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).     

SP‐PLP‐EPR—A Novel Method for Detailed Studies into the Termination Kinetics of Radical Polymerization

Single pulse–pulsed laser polymerization–electron paramagnetic resonance (SP‐PLP‐EPR) has been introduced as a powerful method for the very detailed analysis of termination kinetics. During polymerization an intense laser pulse is applied in order to almost instantaneously produce a burst of radicals. The decay of radical concentration is measured by highly time‐resolved EPR and is analyzed with respect to the rate coefficients for the termination of two radicals of identical size. SP‐PLP‐EPR experiments have been carried out for an itaconate monomer, for several methacrylates in bulk and in a solution of ionic liquids, for methacrylic acid in aqueous solution, and for the solution polymerization of butyl acrylate in toluene at low temperature. The data fully support the composite model, which assumes a stronger chain‐length dependence of termination for radicals of smaller size and a weaker one for large radicals. The SP‐PLP‐EPR technique is also applicable in systems with more than one type of growing radicals, as is the case with butyl acrylate polymerization at higher temperature and with RAFT polymerizations, where the novel method may be used for a comprehensive kinetic analysis.

     

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.     

SP–PLP–EPR Investigations into the Chain‐Length‐Dependent Termination of Methyl Methacrylate Bulk Polymerization

Termination kinetics of methyl methacrylate (MMA) bulk polymerization has been studied via the single pulsed laser polymerization–electron paramagnetic resonance method. MMA‐d₈ has been investigated to enhance the signal‐to‐noise quality of microsecond time‐resolved measurement of radical concentration. Chain‐length‐dependent termination rate coefficients of radicals of identical size, k, are reported for 5–70 °C and up to i = 100. k decreases according to the power‐law expression . At 5 °C, k_t for two MMA radicals of chain‐length unity is k = (5.8 ± 1.3) · 10⁸ L · mol⁻¹ · s⁻¹. The associated activation energy and power‐law exponent are: E_A(k) ≈ 9 ± 2 kJ · mol⁻¹ and α ≈ 0.63 ± 0.15, respectively.

     

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.     

Elementary Steps of Initiation and Termination Processes in Radical Polymerization

Investigations into the kinetics of primary radicals produced in photochemically and thermally induced decomposition of peroxides of type R₁C(O)O-OR₂ are presented. The correlation of peroxide structure with decomposition rate and with initiator efficiency in radical polymerizations is discussed. Termination rate coefficients, k_t, as a function of temperature, pressure, polymer content, and of chain length may be deduced from two types of time-resolved experiments in which, after applying an excimer laser pulse, either monomer conversion is measured via near-infrared spectroscopy or the decay in radical concentration is monitored via electron spin resonance.     

Easy Access to Chain‐Length‐Dependent Termination Rate Coefficients Using RAFT Polymerization

Chain‐length‐dependent termination rate coefficients of the bulk free‐radical polymerization of styrene at 80 °C are determined by combining online polymerization rate measurements (DSC) with living RAFT polymerizations. Full k_t versus chain‐length plots were obtained indicating a high k_t value for short chains (2 × 10⁹ L · mol⁻¹ · s⁻¹) and a weak chain‐length dependence between 10 and 100 monomer units, quantified by an exponent of −0.14 in the corresponding power law 〈k_t^i,i〉 = k_t⁰ · P^−b.

Double logarithmic plots of 〈k_t^i,i〉 versus P, evaluated from experimental time‐resolved R_p data according to the procedure described in the text, for different CPDA and AIBN concentrations. The best linear fit for (10 < P < 100) is indicated as full line.     

Effects of Laplace Pressure on Propagation and Termination in Aqueous Heterogeneous Free Radical Polymerization

Summary: The influence of the Laplace pressure in polymer emulsion particles during aqueous heterogeneous free radical polymerization on the polymerization kinetics has been investigated. Calculations were carried out based on experimentally reported pressure dependences of propagation and termination rate coefficients. The results suggest that in most cases the effects are not likely to be significant, although under conditions of very small particles (diameter <20 nm) and high interfacial tensions effects of the order of a few percent on propagation (increase in rate) and termination (decrease in rate) were predicted.

(k_p/k_t^0.5)/(k_p/k_t^0.5)₀ as a function of particle radius as a result of the Laplace pressure.     

Thioketone‐Mediated Polymerization of Butyl Acrylate: Controlling Free‐Radical Polymerization via a Dormant Radical Species

It is demonstrated by experiment and simulation that the commercially available thioketone 4,4‐bis(dimethylamino)thiobenzophenone is capable of controlling AIBN‐initiated bulk butyl acrylate polymerization at 80 °C. On the basis of molecular weight data and from monomer conversion versus time curves, the associated rate parameters are estimated. The addition rate coefficient, k_ad, for the reaction of a propagating chain with the thioketone is close to 10⁶ L · mol⁻¹ · s⁻¹ and the fragmentation rate coefficient, k_frag, is around 10⁻² s⁻¹ giving rise to large equilibrium constants in the order of 10⁸ L · mol⁻¹. Furthermore, cross‐ and self‐termination of the dormant radical species are identified to be operational.

     

Kinetic Simulations of Atom Transfer Radical Polymerization (ATRP) in Light of Chain Length Dependent Termination

Kinetic simulations using the composite k_t model allows a better understanding of the effects of the persistent radical affecting ATRP or for that matter any activation–deactivation system. It also provides a better fit to experimental data in either bulk or solution conditions for ATRP polymerizations carried out at 110 °C. The results suggest that the composite model has broad utility over a wide range of experimental conditions and temperatures. The advantage of incorporating an accurate k_t model is that one can then use simulations as predictive tool to obtain polymers with higher chain‐end fidelity or polymers with low PDI values. This becomes important when attempting to use the chain‐ends for further functionalization to make complex polymer architectures. This model can also be used in simulations of miniemulsion or seeded emulsions to determine the effect of compartmentalization with particle size.

     

Design Criteria for Accurate Measurement of Bimolecular Radical Termination Rate Coefficients via the RAFT‐CLD‐T Method

The reversible addition‐fragmentation chain transfer chain length dependent termination (RAFT‐CLD‐T) technique allows a simple experimental approach to obtain chain‐length‐dependent termination rate coefficients as a function of conversion, k(x). This work provides a set of criteria by which accurate k(x) can be obtained using the RAFT‐CLD‐T method. Visualization of three‐dimensional plots varying all kinetic rate parameters and starting concentrations demonstrates that only certain combinations give an accurate extraction of k(x). The current study provides hands‐on guidelines for experimentalists applying the RAFT‐CLD‐T method.

     

On the Incorrectness of the Factor 2 in the Radical Termination Equation

The IUPAC recommended factor 2 preceding rate coefficients in the radical termination kinetic equations is claimed to be incorrect and confusing. This recommendation can lead to incorrect analysis of experimental data, especially while applying kinetic Monte Carlo simulations. The statement is based on the derivation of the corresponding relationships.

     

Kinetics and Modeling of Methacrylic Acid Radical Polymerization in Aqueous Solution

Batch radical polymerization of non‐ionized methacrylic acid, 30 wt.‐% in aqueous solution, has been studied at 50 °C and ambient pressure with 2‐mercaptoethanol (ME) as the chain‐transfer agent (CTA). Initial polymerization rate decreases with CTA concentration, which has been varied up to 20 mol‐%. A kinetic model is presented which includes chain‐length‐dependent termination and uses an empirical function to account for the dependence of termination rate on both monomer conversion and molar mass of the polymeric product. In conjunction with PREDICI simulation, this model affords for an adequate representation of the measured monomer conversion vs. time profiles.

     

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     

Free‐Radical Propagation Rate Coefficients via n‐Pulse Periodic Polymerization

Aspects of applying n‐pulse periodic initiation in pulsed laser polymerization/size‐exclusion chromatography (PLP/SEC) experiments are studied via simulation of molecular weight distributions (MWDs). In n‐pulse periodic PLP/SEC, sequences of n laser pulses at successive time intervals Δt₁ up to Δt_n are periodically applied. With the dark time intervals being suitably chosen, n‐modal MWDs with n well separated peaks occur. The n‐pulse periodic PLP/SEC method has the potential for providing accurate propagation rate coefficients, k_p. Among several measures for k_p, the differences in molecular weights at the MWD peak positions yield the best estimate of k_p under conditions of medium and high pulse laser‐induced free‐radical concentration. Deducing k_p from n dark time intervals (corresponding to n regions of free‐radical chain length) within one experiment at otherwise identical PLP/SEC conditions allows addressing in more detail a potential chain‐length dependence of k_p. Simulations are compared with experimental data for 2‐pulse periodic polymerization of methyl methacrylate.

Measured MWD (solid line) and associated first derivative curve (dotted line) for a 2‐pulse periodic bulk polymerization experiment of MMA at 20 °C.     

Nitroxide‐Mediated Radical Polymerization in Dispersed Systems: Compartmentalization and Nitroxide Partitioning

Compartmentalization and nitroxide partitioning in NMP in dispersed systems have been investigated by modeling and simulations. Compartmentalization comprises the segregation effect on termination and the confined space effect on deactivation. Under certain conditions, it is possible to obtain an improvement in both control and livingness. The particle size threshold for compartmentalization, decreases with any system change that leads to a decrease in the number of propagating radicals and/or nitroxides per particle, and vice versa. There is direct competition between the confined space effect on deactivation and nitroxide exit–the more water‐soluble the nitroxide, the weaker the confined space effect. Nitroxide partitioning leads to an increase in polymerization rate and loss in control/livingness.

     

Quantum Chemical Investigation of Secondary Reactions in Poly(vinyl chloride) Free‐Radical Polymerization

Free‐radical polymerization of vinyl chloride is investigated computationally with special attention to the secondary reactions involving mid‐chain radicals (MCRs). Namely, the rate constants of backbiting, chain scission, chain transfer, and propagation reactions are evaluated using a density functional theory method. The rate coefficients of such reactions are estimated taking into account the position of the radical along the chain as well as its distance from the chain‐end. In particular 1:5, 5:1, and 5:9 backbiting are the most relevant secondary reactions, followed by the slower propagation of MCRs. Finally, a kinetic model of suspension polymerization including the investigated reactions is developed, in order to determine their impact on the quality of the final polymer.

     

Addition‐Fragmentation Chain Transfer to Polymer in the Free Radical Ring‐Opening Polymerization of an Eight‐membered Cyclic Allylic Sulfide Monomer

Summary: A detailed investigation of chain transfer to polymer during free radical ring‐opening polymerization of the eight‐membered disulfide monomer 2‐methyl‐7‐methylene‐1,5‐dithiacyclooctane (MDTO) is presented. It has been shown that extensive chain transfer to polymer occurs involving both poly(MDTO) radicals and cyanoisopropyl radicals. Significant decreases in molecular weight were observed when cyanoisopropyl radicals were generated in the presence of poly(MDTO) in the absence of monomer. The molecular weight distribution (MWD) obtained from polymerization of MDTO in the presence of pre‐added poly(MDTO) was markedly different from that obtained without pre‐added polymer. A kinetic model was constructed in an attempt to quantitatively describe the chain transfer to polymer process based on the addition fragmentation chain transfer mechanism. It was found however that the simulated MWDs were considerably broader than the experimental MWDs, which were similar to the Schulz‐Flory distribution.

Mechanism for chain transfer to polymer.