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     

Kinetics and mechanism of the cationic polymerization of trioxane. II. Consideration of hydride transfer

The occurrence of hydride-transfer reactions during the cationic polymerization of trioxane was demonstrated, and rate constants were obtained. The donor of hydride ions in the transfer reactions was the monomer. The hydride-transfer reaction was a first-order reaction with respect to the concentration of the monomer, and it was governed, just as polymerization and depolymerization were (Shieh, Y. T.; Chen. S. A. J. Polym. Sci. Part A: Polym. Chem. 1999, 37, 483–492) by morphological changes. The hydride-transfer rate constants were 5 orders of magnitude smaller than those for polymerizations and depolymerizations. The rate constants for the reactions, including the polymerizations, depolymerizations, and hydride transfers, were smaller for the active centers on the solid surface than for those in solution, that is, k^′_p was less than k_p, k^′_d was less than k_d, and k^′_ht was less than k_ht. As a reaction medium, benzene had special effects on the kinetics of the cationic polymerization of trioxane. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 4198–4204, 1999     

Determination of propagation‐rate constant of vinylidene chloride by emulsion polymerization

The propagation‐rate constant of vinylidene chloride (VDC) was determined at 40 and 50 °C, respectively, by applying the so‐called Ugelstad plot to the polymerization‐rate data of the seeded and unseeded emulsion polymerizations of VDC. The values of the propagation‐rate constant k_p thus determined are k_p = 64 dm³/mol · s at 50 °C and k_p = 52 dm³/mol · s at 40 °C, respectively. From these k_p values, the activation energy for propagation reaction was determined to be E_p = 4.2 kcal/mol, which is close to that of vinyl chloride (3.7 kcal/mol). © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1005–1015, 2001     

Kinetics and mechanism of metallocene‐catalyzed olefin polymerization: Comparison of ethylene,propylene homopolymerizations,and their copolymerization

A series of ethylene, propylene homopolymerizations, and ethylene/propylene copolymerization catalyzed with rac‐Et(Ind)₂ZrCl₂/modified methylaluminoxane (MMAO) were conducted under the same conditions for different duration ranging from 2.5 to 30 min, and quenched with 2‐thiophenecarbonyl chloride to label a 2‐thiophenecarbonyl on each propagation chain end. The change of active center ratio ([C^*]/[Zr]) with polymerization time in each polymerization system was determined. Changes of polymerization rate, molecular weight, isotacticity (for propylene homopolymerization) and copolymer composition with time were also studied. [C^*]/[Zr] strongly depended on type of monomer, with the propylene homopolymerization system presented much lower [C^*]/[Zr] (ca. 25%) than the ethylene homopolymerization and ethylene–propylene copolymerization systems. In the copolymerization system, [C^*]/[Zr] increased continuously in the reaction process until a maximum value of 98.7% was reached, which was much higher than the maximum [C^*]/[Zr] of ethylene homopolymerization (ca. 70%). The chain propagation rate constant (k_p) of propylene polymerization is very close to that of ethylene polymerization, but the propylene insertion rate constant is much smaller than the ethylene insertion rate constant in the copolymerization system, meaning that the active centers in the homopolymerization system are different from those in the copolymerization system. Ethylene insertion rate constant in the copolymerization system was much higher than that in the ethylene homopolymerization in the first 10 min of reaction. A mechanistic model was proposed to explain the observed activation of ethylene polymerization by propylene addition. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 867–875     

Free radical dispersion polymerization of styrene in a mixture of 2-propanol and tetrahydrofuran

Free radical dispersion polymerization of styrene in a mixture of 2-propanol and tetrahydrofuran was carried out at 70°C up to high conversions. The influence of the change of the critical chain length on the evolution of the insoluble polymer component was examined. Monomer conversion and the formation of the insoluble polymer component were measured in order to test a mathematical model presented in our previous article. The critical polymer chain length i₀, the initiation rate constant k_d, and the ratio k_p/k, where k_p and k_t are propagation and termination rate constants, respectively, have been obtained and compared with those reported in the literature. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2757–2761, 1998     

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.     

Kinetic elucidation of comonomer‐induced chemical and physical activation in heterogeneous ziegler‐natta propylene polymerization

We have kinetically elucidated the origins of activity enhancement because of the addition of comonomer in Ziegler‐Natta propylene polymerization, using stopped‐flow and continuously purged polymerization. Stopped‐flow polymerization (with the polymerization time of 0.1–0.2 s) enabled us to neglect contributions of physical phenomena to the activity, such as catalyst fragmentation and reagent diffusion through produced polymer. The propagation rate constant k_p and active‐site concentration [C*] were compared between homopolymerization and copolymerization in the absence of physical effects. k_p for propylene was increased by 30% because of the addition of a small amount of ethylene, whereas [C*] was constant. On the contrary, both k_p (for propylene) and [C*] remained unchanged by the addition of 1‐hexene. Thus, only ethylene could chemically activate propylene polymerization. However, continuously purged polymerization for 30 s resulted in much more significant activation by the addition of comonomer, clearly indicating that the activation phenomenon mainly arises from the physical effects. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

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     

Polymerization of neat 2‐ethylhexyl acrylate induced by a pulsed electron beam

The bulk polymerization of 2‐ethylhexyl acrylate (2‐EHA), induced by a pulsed electron beam, was investigated with pulse radiolysis, gravimetry, and Fourier transform infrared spectroscopy. The roles of the dose rate, pulse frequency, and added acrylic acid (AA) in the polymerization of 2‐EHA were examined at ambient temperature. In the range of 12.6–71.2 Gy/pulse, the polymerization of 2‐EHA was dose‐rate‐dependent: at the same total dose, a lower dose rate yielded a higher conversion. Also, a lower pulse rate gave a higher conversion at the same total dose. The addition of up to 10 wt % AA showed no increase in the conversion of 2‐EHA at a low conversion (8 kGy), but at a higher conversion (16 kGy), a 20 wt % increase in the conversion of 2‐EHA was observed. The estimated values (1.6 ± 0.3) × 10^?3 (dm³ s)^3/2 mol^?1 s^?1/2 for k_p(G/2k_t)^1/2 and 2.6 ± 0.8 dm³ s J^?1 for 2k_tG (where k_p is the rate constant of propagation, k_t is the rate constant of bimolecular termination, and G is the yield of free radicals) were obtained at relatively low conversions. The reaction rate constant of the addition of 2‐EHA^· free radicals to the monomer was measured by pulse radiolysis and found to be 2.8 × 10² mol^?1 dm³ s^?1. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 196–203, 2003     

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     

Modeling the Effects of Chain Length on the Termination Kinetics in Multivinyl Photopolymerizations

A model is presented that predicts photopolymerization kinetics over several orders of magnitude change in initiation rate. The model incorporates polymerization features that have long been assumed negligible when examining multivinyl photopolymerizations. The assumption that radical termination is chain‐length‐independent is relaxed by incorporating a chain‐length‐dependent termination (CLDT) parameter based on Random‐walk theory into the kinetic model. Experiments and modeling of multivinyl free‐radical photopolymerizations clearly demonstrate that CLDT is important at low conversions, where a deviation from the classical square‐root relationship between polymerization rate (R_p) and initiation rate (R_i) is observed (R_p ∝ R _i^α, α = ¹/₂, classically). At moderate conversions, when reaction diffusion dominates termination, a transition region is observed from a chain‐length‐dependent to a chain‐length‐independent region. During this transition, long chain – long chain termination is reaction diffusion controlled while the short chain – short chain termination event remains translational and segmental diffusion controlled. The scaling exponent, α, gradually increases throughout this region until achieving the classical value, where once attained, a plateau is observed. Chain‐length effects were also examined by including chain‐transfer (CT) reactions into the kinetic expressions. Upon CT agent addition, a transition region is still observed; however, at low conversion, α adheres more closely to the classical predictions. Most importantly, the model clearly demonstrates a transition from a CLDT region at low conversion to reaction diffusion controlled termination region at high conversion, where chain length is unimportant.     

Photoinitiated,inverse emulsion polymerization of acrylamide: Some mechanistic and kinetic aspects

The kinetics of photoinitiated, inverse emulsion polymerization of acrylamide with 2,2‐dimethoxy‐2‐phenylacetophenone (DMPA) as a photoinitiator was investigated under three different cases. First, in a quartz reactor transparent to full UV light, the polymerization rate (R_p) increased and then decreased with the change of initiator order from 0.27 to a negative value when the DMPA concentration was increased, and it was particularly unusual that monomer orders at different DMPA concentrations were lower than the first. Second, for polymerization without DMPA in a quartz reactor, the dependence of R_p on monomer concentration was similar to that of R_p on initiator concentration in the aforementioned case. Third, when polymerization was carried out in a Pyrex reactor where the far UV light was filtered, a peak rate was also observed, and initiator orders varied from 0.24 to a negative value; however, under this case monomer orders at different initiator concentrations were greater than the first. These results indicated that the effect of absorbance often observed in bulk or solution photopolymerization also existed in this system, and the self‐initiation of monomer had some influence on polymerization, and the role of primary radical termination could not be neglected, as evidenced by kinetic analysis. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 846–852, 2004     

The kinetics of enhanced spin capturing polymerization: Influence of the nitrone structure

Several nitrones and one nitroso compound have been evaluated for their ability to control the molecular weight of polystyrene via the recently introduced radical polymerization method of enhanced spin capturing polymerization (ESCP). In this technique, molecular weight control is achieved (at ambient or slightly elevated temperatures) via the reaction of a growing radical chain with a nitrone forming a macronitroxide. These nitroxides subsequently react rapidly and irreversibly with propagating macroradicals forming polymer of a certain chain length, which depends on the nitrone concentration in the system. Via evaluation of the resulting number‐average molecular weight, M_n, at low conversions, the addition rate coefficient of the growing radicals onto the different nitrones is determined and activation energies are obtained. For the nitrones N‐tert‐butyl‐α‐phenylnitrone (PBN), N‐methyl‐α‐phenylnitrone (PMN), and N‐methyl‐α‐(4‐bromo‐phenyl) nitrone (pB‐PMN), addition rate coefficients, k_ad,macro, in a similar magnitude to the styrene propagation rate coefficient, k_p, are found with spin capturing constants C_SC (with C_SC = k_ad,macro/k_p) ranging from 1 to 13 depending on the nitrone and on temperature. Activation energies between 23.6 and 27.7 kJ mol⁻¹ were deduced for k_ad,macro, congruent with a decreasing C_SC with increasing temperature. Almost constant M_n over up to high monomer to polymer conversions is found when C_SC is close to unity, while increasing molecular weights can be observed when the C_SC is large. From temperatures of 100 °C onward, reversible cleavage of the alkoxyamine group can occur, superimposing a reversible activation/deactivation mechanism onto the ESCP system. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1098–1107, 2009     

Modeling the polymerization behavior of vegetable‐oil‐derived macromonomers in solution by computer simulation

A computer simulation model was used to study the polymerization behavior of multifunctional, vegetable‐oil‐derived macromonomers. Mixtures of olefins (A) and acrylates (B) were initially randomly dispersed on a cubic lattice of size L³. Interactions between A, B, and the solvent sites were considered with respect to their relative proximity, mobility and some kinetics. The Metropolis algorithm was used to move each functional group (A and B). Stirred and equilibrated samples were prepared before reaction initiation. Reactions between the functional groups were implemented with a bonding probability k_αβ, which was subject to the availability of unsaturated bonds. The conversion factor, that is, the growth of A–B bonds, was analyzed for a range of polymer concentrations (p = 0.2–0.8) with different reaction probabilities (i.e., k_αβ). A stirred (nonequilibrium) sample did not allow sufficient time for the functional groups to arrange according to the interaction parameters. Therefore, the simulations were rerun with equilibrated samples and were found to be consistent with experimental observations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1164–1172, 2004     

Photoinitiated polymerization of methacrylic monomers in a polystyrene matrix: Kinetic,mechanistic, and structural aspects

The kinetics and mechanism of the photoinitiated polymerization of tetrafunctional and difunctional methacrylic monomers [1,6‐hexanediol dimethacrylate (HDDMA) and 2‐ethylhexyl methacrylate (EHMA)] in a polystyrene (PS) matrix were studied. The aggregation state, vitreous or rubbery, of the monomer/matrix system and the intermolecular strength of attraction in the monomer/matrix and growing macroradical/matrix systems are the principal factors influencing the kinetics and mechanism. For the PS/HDDMA system, where a relatively high intermolecular force of attraction between monomer and matrix and between growing macroradical and matrix occurs, a reaction‐diffusion mechanism takes place at low monomer concentrations (<30–40%) from the beginning of the polymerization. For the PS/EHMA system, which presents low intermolecular attraction between monomer and matrix and between growing macroradical and matrix, the reaction‐diffusion termination is not clear, and a combination of reaction‐diffusion and diffusion‐controlled mechanisms explains better the polymerization for monomer concentrations below 30–40%. For both systems, for which a change from a vitreous state to a rubbery state occurs when the monomer concentration changes from 10 to 20%, the intrinsic reactivity and k_p/k_t^1/2 ratio (where k_p is the propagation kinetic constant and k_t is the termination kinetic constant) increase as a result of a greater mobility of the monomer in the matrix (a greater k_p value). The PS matrix participates in the polymerization process through the formation of benzylic radical, which is bonded to some extent by radical–radical coupling with the growing methacrylic radica, producing grafting on the PS matrix. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2049–2057, 2001     

Kinetic study of light-induced polymerization by real-time UV and IR spectroscopy

Real time ultraviolet (RTUV) spectroscopy was used to study the photolysis kinetics of a radical-type morpholino initiator, during the polymerization of a multiacrylate monomer exposed to UV radiation in bulk, in solution, in a polyurethane-acrylate resin, and in a poly(methyl methacrylate) matrix. The photolysis rate constant k was determined from the exponential loss profile recorded; it was found to vary between 0.1 and 3s^?1, depending on the light intensity and on the monomer concentration. The quenching of the photoinitiator excited states by the acrylate monomer was shown to be an important deactivation pathway which substantially reduces the rate of initiation. The observed influence of the film thickness and photoinitiator concentration on the k value were accounted for by the internal filter effect. Conversion versus time curves were recorded by real time infrared (RTIR) spectroscopy for the various systems examined, thus allowing a direct comparison of both the actual polymerization rate and the residual unsaturation content of the cured polymer. Various factors were shown to be responsible for the early stop of the polymerization, such as depletion of the photoinitiator, O₂ inhibition, or vitrification of the polymer. The photoinitiated cationic ring-opening polymerization of a cycloaliphatic diepoxy monomer was also studied in real time by RTUV and RTIR spectroscopy. Despite a very fast photolysis of the triarylsulphonium initiator, the polymerization of the epoxy monomer developed less rapidly than for the acrylic monomer, with shorter kinetic chain lengths. A linear relationship was found to exist between the decay rate constant and the light intensity, for both the radical and the cationic photoinitiators, as expected for a direct photolysis process.     

Ring‐Closing Metathesis Reactions: Interpretation of Conversion–Time Data

Conversion–time data were recorded for various ring‐closing metathesis (RCM) reactions that lead to five‐ or six‐membered cyclic olefins by using different precatalysts of the Hoveyda type. Slowly activated precatalysts were found to produce more RCM product than rapidly activated complexes, but this comes at the price of slower product formation. A kinetic model for the analysis of the conversion–time data was derived, which is based on the conversion of the precatalyst (Pcat) into the active species (Acat), with the rate constant k_act, followed by two parallel reactions: 1) the catalytic reaction, which utilizes Acat to convert reactants into products, with the rate k_cat, and 2) the conversion of Acat into the inactive species (Dcat), with the rate k_dec. The calculations employ two experimental parameters: the concentration of the substrate (c(S)) at a given time and the rate of substrate conversion (?dc(S)/dt). This provides a direct measure of the concentration of Acat and enables the calculation of the pseudo‐first‐order rate constants k_act, k_cat, and k_dec and of k_S (for the RCM conversion of the respective substrate by Acat). Most of the RCM reactions studied with different precatalysts are characterized by fast k_cat rates and by the k_dec value being greater than the k_act value, which leads to quasistationarity for Acat. The active species formed during the activation step was shown to be the same, regardless of the nature of different Pcats. The decomposition of Acat occurs along two parallel pathways, a unimolecular (or pseudo‐first‐order) reaction and a bimolecular reaction involving two ruthenium complexes. Electron‐deficient precatalysts display higher rates of catalyst deactivation than their electron‐rich relatives. Slowly initiating Pcats act as a reservoir, by generating small stationary concentrations of Acat. Based on this, it can be understood why the use of different precatalysts results in different substrate conversions in olefin metathesis reactions.     

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.     

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.     

Kinetic study of high-conversion copolymerization of butyl acrylate with methyl methacrylate in solution

Butyl acrylate (BA) and methyl methacrylate (MMA) have been copolymerized in a 3 mol/L benzene solution using 2,2′-azobis(isobutyronitrile) (AIBN) as initiator over a wide composition and conversion range. The overall copolymerization parameter k_p/k_t^1/2 and the composition of the copolymer formed have been measured as a function of conversion. Theoretical values of the coupled parameter k_p/k_t^1/2 calculated from the implicit penultimate unit model and those of cumulative copolymer composition, determined from the Mayo—Lewis terminal model, have been correlated with those experimentally obtained. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 1961–1965, 1997