The laser-flash-initiated polymerization as a tool of evaluating (individual) kinetic constants of free-radical polymerization, 2. The direct determination of the rate of constant of chain propagation

When a polymerizable system is subjected to periodic light flashes, which induce the formation of primary radicals, a pseudostationary state is established which is characterized by a periodic profile of the (polymer) radical concentration. Within such a period of length t₀ the radical concentration will decay according to a second-order rate law. At the end of this period the radicals, which have escaped termination up to this moment, have propagated up to a chain length L₀ = t₀·k_p·c_M, k_p representing the propagation rate constant and c_M the monomer amount concentration. When the next flash arrives these radicals are opposed to a strongly increased overall concentration of radicals which leads to an enhanced probability for their termination. As a consequence the formation of dead polymer molecules with a chain length close to L₀ is favoured. The chain-length distribution of polystyrene prepared under such pseudostationary conditions, which was evaluated by gel permeation chromatography, in fact exhibits such a peak. The analysis of the theoretical distribution curves, derived in this communication, reveals that it is easily possible to correlate this peak to L₀, independently of the mode of termination (disproportionation or combination). Thus, a method of evaluating k_p is derived without any reference to the termination rate constant k_t and largely independent of all features which usually cause problems in the evaluation of k_p and k_t (such as primary radical termination etc.). The experimental results agree fairly well with the data reported in literature, especially with those obtained from the number of particles and the rate of polymerization in emulsion systems.     

Termination kinetics of styrene free‐radical polymerization studied by time‐resolved pulsed laser experiments

The single pulse (SP)‐pulsed‐laser polymerization (PLP) technique has been applied to measure k_t/k_p, the ratio of termination to propagation rate coefficients, for the free‐radical bulk polymerization of styrene at temperatures from 60 to 100°C and pressures from 1800 to 2 650 bar. k_t/k_p is obtained by fitting monomer concentration vs. time traces that are determined via time‐resolved (μs) near infrared monitoring of monomer conversion induced by single excimer laser pulses of about 20 ns width. Styrene is a difficult candidate for this kind of measurements as conversion per pulse is small for this low k_p and high k_t monomer. Thus between 160 to 300 SP signals were co‐added to yield a concentration vs. time trace of sufficient quality for deducing k_t/k_p with an accuracy of better than ± 20 per cent. With k_p being known from PLP–SEC experiments, chain‐length averaged k_t values are immediately obtained from k_t/k_p. At given pressure and temperature, k_t is independent of the degree of overall monomer conversion, which, within the present study, has been as high as 20%percnt;. The k_t value, however, is found to slightly increase with the amount of free radicals produced by a single pulse in laser‐induced decomposition of the photoinitiator DMPA (2,2‐dimethoxy‐2‐phenyl acetophenone). This remarkable observation is explained by DMPA decomposition resulting in the formation of two free radicals which significantly differ in reactivity. Extrapolation of SP–PLP k_t data from experiments at rather different DMPA levels and laser pulse energies toward low primary free‐radical concentration, yields very satisfactory agreement of the extrapolated k_t values with recent literature data from chemically and photochemically induced styrene polymerizations.     

Evaluation of the kinetic parameters for styrene polymerization and their chain length dependence by kinetic simulation and pulsed laser photolysis

Pulsed laser photolysis (PLP) has been employed to determine propagation rate constants k_p for styrene polymerization in benzene over a wider temperature range (20?80°C) than previously converd. It is proposed that a small chain length dependence of k_p (overall) may, in part, be a consequence of a marked chain length dependence of k_p for the first few propagation steps [i.e. k_p(1) > k_p(2) < k_p(3) ≥ k_p(≥4)]. The propagation rate constant for styrene polymerization is given by the expression: In k_p = 16,0₉ ? 289₅₀/(RT) (overall) or In k_p = 16,4₇ ? 300₈₄/(RT) (chain length ≥ 4). Kinetic simulation has been applied both as an aid in data analysis and to demonstrate the reliability of the PLP technique for evaluation of propagation rate constants (k_p) in radical polymerization. This has been achieved by examining the sensitivity of the molecular weight distribution of polymers formed in PLP experiments to the values of the kinetic parameters associated with polymerization and their chain length dependence. The termination rate constants (k_t = k_c + k_d) and the ratio of combination to disproportionation (k_c: k_d) markedly affect the molecular weight distribution of polymer formed in PLP experiments. The prospects for evaluating the values of k_t, its chain length dependence and k_c : k_d by direct analysis of the molecular weight distribution are discussed in the light of these results.     

Determination of absolute rate constants for radical polymerization and copolymerization of ethyl α-cyanoacrylate in the presence of effective inhibitors against anionic polymerization

The absolute rate constants of propagation k_p and of termination k_t of ethyl α-cyanoacrylate (ECNA) were determined in bulk at 30°C by means of the rotating sector method under conditions to suppress anionic polymerization; k_p = 1 622 1 · mol^?1 · s^?1 and k_t = 4,11 · 10⁸ 1 · mol^?1 · s^?1 for the polymerization in the presence of acetic acid, and k_p = 1610 1 · mol^?1 · s^?1 and k_t = 4,04 · 10⁸ l · mol^?1 · s^?1 for the polymerization in the presence of 1,3-propanesultone. The magnitude of k/k_t determined was 6,39 · 10^?3 l · mol^?1 · s^?1. The absolute rate constants for cross-propagation in ECNA copolymerizations were also evaluated. Quantitative comparison of the rate constants with those of common monomers and polymer radicals shows that the strong electron-withdrawing power of the ethoxycarbonyl and cyano groups enable the poly(ECNA) radical to add to monomers as fast as the other polymer radicals. The relatively high reactivity of ECNA, regardless of the type of attacking polymer radical, is interpreted by a transition state greatly stabilized by both the ethoxycarbonyl and the cyano groups.     

Kinetic and electron paramagnetic resonance studies on radical polymerization. Radical-initiated polymerization of methyl N-phenylitaconamate in N,N-dimethylformamide

The polymerization of methyl N-phenylitaconamate(methyl 2-methylenesuccinanilate ( 1 )) with dimethyl 2,2′-azodiisobutyrate ( 2 ) was studied in N,N-dimethylformamide (DMF) kinetically and by means of electron paramagnetic resonance (EPR) spectroscopy. The polymerization rate (R_p) at 55°C is given by the equation: R_p = k[ 2 ]^0,58 · [ 1 ]^1,6. The overall activation energy of the polymerization was calculated to be 54,2 kJ/mol. The number-average molecular weight of poly( 1 ) was in the range between 5000 and 17000. From an EPR study, the polymerization system was found to involve the EPR-detectable propagating polymer radical of 1 at practical polymerization conditions. Using the concentration of polymer radicals, the rate constants of propagation (k_p) and termination (k_t) were determined for 55°C. The rate constant of propagation k_p (between 8,4 and 12 L · mol^?1 · s^?1) tends to somehow increase with increasing monomer concentration. On the other hand, k_t (between 1,9. 10^?5 L · mol^?1 · s^?1) increases with decreasing monomer concentration, which results from a considerable dependence of k_t on the polymer-chain length. Such monomer-concentration-dependent k_p and k_t values are responsible for the high dependence of R_p on the monomer concentration. Thermogravimetric results showed that thermal degradation of poly( 1 ) occurs rapidly at temperatures higher than 200°C and the residue at 500°C amounts to 26% of the initial polymer. For the copolymerization of 1 (M₁) with styrene (M₂) at 55°C in DMF the following copolymerization parameters were found: r₁ = 0,52, r₂ = 0,31, and Q, e values Q₁ = 1,09 and e₁ = +0,55.     

Termination kinetics of free-radical polymerization of styrene over an extended temperature and pressure range

The termination rate coefficient k_t of the free radical bulk polymerization of styrene is determined between 30 and 90°C up to a maximum pressure of 2800 bar. The majority of polymerization experiments has been carried out at monomer conversions up to 20 per cent. In this range a single value of k_t is sufficient to describe termination rate at constant pressure and temperature. Toward higher conversion, significant changes in k_t are observed. The data are measured by a pulsed laser polymerization technique and partly by conventional chemically initiated experiments, both with 2,2′-azoisobutyronitrile (AIBN) as the initiator. Online spectroscopy is applied toward measurement of styrene conversion. The experimental termination rate coefficients up to 20 per cent monomer conversion are adequately represented by the expression: Activation volume and activation energy of k_t are very close to the corresponding activation parameters that characterize the pressure and temperature dependence of the inverse of styrene monomer viscosity. Varying laser pulse repetition rate has been used to investigate a potential chain-length dependence of k_t at low conversion. It turns out that effects of this kind are not sufficiently pronounced to be safely established in view of the experimental precision of ±25 per cent that is reached in the k_t determinations.     

Online Monitoring of Chain Transfer in Free‐Radical Polymerization

A recently introduced, automated method for online monitoring of polymerization reactions was used to study free‐radical transfer reactions. The persulfate initiated polymerization of acrylamide (AAm) in water was chosen as the test system. Chain transfer properties of ethanol (EtOH) and propanol (PrOH) were investigated. Different methods of computing the transfer constant are compared, including those based on the slope and intercept behavior of the monitored cumulative weight‐average molecular mass as a function of conversion, M̄_w (f), the reduced viscosity, and corresponding size exclusion chromatography analysis of the reaction end products. To a close approximation, the chain transfer agents were found to obey the form expected when ideal free‐radical polymerization takes place and radical transfer from propagating radicals to the chain transfer agent (CTA) is slower than from the CTA to monomer, that is, the polymer molar mass decreases with increasing chain transfer agent, but there is no appreciable effect on the kinetics of monomer conversion. The AAm kinetics were characterized in terms of the ratio k_p² /k_t, where k_p and k_t are the propagation and termination rate constants, respectively.     

Kinetik der radikalischen polymerisation und copolymerisation von N-vinyl-N-methylacetamid

In order to get information on the kinetics of free radical polymerization of N-vinyl-N-methylacetamide (VIMA) polymerizations of the purified monomer were performed in dilatometers using the temperature range from 25 to 70°C, monomer concentrations of 10 to 100% in methanol, and initiation either by γY-irradiation or by radical initiators. Molecular weight meassurements of the polymer were calibrated by light scattering determinations of M_w according to the following equation at 30 °C in methanol: [η]/(ml/g) = 5,02 · 10^?3 · M_w^0,7946. Normal kinetics of free radical polymerization were found to be valid and Arrhenius parameters were calculated for the ratio k_p²/k_t of the propagation rate constant k_p and the termination rate constant k_t as well as for the monomer transfer constant C_M and for the efficiency of initiation f. For copolymerizations of N-vinyl-N-methylacetamide with different comonomers the mean Q-e-values were calculated as follows: Q_VIMA ? 0,06; e_VIMA ? ? 1,8.     

Kinetic and ESR studies on radical polymerization. Radical polymerization behavior of N-octadecylmaleimide in benzene

The polymerization of N-octadecylmaleimide ( 1 ) initiated with azodiisobutyronitrile ( 2 ) was investigated kinetically in benzene. The overall activation energy of the polymerization was calculated to be 94,2 kJ·mol^?1. The polymerization rate (R_p) at 50°C is expressed by the equation, R_p = k[ 2 ]^0,6[ 1 ]^1,7. The homogeneous polymerization system involves ESR-detectable propagating polymer radicals. Using R_p and the polymer radical concentration determined by ESR, the rate constants of propagation (k_p) and termination (k_t) were evaluated at 50°C. k_p (33 L · mol^?1 · s^?1 on the average) is substantially independent of the monomer concentration. On the other hand, k_t (0,3 · 10⁴ – 1,0 · 10⁴ L · mol^?1 · s^?1) is fairly dependent on the monomer concentration, which is ascribable to a high dependence of k_t on the chain length of rigid poly( 1 ). This is the predominant factor for the high order with respect to the monomer concentration in the rate equation. In the copolymerization of 1 (M₁) and St (M₂) with 2 in benzene at 50°C, the following copolymerization parameters were obtained: r₁ = 0,11, r₂ = 0,09, Q₁ = 2,1, and e₁ = +1,4.     

Electron spin resonance (ESR) estimation of propagation rate constants of radical polymerization of butyl methacrylate

Propagation rate constants (k_p) for the free radical polymerization of butyl methacrylate (BMA) in toluene solution were measured by ESR spectroscopy in the temperature range from –30 to 90°C. The polymerization was photochemically induced at a constant initiator concentration of di‐tert‐butyl peroxide (tBPO). The Arrhenius parameters A and E_a were estimated to be (3.40 ± 0.4)>×10⁶ M^–1·s^–1 and (22.0 ± 1.0) kJ/mol, respectively. The k_p values estimated from ESR analysis were compared with the corresponding data obtained from the pulsed laser polymerization (PLP).     

Effect of SnCl4 on the radical-initiated polymerization of diethyl itaconate: Kinetical and ESR studies

The effect of SnCl₄ on the polymerization of diethyl itaconate ( 1 ) with dimethyl 2,2′-azoisobutyrate ( 2 ) in benzene was investigated kinetically and ESR spectroscopically. The polymerization rate (R_p) at 50°C shows a flat maximum on varying the SnCl₄ concentration. The molecular weight of the resulting polymer decreases with increasing SnCl₄ concentration. The overall activation energy of the polymerization is lowered from 52 to 33 kJ · mol^?1 by the presence of SnCl₄, (0,342 mol · L^?1). An NMR study revealed that 1 and SnCl₄ form 1:1 and 2:1 complexes with a large stability constant in benzene. The propagating polymer radicals in the absence and presence of SnCl₄ are ESR-observable as a five-line spectrum under the actual polymerization conditions. The complexed polymer radicals show further three-line splitting due to two methylene hydrogens of the ethyl ester group. The polymer radical concentration increases with the SnCl₄ concentration. The rate constant (k_p) of propagation was determined using R_p and the polymer radical concentration. k_p (6,3–2,9 L · mol^?1 · s^?1 at 50°C) decreases with increasing SnCl₄ concentration. The presence of SnCl₄ (0,342 mol · L^?1) reduces the activation energy of propagation from 29 to 21 kJ · mol^?1. The rate constant (k_t) of termination was estimated from the decay curve of the polymer radicals, k_t (3,1–1,1 · 10⁵ L · mol^?1 s^?1) also decreases with the SnCl₄ concentration. The activation energies of termination in the absence and presence of SnCl₄ (0,342 mol · L^?1) are 30 and 24 kJ · mol^?1, respectively. Suppression of propagation and termination by SnCl₄ seems to be explicable in terms of an entropy factor.     

Termination Kinetics of Methyl Acrylate and Dodecyl Acrylate Free‐Radical Homopolymerizations up to High Pressure

The single pulse (SP) – pulsed laser polymerization (PLP) technique has been applied to measure k_t /k_p, the ratio of termination to propagation rate coefficients, for free‐radical bulk homopolymerizations of methyl acrylate (MA) and dodecyl acrylate (DA) between 10 and 50°C at pressures from 10 to 2 500 bar. k_t /k_p is obtained from experimental monomer concentration vs. time traces that are determined via time‐resolved (μs) near infrared monitoring of monomer conversion induced by single excimer laser pulses of about 20 ns width. With k_p being known from PLP–SEC experiments, chain‐length averaged k_t is immediately obtained from k_t /k_p. For MA, k_t remains constant up to about 15% monomer conversion and clearly decreases upon further polymerization. For DA at pressures of 100 bar and above, a plateau value of constant k_t is observed up to about 60% monomer conversion whereas at lower pressure, e. g. at 10 bar, k_t slightly increases in the very initial conversion region, but also exhibits a plateau k_t value at moderate and high conversions. The occurrence of such plateau k_t values and their pressure and temperature dependence are consistent with the view that plateau regions of k_t are best understood in terms of diffusion control via segmental mobility.     

Radical polymerization of a trimer of methyl acrylate as polymerizable α-substituted acrylate

The radical polymerization of a trimer of methyl acrylate was investigated in relation to the steric hindrance-assisted polymerization of an α-(substituted methyl)acrylic ester. The trimer can also be regarded as a model of the unsaturated end group formed by the addition-fragmentation chain transfer of methyl α-(bromomethyl)acrylate during methyl acrylate polymerization. The trimer polymerizes slowly to a low-molecular-weight polymer at 30–60°C, and electron spin resonance (ESR) quantification of the propagating radical of the trimer allowed the determination of the absolute rate constants of propagation (k_p) and termination (k_t). The k_p and k_t values for the trimer indicate slow propagation and slow termination of polymerizable acrylates bearing a bulky α-substituent. In conformity with a higher reactivity of the trimer of methyl acrylate than the corresponding trimer of methyl methacrylate, poly(methyl acrylate) bearing an unsaturated end group, which is produced by the polymerization of methyl acrylate in the presence of methyl α-(bromomethyl)acrylate, was confirmed to copolymerize with methyl acrylate to yield a branched homopolymer.     

Evaluation of individual rate constants from the chain-length distribution of polymer samples prepared by intermittent (rotating sector) photopolymerization, 3. Theoretical foundations for termination by disproportionation

The chain-length distribution and its moments were calculated for a periodically interrupted photopolymerization with termination by disproportionation and negligible chain transfer. For a wide range of experimental conditions, which are readily accessible in the overwhelming majority of cases, the position of the first point of inflection in the chain-length distribution corresponds exactly to the quantity k_p [M]t₀, k_p representing propagation rate constant, M monomer and t₀ the period length. Thus k_p can be directly evaluated from the chain-length distribution of the polymer. Together with the ratio k/k_t, k_t being the termination rate constant, calculated from the rate and weight-average degree of polymerization according to a universal relationship—the validity of which is also verified — resolution into the individual rate constants is easily accomplished. The dependence on experimental conditions of the ratio weight- to number-average degrees of polymerization P_w /P_n , which is a measure of the width of the molecular weight distribution of the polymer formed, is discussed.     

Effect of alkyl groups on the rate constants of propagation and termination in the radical polymerization of dialkyl itaconates

Polymerization of dialkyl itaconates with dimethyl azoisobutyrate ( 5 ) was studied in benzene at 50°C by means of electron spin resonance (ESR). The monomers used are dimethyl ( 1 ), diethyl ( 2 ), dibutyl ( 3 ) and di-2-ethylhexyl ( 4 ) itaconates. All the polymerization systems involve ESR-observable propagating polymer radicals under the actual polymerization conditions. The polymerization rate (R_p) and degree of polymerization of the resulting polymer increase in going from shorter to longer alkyl groups. The ESR-determined rate constants of propagation (k_p) and termination (k_t) decrease as the alkyl chain becomes longer. k_p of 1 is 3,3 times higher than that of 4 , while k_t of 1 is 590 times higher than that of 4 . Thus, the steric effect due to the alkyl group suppresses much more termination than propagation, leading to the fact that R_p increases as the alkyl group becomes larger.     

Kinetic study of the polymerization of N,N′-methylenebis(acrylamide) in aqueous dispersion systems

The aqueous-phase polymerization of N,N′-methylenebis(acrylamide) initiated by potassium peroxodisulfate in the absence and in the presence of the anionic emulsifier sodium dodecylsulfate was kinetically investigated at 50°C by conventional gravimetric and dilatometric methods. The rate of polymerization is found to be proportional to the 0,75 and 0,24 oder with respect to potassium peroxodisulfate and N,N′-methylenebis(acrylamide) concentrations, respectively. On the other hand, it is independent of the concentration of sodium dodecylsulfate. This agrees with the polymerization of a monomer soluble in water. Therefore, the equations for a homogeneous polymerization were applied to evaluate the experimental results. The calculated ratio k_p/k_t^0,5 of the rate constants of propagation k_p and termination k_t for the N,N′-methylenebis(acrylamide) polymerization at zero conversion in the absence of emulsifier are scattered in the interval between 3,1 and 3,4 dm^1,5 · mol^?0,5 · s^?0,5 and in the presence of emulsifier in the interval between 2,4 and 3,5 dm^1,5 · mol^?0,5 · s^?0,5. They are close to those obtained for the homogeneous polymerization of acrylamide in the aqueous phase. The lower values of k_p/k_t^0,5 ≈ 0,3–0,6 dm^1,5 · mol^?0,5 · s^?0,5 determined for the polymerization of N,N′-methylenebis(acrylamide) for conversions between 30 and 60% follow from the hindered termination reaction within the polymer particles. The polymer dispersions formed are unstable. The growth of the polymer particles proceeds predominantly by coalescence. This suggests a kinetics which does not follow the Smith-Ewart theory but is characterized by a continuous particle nucleation and agglomeration. The interval 1 occurs at the beginning of the dispersion polymerization when polymer particles are being formed. Interval 2 follows, once the number of polymer particles has been fixed.     

A kinetic study of butyl acrylate free radical polymerization in benzene solution

The free radical polymerization of butyl acrylate has been studied in benzene solutions ranging from 1 to 5 mol·L^–1 at 50°C using 2,2′‐azobisisobutyronitrile as initiator. Under the conditions of our experiments, both the effective rate coefficient for initiation, 2 f k_d , and the coupled parameter, k_p/k_t^1/2, (where k_p and k_t are the constants for propagation and termination reactions, respectively) are dependent on the monomer concentration. The 2 f k_d value shows little increase with monomer concentration. The variation of the k_p/k_t^1/2 parameter has been correlated with the chain length dependence of the termination rate coefficient. This effect is also responsible for the high dependence of the overall polymerization rate, R_p, onthe monomer concentration (1.49).     

Exciplex laser-induced polymerization of pure ethylene at high pressure

Pure ethylene is photo-polymerized with an exciplex laser on the KrF line (248 nm) at temperatures from 190°C to 230°C and for pressures up to 3 200 bar. The radical reaction is directly monitored via quantitative high-pressure high-temperature near infrared spectroscopy. Toward higher densities and temperatures, the overall quantum yield increases and up to several thousand ethylene molecules are polymerized by one absorbed laser photon. A kinetic scheme is presented which adequately describes the polymerization kinetics as a function of temperature, overall density, laser pulse energy, and conversion. Termination rate coefficient k_t is found to decrease in the initial polymerization period, whereas a single value of k_t is sufficient to represent kinetic data in the extended conversion range from 20% to 70%.     

Kinetic and ESR studies of the radical-initiated polymerization of N-(2,6-dimethylphenyl)itaconimide

The polymerization of N-(2,6-dimethylphenyl)itaconimide (1) with azoisobutyronitrile (2) was studied in tetrahydrofuran (THF) kinetically and spectroscopically with the electron spin resonance (ESR) method. The polymerization rate (R_p) at 50°C is given by the equation: R_p = K [2] ^0,5 · [1] ^2,1. The overall activation energy of the polymerization was calculated to be 91 kJ/mol. The number-average molecular weight of poly (1) was in the range of 3500–6500. From an ESR study, the polymerization system was found to involve ESR-observable propagating polymer radicals of 1 under the actual polymerization conditions. Using the polymer radical concentration, the rate constants of propagation (k_p) and termination (k_t) were determined at 50°C. k_p (24–27 L · mol^?1 · s^?1) is almost independent of monomer concentration. On the other hand, k_t (3,8 · 10⁴–2,0 · 10⁵ L · mol^?1 · s^?1) increases with decreasing monomer concentration, which seems mainly responsible for the high dependence of R_p on monomer concentration. Thermogravimetric results showed that thermal degradation of poly (1) occurs rapidly at temperatures higher than 360°C and the residue at 500°C was 12% of the initial polymer. For the copolymerization of 1 (M₁) with styrene (M₂) at 50°C in THF the following copolymerization parameters were found; r₁ = 0,29, r₂ = 0,08, Q₁ = 2,6, and e₁ = +1,1.     

On the kinetics of polymerization and copolymerization of poly(oxyethylene) macromonomers and styrene

The homogeneous and the dispersion polymerzation and copolymerization of methacryloyl-terminated poly(oxyethylene) (MMA-PEG) and of p-vinylbenzyl-terminated poly(oxyethylene) (St-PEG) macromonomers and styrene, initiated by a radical initiator, was investigated using conventional gravimetric and NMR methods at 60°C. The batch polymerizations in N,N-di-methylformamide and in ethanol/water were conducted to either low or high conversion. The fractional conversion rates of the solution polymerization and copolymerization indicate that the homopolymerizations of macromonomers involve steady-state conditions, whereas copolymerizations proceed under non-stationary conditions. The ratios of the rate constants for propagation and termination (k_p/k) for polymerization and copolymerization of MMA-PEG and St-PEG are by one order of magnitude higher than that for styrene. The increase in k_p/k is more pronounced in dispersion polymerization, which is ascribed to the decrease of both k_p and k_t. The rates of dispersion polymerization are proportional to the particle concentration. The number of particles increses up to 50% conversion. The particle growth is suggested to proceed via association of partcles and by propagation within polymer particles. The decrese of the number of radicals per particles as conversion proceeds is ascribed to the decrese of the growing radical activity and to the transfer of monomeric radicals to the continuous phase. The molecular weights correlate inversely with the particle size.