation of the rate coefficient of bimolecular termination kt for the reference system styrene in bulk at 25°C

Following earlier suggestions the values for the rate coefficient of chain termination k_t in the bulk polymerization of styrene at 25°C were formally calculated (a) from the second moment of the chainlength distribution (CLD) and (b) from the rate equation for laser-initiated pseudostationary polymerization (both expressions originally derived for chain-length independent termination) by inserting the appropriate experimental data including the rate constant of chain propagation k_p. These values were treated as average values, k and k , respectively. They exhibited good mutual agreement, even the predicted gradation (k < k by about 20%) was recovered. The log-log plot of k_t vs. the number-average degree of polymerization of the chains at the moment of their termination yielded exponents b of 0.16–0.18 in the power-law k_t = A · P_n ^−b, A ranging from 2.3 × 10⁸ to 2.7 × 10⁸ L · mol⁻¹ · s⁻¹. These data are only slightly affected if termination is not assumed to occur by recombination only and a small contribution of disproportionation is allowed for.     

Catalytic‐chain‐transfer polymerization of styrene revisited: The importance of monomer purification and polymerization conditions

The cobaloxime‐mediated catalytic‐chain‐transfer polymerization of styrene at 60 °C was studied with an emphasis on the effects of monomer purification and polymerization conditions. Commonly used purification methods, such as column chromatography and simple vacuum distillation, were not adequate for obtaining kinetic data to be used in mechanistic modeling. A purification regime involving inhibitor removal with basic alumina, followed by polymerization of the styrene in the presence of the cobaloxime and subsequent vacuum distillation, was found to be essential to this end. It was then possible to quantitatively investigate effects such as the initiator concentration and conversion dependencies of the apparent chain‐transfer constant that resulted from the occurrence of cobalt–carbon bond formation. A value of about 9 × 10³ was found for the true chain‐transfer constant to cobaloxime boron fluoride, that is, its value in the absence of cobalt–carbon bond formation. Furthermore, previous predictions were confirmed: the measured chain‐transfer constant decreased with increasing initiator concentration and conversion. Finally, it was confirmed that the presence of light increased the amount of free Co(II) catalyst in agreement with other studies. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 752–765, 2003     

Kinetics of the microemulsion polymerization of styrene with short‐chain alcohols as the cosurfactant

The kinetics of styrene microemulsion polymerization stabilized by sodium dodecyl sulfate (SDS) and a series of short‐chain alcohols (n‐C_iH_2i+1OH, abbreviated as C_iOH, where i = 4, 5, or 6) at 60 °C was investigated. Sodium persulfate was used as the initiator. The microemulsion polymerization process can be divided into two intervals: the polymerization rate (R_p) first increases to a maximum at about a 20% conversion (interval I) and thereafter continues to decrease toward the end of the polymerization (interval II). For all the SDS/C_iOH‐stabilized polymerization systems, R_p increases when the initiator or monomer concentration increases. The average number of free radicals per particle is smaller than 0.5. The molecular weight of the polymer produced is primarily controlled by the chain‐transfer reaction. In general, the reaction kinetics for the polymerization system with C₄OH as the cosurfactant behaves quite differently from the kinetics of the C₅OH and C₆OH counterparts. This is closely related to the different water solubilities of these short‐chain alcohols and the different concentrations of the cosurfactants used in the preparation of the microemulsion. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 898–912, 2001     

Fluorescent probes for monitoring the pulsed‐laser‐induced photocuring of poly(urethane acrylate)‐based adhesives

Fluorescence spectroscopy was used to study the kinetics of polymerization of acrylic adhesive formulations exposed to a 355‐nm pulsed emission from an Nd‐YAG laser. Nine fluorescent probes were used for monitoring the laser curing, showing different sensitivities. In general, the fluorescence intensity emission increased as crosslinking occurred. In addition, solvatochromic fluorescent probes showed a blueshift in their emission. A relative method was applied for the evaluation of the polymerization rates in three different acrylic systems. Special features of pulsed‐laser‐induced polymerization were treated in detail, such as the influence of the laser pulse frequency and the incident laser beam intensity. The polymerization rate slowed down as the pulse repetition rate decreased. An inhibition period due to oxygen quenching was observed, and it was highly dependent on the laser repetition rate and the nature of the photoinitiator. The effect of the laser beam intensity on the kinetics of such fast reactions was studied. In general, increasing the laser energy improved the rate of polymerization. The degree of cure improved as the polymerization rate increased as a result of faster crosslinking, rather than relaxation volume kinetics. Moreover, a saturation rate effect occurred that depended on the photoinitiator. The different behaviors of the two photoinitiators in the curing of the same acrylic formulation was explained on the basis of primary radical termination. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1227–1238, 2004     

Pulsed‐laser polymerization‐gel permeation chromatographic determination of the propagation‐rate coefficient for the methyl acrylate dimer: A sterically hindered monomer

The methyl acrylate dimer (MAD) is a sterically hindered macromonomer, and the propagating radical can fragment to an unsaturated end group. The propagation‐rate coefficient (k_p) for MAD was obtained by pulsed‐laser polymerization (PLP). The Mark–Houwink–Sakaruda parameters required for the analysis of the molecular weight distributions (MWDs) were obtained by multiple‐detector gel permeation chromatography (GPC) with on‐line viscometry. The small radical created by the fragmentation results in a short‐chain polymer that means the MWD may no longer be given by that expected for “ideal” PLP conditions; simulations suggest that the degree of polymerization required for “ideal” PLP conditions can be obtained from the primary point of inflection provided the GPC traces also show a clear secondary inflection point (radicals terminated by the second, rather than the first, pulse subsequent to initiation). Over the temperature range of 40–75 °C, the data can be best fitted by k_p/dm³ mol^?1 s^?1 = 10^6.1 exp(?29.5 kJ mol^?1), with a moderately large joint confidence interval for the Arrhenius parameters. The data are consistent with an increased activation energy and reduced frequency factor as compared with acrylate or methacrylate; both of these changes can be ascribed to hindrance. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3902–3915, 2001     

The syndiospecific polymerization of styrene in the presence of fluorine‐containing half‐sandwich metallocenes

The syndiospecific polymerization of styrene was investigated with the fluorine‐containing half‐sandwich complexes η⁵‐pentamethylcyclopentadienyl titanium bis(trifluoroacetate) dimer, η⁵‐octahydrofluorenyl titanium tristrifluoro‐acetate, η⁵‐octahydrofluorenyl titanium dimethoxymonotrifluoroacetate, and η⁵‐octahydrofluorenyl titanium tris(pentafluorobenzoate) in comparison to known chloride and methoxide complexes in the presence of relatively low amounts of methylalumoxane and triisobutylaluminum. After the selection of effective reaction conditions for a solvent‐free polymerization, the following orders of decreasing polymerization activity of the titanium complexes can be observed: for pentamethylcyclopentadienyl compounds, Cp*Ti(OMe)₃ > [Cp*Ti(OCOCF₃)₂]₂O ≈ Cp*TiCl₃, and for octahydrofluorenyl compounds, [656]Ti(OMe)₃ > [656]Ti(OCOC₆F₅)₃ > [656]Ti(OCH₃)₂(OCOCF₃) > [656]Ti (OCOCF₃)₃. The [656]Ti complexes, showing the highest polymerization conversions at 70 °C and in comparison with the Cp* Ti compounds, turned out to be highly efficient catalysts for the syndiospecific styrene polymerization. The fluorine‐containing Cp* and [656]Ti complexes lead to much higher molecular weights than the chloride and methoxide compounds because of a reduction in chain‐limiting transfer reactions. The introduction of only one fluorine‐containing ligand into the coordination sphere of the metal compound is obviously sufficient for a significant increase in molecular weight. The active polymerization sites of the [656]Ti complexes with methylalumoxane and triisobutylaluminum are extremely stable during storage at room temperature in regard to their polymerization activity. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2428–2439, 2000     

Chain-length dependent termination in pulsed-laser polymerization, 6. The evaluation of the rate coefficient of bimolecular termination kt for the reference system methyl methacrylate in bulk at 25°C

The values for the rate coefficient of chain termination k_t in the bulk polymerization of methyl methacrylate at 25°C were formally calculated (i) from the second moment of the chain-length distribution and (ii) from the rate equation for laser-initiated pseudostationary polymerization (both expressions were originally derived for chain-length independent termination) by inserting the appropriate experimental data including the rate constant of chain propagation k_p. These values were treated as average values, k and k , respectively. They exhibited good mutual agreement, even the predicted gradation (k < k by about 20%) was recovered. The log-log plot of k_t vs. the average degree of polymerization of the chains at the moment of their termination v′ yielded exponents b of 0.16–0.17 in the power-law k _t = A · v′^−b, A ranging from 1.1 × 10⁸ to 1.3 × 10⁸ (L · mol⁻¹ · s⁻¹). A 70% contribution of disproportionation to overall termination has been assumed in the calculations.     

Mechanism and kinetics of dithiobenzoate‐mediated RAFT polymerization. I. The current situation

Investigations into the kinetics and mechanism of dithiobenzoate‐mediated Reversible Addition–Fragmentation Chain Transfer (RAFT) polymerizations, which exhibit nonideal kinetic behavior, such as induction periods and rate retardation, are comprehensively reviewed. The appreciable uncertainty in the rate coefficients associated with the RAFT equilibrium is discussed and methods for obtaining RAFT‐specific rate coefficients are detailed. In addition, mechanistic studies are presented, which target the elucidation of the fundamental cause of rate retarding effects. The experimental and theoretical data existing in the literature are critically evaluated and apparent discrepancies between the results of different studies into the kinetics of RAFT polymerizations are discussed. Finally, recommendations for further work are given. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5809–5831, 2006     

The nature of the chain-length dependence of the propagation rate coefficient and its effect on the kinetics of free-radical polymerization. 1. Small-molecule studies

In this paper we summarize and analyze the currently available small-molecule data, both experimental and theoretical, that is relevant to chain-length-dependent propagation in free-radical polymerization (FRP). We do this in order to appreciate the nature of chain-length-dependent propagation, because workers are becoming increasingly cognizant of its necessity in reaching a complete understanding of FRP kinetics. We show that studies of addition in small-molecule (model) systems support a chain-length dependence (at short chain lengths i) which is described by the following functional form, which therefore can be said to be physically realistic: , where the values of C₁ and i_1/2 are of the order of 10 and 1, respectively. These results are supported by transition state theory, which predicts a very similar behavior for the Arrhenius frequency factor. We illustrate that in systems with low number-average degree of polymerization (DP_n), this chain-length dependence can dramatically affect the observed (chain-length-averaged) propagation rate coefficient 〈k_p〉, which can be significantly higher than the long chain value, k_p. However, this effect is only observed if the activation energy for the first radical addition is similar to that for propagation. In the case that the former is significantly higher (e.g., when choosing a less than optimal initiator or in the case of retardative chain transfer), the chain-length-dependent propagation predicted by our model will not be observed, and in fact a significant lowering of 〈k_p〉 can in cases be expected up to relatively high DP_n.     

Laser Single Pulse Initiated RAFT Polymerization for Assessing Chain‐Length Dependent Radical Termination Kinetics

Summary: A novel method combining RAFT polymerization with pulsed‐laser initiation for determining chain‐length dependent termination rate coefficients, k_t, is presented. Degenerative chain‐transfer in RAFT enables single‐pulse pulsed‐laser polymerization (SP‐PLP) traces to be measured on systems with a narrow radical distribution that remains essentially unchanged during the experiment. SP‐PLP‐RAFT experiments at different polymerization times allow for determining k_t as a function of chain length via classical kinetics assuming chain‐length independent k_t.

Single‐pulse pulsed‐laser polymerization trace for BMPT‐mediated RAFT polymerization of butyl acrylate.     

Controlled radical polymerization of styrene in the presence of cyclic 1,2‐disulfides

The thermal polymerization of styrene (St) in the presence of cyclic 1,2‐disulfides at 120 °C was investigated. In the polymerization of St in the presence of 1,2‐dithiane (DT), that is, six‐member cyclic 1,2‐disulfide, the polymer yields and molecular weights increased with the reaction time. The linear relation between the polymer yields and molecular weights was observed, and the line passed through an original point. The molecular weight distributions of the polymers remained almost constant but were not narrow. For this polymerization with a living nature, we proposed the following mechanism: the propagating St radical reacted with thiyl radicals derived from DT, leading to the formation of dormant species, and the formed C S bond of the dormant was dissociated again to give the propagating polystyryl radical and thiyl radical. Similar results were obtained in the thermal polymerization of St at 120 °C in the presence of 1,2‐dithiacycloheptane, that is, seven‐member cyclic 1,2‐disulfide. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 145–151, 2001     

Atom transfer radical polymerization of styrene using the novel initiator ethyl 2‐N,N‐(diethylamino)dithiocarbamoyl‐butyrate

The atom transfer radical polymerizations (ATRPs) of styrene initiated by a novel initiator, ethyl 2‐N,N‐(diethylamino)dithiocarbamoyl‐butyrate (EDDCB), in both bulk and solution were successfully carried out in the presence of copper(I) bromide (CuBr) and N,N,N′,N″,N″‐pentamethyldiethylenetriamine at 115 °C. The polymerization rate was first‐order with respect to the monomer concentration, and the molecular weights of the obtained polymers increased linearly with the monomer conversions with very narrow molecular weight distributions (as low as 1.17) up to higher conversions in both bulk and solution. The polymerization rate was influenced by various solvents in different degrees in the order of cyclohexanone > dimethylformamide > toluene. The molecular weight distributions of the produced polymers in cyclohexanone were higher than those in dimethylformamide and toluene. The results of ¹H NMR analysis and chain extension confirmed that well‐defined polystyrene bearing a photo‐labile N,N‐(diethylamino)dithiocarbamoyl group was obtained via ATRP of styrene with EDDCB as an initiator. The polymerization mechanism for this novel initiation system is a common ATRP process. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 32–41, 2006     

Single‐pulse pulsed laser polymerization–electron paramagnetic resonance investigations into the termination kinetics of n‐butyl acrylate macromonomers

The termination of model mid‐chain radicals (MCRs), which mimic radicals that occur in acrylate polymerization over a broad range of reaction conditions, has been studied by single‐pulse pulsed laser polymerization (SP‐PLP) in conjunction with electron paramagnetic resonance spectroscopy. The model radicals were generated by initiator‐fragment addition to acrylic macromonomers that were preformed prior to the kinetic experiments, thus enabling separation of termination from the propagation reaction, for these model radicals propagate sparingly, if at all, on the timescale of SP‐PLP experiments. Termination rate coefficients of the MCRs were determined in the temperature range of 0–60°C in acetonitrile and butyl propionate solution as well as in bulk macromonomer over the range of 0–100 °C. Termination rate coefficients slightly below those of the corresponding secondary radicals were deduced, demonstrating the relatively high termination activity of this species, even when undergoing MCR–MCR termination. For chain length of 10, a reduction by a factor of 6 is observed. Unusually high activation energies were found for the termination rate coefficient in these systems, with 35 kJ mol^?1 being determined for bulk macromonomer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Addition‐Fragmentation Chain Transfer Involving Dimers of α‐Methylvinyl Monomers Studied by ESR Spectroscopy: Competition between Fragmentation and Bimolecular Termination

Detection of the adduct radical by ESR spectroscopy and after‐effect ESR measurements of the adduct radical concentrations in the photosensitized polymerization of styrene (St) in the presence of dimers of α‐methylstyrene (MSD) and methyl methacrylate have revealed that the dominant mechanism of adduct radical loss changes from bimolecular termination to fragmentation as the temperature is increased beyond 90 °C for St/MSD.

     

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     

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