Dark‐cure studies of cationic photopolymerizations of epoxides: Characterization of the active center lifetime and kinetic rate constants

We have characterized the effective rate constants for termination/trapping (k_t/t) and propagation (k_p) for solvent‐free cationic photopolymerizations of phenyl glycidyl ether for conversions up to 50%. We have performed dark‐cure experiments in which active centers are produced photochemically for a specified period of time until the initiating light is shuttered off, and then the polymerization rate is monitored in the dark. This method is especially well suited for characterizing cationic polymerizations because of the long active center lifetimes. Our analysis provides profiles of the instantaneous kinetic rate constants as functions of conversion (or time). For photopolymerizations of phenyl glycidyl ether initiated with iodonium photoinitiators, k_t/t and k_p remain essentially invariant for conversions up to 50%. For the photoinitiator (tolycumyl) iodonium tetrakis (pentafluorophenyl) borate (IPB), the values of k_t/t at 50 and 60 °C are 0.027 and 0.033 min^?1, respectively. The corresponding values of k_t/t for diaryliodonium hexafluoroantimonate (IHA) are 0.041 and 0.068 min^?1. The values of k_p at 50 °C for IPB and IHA are 0.6 and 0.4 L mol^?1 s^?1, respectively. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2064–2072, 2003     

Variations of Rate Coefficients and Termination Mechanism During the After‐Effects of a Light‐ Induced Polymerization of a Dimethacrylate Monomer

This work was aimed at studying variations in the termination mechanism occurring during the after‐effects of a light‐induced polymerization of a dimethacrylate monomer after the irradiation had been discontinued. The experimental method was based on differential scanning calorimetry. The initiation was stopped at various moments of the reaction corresponding to different degrees of double‐bond conversion (starting conversions). Three termination models: monomolecular, bimolecular, and mixed were used to calculate the ratio of the bimolecular termination and propagation rate coefficients k_t^b/k_p and/or the monomolecular termination rate coefficient k_t^m. The models were determined over short time intervals (conversion increments) of the dark reaction giving different values of rate coefficients for each time interval (interval approximation method). Two‐stage statistical analysis was used to find the model that best reproduced the experimental data obtained for each conversion increment. This enabled variations in the termination mechanism during the after‐effects to be followed. It was found that the termination mechanism changed with the time of the dark reaction from the bimolecular reaction to the mixed reaction when the light was cut off at low and medium double‐bond conversions. At higher starting conversions a monomolecular termination mechanism dominated from the beginning of the dark reaction. The mixed termination model was the only model to describe correctly the variations of rate coefficients in the dark, i. e., the increase in k_t^m and the decreasein the k_t^b/k_p ratio.     

Estimation of molecular weight distribution based on chain length dependence of termination rate

When a chain length dependence of polymer-polymer termination is given by k_t,ns = const. (n^?2a + s^?2a) where n and s are the chain lengths for the polymer radicals and a is parameter, an instantaneous weight fraction of the non-reacting polymers is derived as: where h and k? are the kinetic parameters, p is a parameter depending on a, and p_n is instantaneous number-average chain length. Such a weight fraction corresponds to the experimental one over a wide range of conversion in the polymerization of styrene. On the scope of this correspondence, the polymer-polymer termination rate is estimated as: k?_t = 8πR₀D₁/100 ( = 4πR_sD_s) where R₀ is reaction radius between monomer radicals and D₁ is the diffusion coefficient of the monomer; R_s is reaction radius between segment radicals with n ? 100 and D_s is the diffusion coefficient of the segment. The Fujita-Doolittle theory applies to such a rate. Further, the rate also yields 1.5 × 10⁷1./mole-sec, which is the observable extent at conversions less than 0.2.     

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.     

Dark cure studies of cationic photopolymerizations of epoxides: Characterization of kinetic rate constants at high conversions

The effective propagation rate constant (k_p; averaged over all the propagating active centers) was characterized for solvent‐free cationic photopolymerizations of phenyl glycidyl ether over the entire range of conversions, including the high conversion regime in which mass transfer limitations become important. The profile for the k_p as a function of conversion was found to exhibit a constant plateau value at low to intermediate conversions, followed by a monotonic increase above a threshold value of conversion. To explain this trend, it is proposed that at high conversion the diffusional mobility of the photoinitiator counterion is reduced whereas the mobility of the cationic active center remains high because of reactive diffusion. Therefore, with increasing conversion, the average distance between the active centers and counterions may increase, resulting in an increase in the propagation rate constant. The profiles for the k_p values were investigated as a function of the temperature, photoinitiator anion, and photoinitiator concentration. As the photoinitiator concentration was increased, the plateau value of the effective propagation rate constant decreased whereas the threshold conversion increased. All of the experimental trends are consistent with the proposed increase in ion separation at high conversions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4409–4416, 2004     

Photoinitiated polymerization of methacrylic monomers in a polybutadiene matrix (PB): Kinetic,mechanistic, and structural aspects

The kinetics and mechanism of the photoinitiated polymerization of tetrafunctional and difunctional methacrylic monomers [1,6‐hexanediol dimethacylate (HDDMA) and 2‐ethylhexyl methacrylate (EHMA)] in a polybutadiene matrix (PB) have been studied. The maximum double‐bond conversion, the maximum polymerization rate, the intrinsic reactivity, and the kinetic constants for propagation and termination have been calculated. Unlike the behavior followed by the SBS‐HDDMA and PS‐HDDMA systems, where a reaction‐diffusion mechanism occurs from the start of the polymerization at low monomer concentrations (<30–40%), in the PB‐HDDMA system the reaction diffusion controls the termination process only after approximately 10% conversion is reached, as for the bulk polymerization of polyfunctional methacrylic monomers. Before reaching 10% conversion the behavior observed can be better explained by a combination of segmental diffusion‐controlled (autoaccelerated) and reaction‐diffusion mechanisms. This is probably a consequence of the lower force of attraction between the monomer and the matrix and between the growing macroradical and the matrix than those corresponding to the other systems mentioned. For the PB‐EHMA system, the termination mechanism is principally diffusion‐controlled from the beginning of the polymerization for monomer concentrations below 30–40%, and for higher monomer concentrations, a standard termination mechanism takes place (k_t ≈ 10⁶) at low double‐bond conversions, which is diffusion‐controlled for high conversions (>40%). For PB‐HDDMA and PB‐EHMA systems, crosslinked polymerized products are obtained as a result of the participation of the double bonds of the matrix in the polymerization process. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2444–2453, 2001     

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     

Free‐Radical Termination Kinetics Studied Using a Novel SP‐PLP‐ESR Technique

Summary: A novel method for measuring termination rate coefficients, k_t, in free‐radical polymerization is presented. A single laser pulse is used to instantaneously produce photoinitiator‐derived radicals. During subsequent polymerization, radical concentration is monitored by time‐resolved electron spin resonance (ESR) spectroscopy. The size of the free radicals, which exhibits a narrow distribution increases linearly with time t, which allows the chain‐length dependence of k_t to be deduced. The method will be illustrated using dodecyl methacrylate polymerization as an example.

Two straight lines provide a very satisfactory representation of the chain‐length dependence of k_t over the entire chain‐length region (c_R = radical concentration).     

Initiator efficiency of 2,2′‐azobis(isobutyronitrile) in bulk dodecyl acrylate free‐radical polymerizations over a wide conversion and molecular weight range

An Erratum has been published for this article in J. Polym. Sci. Part A: Polym. Chem. (2004) 42(21) 5559 . The initiator efficiency, f, of 2,2′‐azobis(isobutyronitrile) (AIBN) in dodecyl acrylate (DA) bulk free‐radical polymerizations has been determined over a wide range of monomer conversion in high‐molecular‐weight regimes (M_n ? 10⁶ g mol^?1 [? 4160 units of DA)] with time‐dependent conversion data obtained via online Fourier transform near infrared spectroscopy (FTNIR) at 60 °C. In addition, the required initiator decomposition rate coefficient, k_d, was determined via online UV spectrometry and was found to be 8.4 · 10^?6 s^?1 (±0.5 · 10^?6 s^?1) in dodecane, n‐butyl acetate, and n‐dodecyl acetate at 60 °C. The initiator efficiency at low monomer conversions is relatively low (f = 0.13) and decreases with increasing monomer to polymer conversions. The evolution of f with monomer conversion (in high‐molecular‐weight regimes), x, at 60 °C can be summarized by the following functionality: f^{60 °C} (x) = 0.13–0.22 · x + 0.25 · x² (for x ≤ 0.45). The reported efficiency data are believed to have an error of >50%. The ratio of the initiator efficiency and the average termination rate coefficient, 〈k_t±, (f/〈k_t〉) has been determined at various molecular weights for the generated polydodecyl acrylate (M_n = 1900 g mol^?1 (? 8 units of DA) up to M_n = 36,500 g mol^?1 (? 152 units of DA). The (f/〈k_t〉) data may be indicative of a chain length‐dependent termination rate coefficient decreasing with (average) chain length. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5170–5179, 2004     

Relationship between chain termination rate constant and conversion in radical polymerization

At low and high conversions, the chain termination rate constant for bimolecular termination between polymeric radicals given by k_t = A_tD_s, where A_t is a constant and D_s is the diffusion constant of radical chain end, is completely correct. This termination rate constant does not depend on solution viscosity, but conversion.     

Kinetics of Bulk Free‐Radical Polymerization of Butyl Methacrylate Isomers Studied by Reaction Calorimetry

The kinetics of bulk free‐radical polymerizations of n‐butyl methacrylate (n‐BMA), iso‐butyl methacrylate (i‐BMA), and tert‐butyl methacrylate (t‐BMA) are studied by differential scanning calorimetry and with the aid of a mathematical model previously reported by the authors. In all the cases, the rate of polymerization (R_p) evolution curve exhibits a minimum at low conversions and the characteristic maximum of the autoacceleration effect. It is found that the monomer conversion x_min at which the minimum is observed, follows the order n‐BMA > i‐BMA > t‐BMA and that for monomer conversions (x) smaller than x_min, the termination rate coefficient (k_t) shows a plateau. According to the model results it is obtained that for x > x_min, the termination reaction is chemically controlled whereas for x > x_min, it is diffusion‐controlled and that the x_min values are related to the value of the termination rate coefficient of the chemical step (k_t0) of every isomer, which is highly influenced by the steric hindrance of the alkyl substituent group.     

Degradative chain transfer in vinyl acetate polymerizations using toluene as solvent

In this work, we propose that retardation in vinyl acetate polymerization rate in the presence of toluene is due to degradative chain transfer. The transfer constant to toluene (C_trs) determined using the Mayo method is equal to 3.8 × 10^?3, which is remarkably similar to the value calculated from the rate data, assuming degradative chain transfer (2.7 × 10^?3). Simulations, including chain‐length‐dependent termination, were carried out to compare our degradative chain transfer model with experimental results. The conversion–time profiles showed excellent agreement between experiment and simulation. Good agreement was found for the M_n data as a function of conversion. The experimental and simulation data strongly support the postulate that degradative chain transfer is the dominant kinetic mechanism. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3620–3625, 2007     

Modeling the Effects of Primary Radicals in Free‐Radical Polymerization

The effects of non‐ideal initiator decomposition, i.e., decomposition into two primary radicals of different reactivity toward the monomer, and of primary radical termination, on the kinetics of steady‐state free‐radical polymerization are considered. Analytical expressions for the exponent n in the power‐law dependence of polymerization rate on initiation rate are derived for these two situations. Theory predicts that n should be below the classical value of 1/2. In the case of non‐ideal initiator decomposition, n decreases with the size of the dimensionless parameter α ≡ (k_tz /k_dz) √r_ink_t, where k_tz is the termination rate coefficient for the reaction of a non‐propagating primary radical with a macroradical, k_dz is the first‐order decomposition rate coefficient of non‐propagating (passive) radicals, r_in is initiation rate, and k_t is the termination rate coefficient of two active radicals. In the case of primary radical termination, n decreases with the size of the dimensionless parameter β ≡ k_t,s r_in^1/2/k_p,s M r_t,l^1/2, where k_t,s is the termination rate coefficients for the reaction of a primary (“short”) radical with a macroradical, k_t,l is the termination rate coefficients of two large radicals, k_p,s is the propagation rate coefficient of primary radicals and M is monomer concentration. As k_t is deduced from coupled parameters such as k_t /k_p, the dependence of k_p on chain length is also briefly discussed. This dependence is particularly pronounced at small chain lengths. Moreover, effects of chain transfer to monomer on n are discussed.     

Kinetic investigation of the RAFT polymerization of p‐acetoxystyrene

The kinetics of the RAFT polymerization of p‐acetoxystyrene using a trithiocarbonate chain transfer agent, S‐1‐dodecyl‐S′‐(α,α′‐dimethyl‐α″‐acetic acid)trithiocarbonate, DDMAT, was investigated. Parameters including temperature, percentage initiator, concentration, monomer‐to‐chain transfer agent ratio, and solvent were varied and their impact on the rate of polymerization and quality of the final polymer examined. Linear kinetic plots, linear increase of M_n with monomer conversion, and low final molecular weight dispersities were used as criteria for the selection of optimized polymerization conditions, which included a temperature of 70 or 80 °C with 10 mol % AIBN initiator in bulk for low conversions or in 1,4‐dioxane at a monomer‐to‐solvent volume ratio of 1:1 for higher conversions This study opens the way for the use of DDMAT as a chain transfer agent for RAFT polymerization to incorporate p‐acetoxystyrene together with other functional monomers into well‐defined copolymers, block copolymers, and nanostructures. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2517–2524, 2010     

Bimolecular radical termination: New perspectives and insights

The reversible addition‐fragmentation chain transfer‐chain length dependent termination (RAFT‐CLD‐T) method has allowed us to answer a number of fundamental questions regarding the mechanism of diffusion‐controlled bimolecular termination in free‐radical polymerization (FRP). We carried out RAFT‐mediated polymerizations of methyl acrylate (MA) in the presence of a star matrix to develop an understanding of the effect of polymer matrix architecture on the termination of linear polyMA radicals and compared this to polystyrene, polymethyl methacrylate, and polyvinyl acetate systems. It was found that the matrix architecture had little or no influence on termination in the dilute regime. However, due to the smaller hydrodynamic volumes of the stars in solution compared to linear polymer of the same molecular weight, the gel onset point occurred at greater conversions, and supported the postulate that chain overlap (or c*) is the main cause for the observed autoacceleration observed in FRP. Other theories based on “short–long” termination or free‐volume should be disregarded. Additionally, since our systems are well below the entanglement molecular weight, entanglements should also be disregarded as the cause of the gel onset. The semidilute regime occurs over a small conversion range and is difficult to quantify. However, we obtain accurate dependencies for termination in the concentrated regime, and observed that the star polymers (through the tethering of the arms) provided constriction points in the matrix that significantly slow the diffusion of linear polymeric radicals. Although, this could at first sight be postulated to be due to reptation, the dependencies showed that reptation could be considered only at very high conversions (close to the glass transition regime). In general, we find from our data that the polymer matrix is much more mobile than what is expected if reptation were to dominate. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3155–3173, 2008     

Polymerization of methyl acrylate with triphenylbismuthonium 1,2,3,4‐tetraphenylcyclopentadienylide as a new radical initiator

Triphenylbismuthonium 1,2,3,4‐tetraphenylcyclopentadienylide in 1,4‐dioxan initiated radical polymerization of methyl acrylate to ～30% conversion without gelation because of autoacceleration. The polymer had a viscosity‐average molecular weight of 200,000. The kinetic expression was R_pα[I]^0.3[M]^1.16, that is, the system followed nonideal kinetics because of primary radical termination and degradative chain‐transfer reactions. The values of kk_t and the energy of activation were computed as 3.12 × 10^?5 Lmol^?1s^?1 and 28 kJ/mol, respectively. The ylide dissociated to form a phenyl radical, which brought about polymerization of methyl acrylate. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2060–2065, 2004     

Effect of viscosity on termination rate constant in radical polymerization at low conversion

By using the expression, k_t = A₁D_s for the chain termination rate constant (where A₁ is a constant and D_s is the diffusion constant of radical chain end), a familiar chain termination rate constant, k_t = A₂/η_s (where A₂ is a constant and η_s is solvent viscosity) was examined with variation of conversion x. It was found that the proportionality of chain termination rate constant and solution viscosity is a valid relation at conversion 0 but is approximate at conversion x_c ≥ x > 0. Here x_c denotes a critical conversion under the average distance around spherical polymers formed in polymerization solution is zero. At conversions above x_c, the inverse relation between chain termination rate constant and solution viscosity is not correct.     

Modeling termination kinetics in free‐radical polymerization using a reduced number of parameters

An approach for modeling chain‐length dependent termination rate coefficients is presented. The method is based on the assumption that free‐radical chain length may be considered as a continuous variable. As compared to discrete numerical methods, in continuous modeling the number of independent dimensionless parameters can be significantly reduced. As a consequence, for a wide variety of monomers the conversion dependence of k_t can be predicted without extensive numerical calculations. The method may also be used to determine polymerization conditions under which simpler models of k_t (which neglect effects arising from the dependence of k_t on chain length) may be applied. Calculations for methyl methacrylate, styrene, and butyl acrylate bulk polymerizations up to high degrees of monomer conversion show that the impact of chain length on termination varies with conversion and strongly depends on the type of monomer.     

Dynamic light scattering studies of atactic and syndiotactic poly(methyl methacrylate)s in dilute theta solution

The present article considers the coil‐to‐globule transition behavior of atactic and syndiotactic poly(methyl methacrylates), (PMMA) in their theta solvent, n‐butyl chloride (nBuCl). Changes in Rh in these polymers with temperature in dilute theta solutions were investigated by dynamic light scattering. The hydrodynamic size of atactic PMMA (a‐PMMA‐1) in nBuCl (M_w: 2.55 × 10⁶ g/mol) decreases to 61% of that in the unperturbed state at 13.0°C. Atactic PMMA (a‐PMMA‐2) with higher molecular weight (M_w: 3.3 × 10⁶ g/mol) shows higher contraction in the same theta solvent (α_η = R_h(T)/R_h (θ) = 0.44) at a lower temperature, 7.25°C. Although syndiotactic PMMA (s‐PMMA) has lower molecular weight than that of atactic samples (M_w: 1.2 × 10⁶), a comparable chain collapse was observed (α_η = 0.63) at 9.0°C. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2253–2260, 1999     

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