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.     

Solid-state polymerization of long-chain vinyl compounds. III. Mechanism of γ-ray-initiated postpolymerization in layered structures of octadecyl methacrylate and acrylate

The mechanism and kinetics of the γ-ray-initiated postpolymerization of octadecyl methacrylate and acrylate in lamellar crystals were investigated by a simple model. This model assumes that the initiation points are distributed as in a checkerboard and that polymerization probability of the monomer molecules decreases conically around each initiation point. The two-dimensional polymerization can be characterized in this cone model by two parameters, a and r; a represents the polymerizability of the monomer for a given condition, and r depends on the number of initiation points per unit area. G values for the initiation reaction of octadecyl methacrylate and acrylate were estimated as 0.8 and 1.6, respectively. The two-dimensional postpolymerization of long-chain compounds proceeds in two stages. The rate of polymerization is very high and zero order with respect to monomer concentration in the first stage. It is lower and obeys first-order kinetics in the second stage. The rate constants of the zero-and first-order polymerizations were k_p0 = 1.73 molecule sec^-1 and k_p1 = 0.93 sec^?1, respectively, for octadecyl acrylate at 20°C.     

Synthesis and radical polymerization of hydrophilic methacrylates with oxyethylene units in the pendant chain

The syntheses of methacrylic monomers of the general structure where n is 3, 4, 5, or 6, were performed by the reaction of the corresponding alcohol ethers with methacryloyl chloride. The alcohol ethers were previously prepared by different synthetic procedures involving the monoetherification of the starting glycols. The polymerizations kinetics of the monomers were examined at several temperatures in the bulk and in dioxane solutions. NMR spectroscopy and electron paramagnetic resonance techniques were used to study the kinetics of polymerization. The polymerization rate parameter, expressed as (2f)^1/2k_p/〈k_t〉^1/2, and the values of the propagation rate coefficient k_p and the termination rate coefficient 〈k_t〉/f, where f is the efficiency factor of the initiator, were determined. The reactivity of the monomers depended on the size of the ester residue in such a way that the longer the lateral chain was, the higher the polymerization rate was and the lower the termination rate coefficient was. On the contrary, the dependence of k_p on the chemical structure was very small. In the solution polymerizations of all these monomers (monomer concentration = 1 mol L^?1), the radical concentrations remained almost constant until very high conversions, whereas in the bulk, a different behavior was observed that depended on the number of oxyethylene units in the side chain of the monomer. In this sense, for n = 4, 5, or 6, the radical concentration remained almost invariable with the reaction time, whereas for n = 3, a moderate increase occurred at low conversions, contrasting with the important increase observed at similar conversions for n = 1. This showed that the gel effect in these methacrylic monomers was greatly dependent on the number of bonds of the lateral chain. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1567–1579, 2003     

Molecular weight distributions and moments for condensation polymerizations characterized by two rate constants

Molecular weight distributions (MWD) and moments have been computed for condensation polymerizations of ARB-type monomers wherein the reactions involving the monomer are characterized by a rate constant k₁₁ and those involving other species, by k_p. For k₁₁/k_p < unity, the MWD curves are found to split into two, one for even n and one for odd values of n. Substantial amounts of unreacted monomer are found in the reaction mass for this case and so moments and the polydispersity index computed without the monomer are better representations of the distributions. For k₁₁/k_p > unit, conventional MWDs are observed with dispersions different from those representing polymerizations satisfying the equal reactivity hypothesis.     

Determination of absolute rate constants for free radical polymerization of ethyl α-fluoroacrylate and characterization of the polymer

The absolute rate constants for propagation (k_p) and for termination (k_t) of ethyl α-fluoroacrylate (EFA) were determined by means of the rotating sector method; k_p = 1120 and k_t = 4.8 × 10⁸ L/mol.s at 30°C. The monomer reactivity ratios for the copolymerizations with various monomers were obtained. By combining the k_p values for EFA from the present study and those for common monomers with the monomer reactivity ratios, the absolute values of the rate constants for cross-propagations were also evaluated. Reactivities of EFA and poly(EFA) radical, being compared with those of methyl acrylate and its polymer radical, were found to be little affected by the α-fluoro substitution. Poly(EFA) prepared with the radical initiator was characterized by differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Although the glass transition temperature obtained by DSC for poly(EFA) resembled that of poly(ethyl α-chloroacrylate), its TGA thermogram showed fast chain de polymerization to EFA that was distinct from complicated degradation of poly(ethyl α-chloroacrylate).     

Propagation rate coefficients of isobornyl acrylate,tert‐butyl acrylate and 1‐ethoxyethyl acrylate: A high frequency PLP‐SEC study

Pulsed laser polymerization (PLP) coupled to size exclusion chromatography (SEC) is considered to be the most accurate and reliable technique for the determination of absolute propagation rate coefficients, k_p. Herein, k_p data as a function of temperature were determined via PLP‐SEC for three acrylate monomers that are of particular synthetic interest (e.g., for the generation of amphiphilic block copolymers). The high‐T_g monomer isobornyl acrylate (iBoA) as well as the precursor monomers for the synthesis of hydrophilic poly(acrylic acid), tert‐butyl acrylate (tBuA), and 1‐ethoxyethyl acrylate (EEA) were investigated with respect to their propagation rate coefficient in a wide temperature range. By application of a 500 Hz laser repetition rate, data could be obtained up to a temperature of 80 °C. To arrive at absolute values for k_p, the Mark‐Houwink parameters of the polymers have been determined via on‐line light scattering and viscosimetry measurements. These read: K = 5.00 × 10⁵ dL g⁻¹, a = 0.75 (piBoA), K = 19.7 × 10⁵ dL g⁻¹, a = 0.66 (ptBA) and K = 1.53 × 10⁵ dL g⁻¹, a = 0.85 (pEEA). The bulky iBoA monomer shows the lowest propagation rate coefficient among the three monomers, while EEA is the fastest. The activation energies and Arrhenius factors read: (iBoA): log(A/L mol⁻¹ s⁻¹) = 7.05 and E_A = 17.0 kJ mol⁻¹; (tBuA): log(A/L mol⁻¹ s⁻¹) = 7.28 and E_A = 17.5 kJ mol⁻¹ and (EEA): log(A/L mol⁻¹ s⁻¹) = 6.80 and E_A = 13.8 kJ mol⁻¹. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6641–6654, 2009     

A calorimetric study of acrylate photopolymerization

The kinetics of the photoinitiated polymerization of lauryl acrylate (LA), 1,6-hexanedioldiacrylate (HDDA) and pentaerythritol tetraacrylate (PET₄A) have been investigated using differential scanning calorimetry (DSC). An autoacceleration phenomenon is observed with the multifunctional acrylates, but not with lauryl acrylate. The empirical dependences of reaction rate on such parameters as incident light intensity, initiator concentration, and temperature have been established and are in general found to vary with monomer conversion. Apparent activation energies for the photopolymerizations have been determined from rate versus temperature data. The multifunctional acrylates show an increasing activation energy with monomer conversion, whereas the apparent activation energy for lauryl acrylate not only decreases with conversion, but becomes negative at conversions greater than about 30%. The ratio k_p/k is calculated from rate versus conversion data under constant illumination and the (independently determined) initiation rate. Analysis of rate versus time data under nonsteady-state conditions (light turned off) yields the ratio k_t/k_p. With these two ratios the rate constants for propagation (k_p) and termination (k_t) may be separated and their respective values calculated. Both k_p and k_t are found to decrease substantially with monomer conversion, indicating a significant change in the rates of both the propagation and termination steps as the polymerization advances. These observations are explained in terms of a radical isolation phenomenon and diffusion control of the propagation step.     

Free-radical polymerization of vinyl ferrocene

The results of quantitative studies of the rates of free-radical polymerization of vinyl ferrocene indicate that the latter has polymerization characteristics similar to those of styrene. The rates of homopolymerization of these two monomers in benzene at 70°C. were measured with the use of azobisisobutyronitrile as catalyst. The rate constants (k = R_p/[M][I]^1/2) are k_VF = (1.1 ? 1.8) × 10^?4, k_STY = 1.65 × 10^?4. Small amounts of vinyl ferrocene and styrene have similar effects on the rates of polymerizations of methyl methacrylate and ethyl acrylate and on the molecular weights of the resulting polymer. Polystyrene and poly(vinyl ferrocene) with similar molecular weights are isolated from polymerizations carried out under identical conditions. The rates of copolymerization of vinyl ferrocene—methyl methacrylate, vinyl ferrocene—styrene, and styrene—methyl methacrylate were determined by following the disappearance of monomers by means of gas chromatographic analyses. The relative reactivity for vinyl ferrocene is slightly lower than that for styrene.     

Comparative study of the absolute reactivity of vinyl monomers: Kinetics of polymerization of vinyl monomers initiated by Mn3+–thiodiglycolic acid redox system

The kinetics and mechanism of polymerization of methacrylic acid (MAA) and ethyl acrylate (EA) initiated by the redox system, Mn³⁺–thiodiglycolic acid (TDGA) were investigated in the 15–35°C temperature range. The polymerization kinetics of both the monomers followed the same mechanism, viz., initiation by primary radical and termination by Mn³⁺–thiodiglycolic acid complex. The rate coefficients k_i/k₀ and k_p/k_t were related to the monomer reactivity and polymer radical reactivity, respectively. It was observed that both monomer reactivity and polymer radical reactivity followed the same order, viz., EA > MAA. The polymer radical reactivity varied inversely with the Q values of the monomers.     

Photosensitization of vinyl polymerization by uranyl ions

Monomer acrylamide was used as quencher of uranyl ion fluorescence and Stern-Volmer plots were constructed at three monochromatic wavelengths of exciting radiation. The results indicated that the reaction between excited uranyl ion and monomer is one of energy transfer. The rate parameters k_p/k_p^½ and k_d′/k_i were calculated from the polymerization kinetics at high monomer concentrations. A general mechanism for the photopolymerization of vinyl monomers sensitized by uranyl ions is proposed and discussed.     

Propagation Kinetics of Isoprene Radical Homopolymerization Derived from Pulsed Laser Initiated Polymerizations

The propagation kinetics of isoprene radical polymerizations in bulk and in solution are investigated via pulsed laser initiated polymerizations and subsequent polymer analyses via size‐exclusion chromatography, the PLP‐SEC method. Because of low polymerization rate and high volatility of isoprene, the polymerizations are carried out at elevated pressure ranging from 134 to 1320 bar. The temperatures are varied between 55 and 105 °C. PLP‐SEC yields activation parameters of k_p (Arrhenius parameters and activation volume) over a wide temperature and pressure range that allow for the calculation of k_p at technically relevant ambient pressure conditions. The k_p values determined are very low, e.g., 99 L mol^?1 s^?1 at 50 °C, which is even lower than the corresponding value for styrene polymerizations. The presence of a polar solvent results in a slight increase of k_p compared to the bulk system. The k_p values reported are important for determining rate coefficients of other elemental reactions from coupled parameters as well as for modeling isoprene free‐radical polymerizations and reversible deactivation radical polymerization with respect to tailored polymer properties and optimizing the polymerization processes.     

Aqueous Polymerization on Clay Surface. 2. The Polymerization of Methyl Methacrylate on Hydrogen Bentonite: Effect of Monomer Concentration and Temperature

Aqueous free radical polymerizations of methyl methacrylate with the hydrogen bentonite/ethanol system have been accomplished with less transfer to monomer in spite of high monomer concentrations and temperature. The overall initial rate has a first-order dependence on monomer. It is proposed that initiation does not occur in the aqueous phase. The apparent activation energy of 15 kcal/mol corroborates a twofold increase in rate for a 10°C rise in temperature. The frequency of bimolecular termination is quite small as is evident from k_p ² /k_t, values at various temperatures.     

A simplified data treatment for dead-end and high conversion polymerization kinetics

A simplified approximation method for the treatment of dead-end and high conversion polymerization kinetics is presented. The method is based on the treatment of dead-end polymerization first described by Tobolsky. In appropriate circumstances, by contrast with Tobolsky's method, this method provides measurements of k_d and k_p/k_t^1/2 without recourse to the measurement of the monomer conversion at infinite time. Kinetic studies of free radical polymerizations are normally confined to measurements of initial rates. At low conversions the predictions of the general mechanism for chain-growth polymerization involving initiation, propagation, and termination steps are generally obeyed. Thus the polymerization rate should be first order in the vinyl monomer and half-order in the initiator concentrations. At high conversions, however, large deviations which can be ascribed to various effects can occur; for example, (1) the effect of the increasing viscosity of the polymerization medium on the termination rate constant k_t, and possibly also on the propagation rate constant k_p, which have been considered by North¹ and Cardenas and O'Driscoll,² or (2) depletion of the initiator as the polymerization progresses. This depletion will occur in all polymerizations but its significance will depend on the magnitude of the rate constant for initiator decomposition (k_d) and the period of polymerization. Appropriate conditions will lead to limiting monomer conversion even after infinite polymerization time; this phenomenon has been called dead-end polymerization by Tobolsky.³ Free radical polymerizations to high conversion are particularly important in the industrial context when initial kinetics are obviously inadequate. Suitable treatment of the conversion/time relationship is highly desirable. Senogles and Woolf⁴ have examined the polymerization of n-lauryl methacrylate at 60°C with 2-azobisisobutyronitrile as initiator under dead-end conditions. Here we propose a modification of Tobolsky's treatment of such polymerizations by using an approximation for the exponential decay in the initiator concentration. This method permits easy manipulation of the experimental data and the estimation of values for the kinetic parameters in favorable circumstances without recourse to the measurement of the conversion at infinite time or the evaluation of complicated functions of the monomer conversion. The method thus allows the duration of the laboratory experimentation to be significantly shortened and the complexity of the subsequent data analysis to be considerably reduced.     

On the origin of ionic liquid‐induced variations in hydroxypropyl methacrylate propagation rate coefficients

Pulsed laser polymerizations were used to study the propagation kinetics of hydroxypropyl methacrylate (HPMA) in ionic liquids (ILs) and common organic solvents. The functional monomer was chosen to investigate the complex interplay of all interactions between monomer molecules and between monomer and solvent molecules and to obtain a deeper understanding of the impact of these interactions. The solvent effect on the HPMA propagation rate coefficient (k_p) was examined using a linear solvation energy relationship (LSER) based on Kamlet‐Taft solvatochromic parameters π*, α, and β. The results suggest that dipolarity/polarizability, associated with π*, and hydrogen bond–donating ability of the solvents, accounted for by α, majorly contribute to variations in k_p. Hydrogen bond–accepting (electron pair donating) ability of the solvents (β parameter) is of much lesser importance. In addition, LSER enables the prediction of HPMA k_p based on solvatochromic parameters of the solvents. The results suggest that interactions between the hydroxyl group of the monomer and the anion are dominant compared with classical hydrogen bonding between carbonyl and hydroxyl groups of the monomer units. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3188–3199, 2010     

The influence of steric factors on the mechanism of copolymerization of phenylvinyl alkyl ethers and maleic anhydride

By assuming that the initial rate of copolymerization (R_p) of phenylvinyl alkyl ether (I) and maleic anhydride (MAn) equals the sum of the rate of polymerization of free monomers R_p(f) and CT complex monomers R_p(CT) the reactivity ratios k_1c/k₁₂ and k_2c/k₂₁ were calculated for copolymerization of I(R = Me, n-Pr, iso-Pr, and sec-Bu) and MAn from the change of copolymerization rate with monomer feed at a constant total monomer concentration. From the equation R_p = R_p(f) + R_p(CT) were calculated R_p(f) and R_p(CT) by applying the generalized model described by Shirota and coworkers and it was found that the participation of CT complex monomers increases with an increase in total monomer concentration in the feed. It was also found that the degree of CT complex monomer participation depends largely on the steric factors. In the copolymerization of I which contains bulky isopropyl or sec-butyl group even in the dilute solutions, copolymerization proceeds by the addition of CT complex monomers.     

Polymerization Kinetics of Water-Soluble N-Vinyl Monomers in Aqueous and Organic Solution

Summary: Free-radical batch polymerization (FRP) of N-vinyl pyrrolidone (NVP) and N-vinyl formamide (NVF) monomers in aqueous solution as well as NVP polymerization in organic (n-butanol) solution has been studied. The differences found in rate of monomer conversion with monomer and solvent choice correlates well with the differences in values of the propagation rate coefficients (k_p) and their variation with monomer concentration measured in independent pulsed-laser polymerization studies, a result demonstrating that a generalized understanding of water-soluble vinyl monomers can be obtained once their k_p differences have been accounted for. A reasonable representation of polymer molecular mass averages and the complete molecular mass distributions for the three systems was obtained by assuming that the rate coefficient for transfer to monomer, polymer, and organic solvent also vary as a function of monomer concentration.     

Synthesis and kinetics of polymerization of hydrophilic monomers: 2,3-dihydroxypropylacrylate and 2,3-dihydroxypropylmethacrylate

Unsaturated monomers containing none, one, or two hydroxyl groups were obtained by the reaction of glycerol (1,2,3-trihydroxypropane) with acrylic and methacrylic chloride. The experimental values of the mole fractions of the different monomers were compared with those theoretically obtained by considering different mechanisms involving two or seven kinetic constants. Agreement between the theoretical and experimental results could only be achieved by assuming that the reactivity of the hydroxyl groups changed with the presence of the substituents. The investigation of the radical polymerizations 2,3-dihydroxypropylacrylate (GA) and 2,3-dihydroxypro- pylmethacrylate (GM) was carried out at several temperatures in water–dioxane solutions. Ultraviolet spectroscopic techniques were used to determine the kinetic constants, and the results were compared with those obtained in the same conditions for methyl acrylate, methyl methacrylate, 2-hydroxyethylacrylate, and 2-hydroxyethylmethacrylate. The values of the ratio k_p/k_t^1/2 for the methacrylic monomer GM were higher than 0.5 L^1/2 mol^−1/2 s^−1/2 at temperatures between 50 and 65 °C. These values exceeded 2 L^1/2 mol^−1/2 s^−1/2 for the acrylic monomer GA, perhaps the highest values reported for this kind of monomer. Electron paramagnetic resonance spectroscopy was also used to study the polymerization of GM. All the polymers were soluble in the reaction mixture until very high conversions, and the gel effect was never detected at monomer concentrations equal to or lower than 1 mol L⁻¹. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1843–1853, 2001     

Influence of the stereochemical configuration on the radical polymerization of methacrylic monomers: cis‐ and trans‐(2‐cyclohexyl‐1,3‐dioxan‐5‐yl) methacrylate

The synthesis of two new isomeric monomers, cis‐(2‐cyclohexyl‐1,3‐dioxan‐5‐yl) methacrylate (CCDM) and trans‐(2‐cyclohexyl‐1,3‐dioxan‐5‐yl) methacrylate (TCDM), starting from the reaction of glycerol and cyclohexanecarbaldehyde, is reported. The process involved the preparation of different alcohol acetals and esterification with methacryloyl chloride of the corresponding cis and trans 5‐hydroxy compounds of 2‐cyclohexyl‐1,3‐dioxane. The radical polymerization reactions of both monomers, under the same conditions of temperature, solvent, monomer, and initiator concentrations, were studied to investigate the influence of the monomer configuration on the values of the propagation and termination rate constants (k_p and k_t ).The values of the ratio k_p /k_t ^1/2 were determined by UV spectroscopy by the measurement of the changes of absorbance with time at several wavelengths in the range 275–285 nm, where an appropriate change in absorbance was observed. Reliable values of the kinetics constants were determined by UV spectroscopy, showing a very good reproducibility of the kinetic experiments. The values of k_p /k_t ^1/2, in the temperature interval 45–65 °C, lay in the range 0.40–0.50 L^1/2/mol^1/2s^1/2 and 0.20–0.30 L^1/2/mol^1/2s^1/2 for CCDM and TCDM, respectively. Measurements of both the radical concentrations and the absolute rate constants k_p and k_t were also carried out with electron paramagnetic resonance techniques. The values of k_p at 60 °C were nearly identical for both the trans and cis monomers, but the termination rate constant of the trans monomer was about three times that of the cis monomer at the same temperature. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3883–3891, 2000     

Photopolymerization of styrene,p-chlorostyrene,methyl methacrylate,and butyl methacrylate with polymethylphenylsilane as photoinitiator

The rates of photochemical polymerization of styrene (St), p-chlorostyrene (Cl-St), methyl methacrylate (MMA), and butyl methacrylate (BMA) with polymethylphenylsilane (PMPS) as an initiator were measured. Polymethylphenylsilane is photodegrated to form silyl radicals that may initiate polymerization of vinyl monomers. Rate constants k_p and k_t have been determined for these systems. A good correlation (log P = α + βμ) of the resonance stabilization (P) of the chain radicals and the dipole moment (μ) of the monomers is observed for these polymerization systems. This equation may be used to estimate the resonance stabilization (P) of a monomer and the polymerization rate constant (k_p). © 1996 John Wiley & Sons, Inc.     

Tricarbonylchromium complexes of styrenes in radical copolymerization

The organometallic monomers styrenetricarbonylchromium and p‐methylstyrenetricarbonylchromium were copolymerized in ethyl acetate solutions with methyl methacrylate and butyl acrylate using azobisisobutyronitrile at 50 °C and a binary system including di‐tert‐butylperoxytriphenylantimony at 30 °C as the free‐radical initiators. Comonomers are proposed to form a molecular complex based on the results of ultraviolet and electron spin resonance spectroscopy. A kinetic study shows that chromium‐containing monomers at high concentrations in the mixture reduce the rate of copolymerization. The addition of styrenetricarbonylchromium to butyl acrylate significantly slows down the autoacceleration. The reactivity ratios of the comonomer pairs, namely, styrenetricarbonylchromium–methyl methacrylate, styrenetricarbonylchromium–butyl acrylate and p‐methylstyrenetricarbonylchromium–methyl methacrylate, were determined using the method of Kelen–Tudos for low conversion polymerizations.Copyright © 2001 John Wiley & Sons, Ltd.