Collision between polymeric radicals for termination rate constants

The motion of each polymeric radical during a collision between the polymeric radicals with the same radius is treated as completely random motion. The result obtained is: k_t = 0.250k_s (where k_t is the chain-termination rate constant and k_s is the reaction rate constant between radical chain ends). On taking the motion of the primary radical during a collision between a primary radical and a large polymeric radical to be completely random, the result obtained is: k_ti = 0.250k_si (where k_ti is the primary radical termination rate constant and k_si is the reaction rate constant between primary radical and radical chain end). On substituting k_s for k_si in the second equation, the rate constant obtained becomes the chain termination rate constant between the very small polymeric radical and the very large polymeric radical, and identical to the former equation. This identity indicates that the effect of the difference of the size of the polymeric radicals on the collision process relating to the chain termination rate constant should not be large.     

Kinetics of polymerization rate based on the dependence of termination rate on chain length

When the structure of a primary radical resembles that of the chain end of the polymer radical, the rate of the primary radical termination is approximately the same as the termination rate between the oligomer radical and the polymer radical. The rate constant of termination between polymer radicals of chain length n and s, which involve the primary radicals, is k_t,ns = const.(ns)^?a. In the polymerization of methacrylonitrile initiated by 2,2′-azobisisobutyronitrile in dimethylformamide at 60.0°C, the value of a is found to be 0.091. From data obtained previously in the bulk polymerization of styrene initiated by 1-azobis-2-phenylethane at 60.0°C, the value of a is found to be 0.167. Because such a values are so large that they are not estimated by the excluded volume, the termination rates are discussed by adding the dependence of the diffusion of the segments to that for chain length.     

Relationship between chain termination rate constant and conversion in radical polymerization

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

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).     

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 analysis of styrene atom transfer radical polymerization: Extraction of radical‐radical termination rate coefficients

Kinetic studies of the atom transfer radical polymerization (ATRP) of styrene are reported, with the particular aim of determining radical‐radical termination rate coefficients (<k_t>). The reactions are analyzed using the persistent radical effect (PRE) model. Using this model, average radical‐radical termination rate coefficients are evaluated. Under appropriate ATRP catalyst concentrations, <k_t> values of approximately 2 × 10⁸ L mol^?1 s^?1 at 110 °C in 50 vol % anisole were determined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5548–5558, 2004     

Gas phase decomposition and isomerization reactions of 2-pentoxy radicals

The rate of decomposition of 2-pentoxy radical to acetaldehyde and n-propyl radical has been studied in the presence of NO in competition with nitrite formation at and above 200 kPa pressure over the temperature range of 363-413 K. The rate coefficient for the decomposition is given as log(k_la/s^?1) = (14.2 ± 0.4) - (13.8 ± 0.8) kcal mol^?1/RT ln 10. Isomerization of 2-pentoxy radical by 1,5-hydrogen shift has been investigated in the range 279–385 K in competition with the decomposition in a static system, with methyl radicals present in high concentration to ensure trapping of the isomerized free radicals. The rate coefficient for isomerization is given as log(k₃/s^?1) = (11.1 ± 0.7) - (9.5 ± 1.1) kcal mol^?1/RT ln 10. The implications of the results for atmospheric chemistry are discussed.     

Modeling the reversible addition–fragmentation chain transfer process in cumyl dithiobenzoate‐mediated styrene homopolymerizations: Assessing rate coefficients for the addition–fragmentation equilibrium

A full kinetic scheme for the free‐radical reversible addition–fragmentation chain transfer (RAFT) process is presented and implemented into the program package PREDICI®. With the cumyl dithiobenzoate‐mediated bulk polymerization of styrene at 60 °C as an example, the rate coefficients associated with the addition–fragmentation equilibrium are deduced by the careful modeling of the time‐dependent evolution of experimental molecular weight distributions. The rate coefficient for the addition reaction of a free macroradical to a polymeric RAFT species (k_β) is approximately 5 · 10⁵ L mol^?1 s^?1, whereas the fragmentation rate coefficient of the formed macroradical RAFT species is close to 3 · 10^?2 s^?1. These values give an equilibrium constant of K = k_β/k_?β = 1.6 · 10⁷ L mol^?1. Conclusive evidence is given that the equilibrium lies well on the side of the macroradical RAFT species. The high value of k_β is comparable in size to the propagation rate coefficients reported for acrylates. The transfer rate coefficient to cumyl dithiobenzoate is close to 3.5 · 10⁵ L mol^?1 s^?1. A careful sensitivity analysis was performed, which indicated that the reported rate coefficients are accurate to a factor of 2. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1353–1365, 2001     

Modeling Termination Kinetics of Non‐Stationary Free‐Radical Polymerizations

Pulsed‐laser induced polymerization is modeled via an approach presented in a previous paper.^[1] An equation for the time dependence of free‐radical concentration is derived. It is shown that the termination rate coefficient may vary significantly as a function of time after applying the laser pulse despite of the fact that the change in monomer concentration during one experiment is negligible. For the limiting case of t ≫ c^–1 (k_pM)^–1, where c is a dimensionless chain‐transfer constant, k_p the propagation rate coefficient and M the monomer concentration, an analytical expression for k_t is derived. It is also shown that time‐resolved single pulse‐laser polymerization (SP–PLP) experiments can yield the parameters that allow the modeling of k_t in quasi‐stationary polymerization. The influence of inhibitors is also considered. The conditions are analyzed under which M (t) curves recorded at different extents of laser‐induced photo‐initiator decomposition intersect. It is shown that such type of behavior is associated with a chain‐length dependence of k_t.     

Initial Radical Separation after Photolysis of 2,2′‐Azobis(isobutyronitrile) (AIBN) in Solution: Modeling the Primary Cage Effect for Polar Radicals

There is a contradiction as to the initial spatial separation r_i of the two transient 2‐cyanoprop‐2‐yl radicals (Me₂ ? CN) formed by flash photolysis of 2,2′‐azobis(isobutyronitrile) (AIBN) in solvents of various viscosities. The cage effect, expressed in terms of the in‐cage termination probability of the resulting radicals, is predicted correctly by classical Langevin models assuming a decrease of r_i with increasing viscosity. However, the electron‐spin polarization of the radicals escaping the primary cage clearly indicates that the initial separation distance r_i is independent of the solution viscosity. This obvious discrepancy can be reconciled by accounting for the strong electric dipole moments of these radicals and the resulting inter‐radical dipole? dipole interaction potential. We propose a primary‐caging model for polar radicals in solution based on an attractive inter‐radical mean‐force potential. The model is applied to the flash photolysis of AIBN and shown to describe properly the viscosity dependence of both the in‐cage termination probability (cage effect) and the electron‐spin polarization of the escaping 2‐cyanoprop‐2‐yl radicals.     

Photopolymerization of methyl methacrylate with azo-containing polydimethylsiloxane as photoinitiator: Effect of siloxane chain length

The kinetics of the free radical photopolymerization of methyl methacrylate (MMA) initiated by azo-containing polydimethylsiloxane (PSMAI) and azobisisobutyronitrile (AIBN) was investigated. The greater polymerization rate R_p in MMA/PSMAI systems may be due to the higher value of the initiation rate R_i and the lower value of the termination rate constant k_t than that in MMA/AIBN system. The reaction orders with respect to initiators PSMAI decreased with an increase in polydimethylsiloxane chain length (SCL) in PSMAI. The observed deviations in polymerization rate from rate equation could be explained in terms of primary radical termination. The photoinitiator efficiency Φ of initiators decreased with increase in SCL, while the ratio of the rate constants for chain termination and chain initiation by primary radical increased with SCL. The fraction β of primary radicals entering into termination in MMA/PSMAI systems were larger than that in MMA/AIBN system. © 1996 John Wiley & Sons, Inc.     

Radical and cationic polymerizations of 3‐ethyl‐3‐methacryloyloxymethyloxetane

3‐Ethyl‐3‐methacryloyloxymethyloxetane (EMO) was easily polymerized by dimethyl 2,2′‐azobisisobutyrate (MAIB) as the radical initiator through the opening of the vinyl group. The initial polymerization rate (R_p) at 50 °C in benzene was given by R_p = k[MAIB]^0.55 [EMO]^1.2. The overall activation energy of the polymerization was estimated to be 87 kJ/mol. The number‐average molecular weight (M?_n) of the resulting poly(EMO)s was in the range of 1–3.3 × 10⁵. The polymerization system was found to involve electron spin resonance (ESR) observable propagating poly(EMO) radicals under practical polymerization conditions. ESR‐determined rate constants of propagation (k_p) and termination (k_t) at 60 °C are 120 and 2.41 × 10⁵ L/mol s, respectively—much lower than those of the usual methacrylate esters such as methyl methacrylate and glycidyl methacrylate. The radical copolymerization of EMO (M₁) with styrene (M₂) at 60 °C gave the following copolymerization parameters: r₁ = 0.53, r₂ = 0.43, Q₁ = 0.87, and e₁ = +0.42. EMO was also observed to be polymerized by BF₃OEt₂ as the cationic initiator through the opening of the oxetane ring. The M?_n of the resulting polymer was in the range of 650–3100. The cationic polymerization of radically formed poly(EMO) provided a crosslinked polymer showing distinguishably different thermal behaviors from those of the radical and cationic poly(EMO)s. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1269–1279, 2001     

The Influence of Chain Length‐Dependent Propagation on the Evaluation of the Chain Length Dependence of the Rate Coefficient of Bimolecular Termination, 1. PLP–SEC Methods

Chain length distributions have been calculated for polymers prepared by pulsed laser polymerization (PLP) under the condition that not only chain termination but also chain propagation is subject to chain length dependence. The interplay between these two features is analyzed with the chain length dependence of the rate coefficient of termination k_t introduced in the form of a power law and that of propagation k_p modeled by a Langmuir‐type decrease from an initial value for zero chain length to a constant value for infinite chain lengths. The rather complex situation is governed by two important factors: the first is the extent of the decay of radical concentration [R] during one period under pseudostationary conditions, while the second is that termination events are governed by [R]² while the propagation goes directly with [R]. As a consequence there is no general recommendation possible as to which experimental value of k_p is best taken as a substitute for the correct average of k_p characterizing a specific experiment. The second point, however, is apparently responsible for the pleasant effect that the methods used so far for the determination of k_t and its chain length dependence (i.e., plotting some average of k_t versus the mean chain‐length of terminating radicals on a double‐logarithmic scale) are only subtly wrong with regard to a realistic chain length dependence. This is especially so for the quantity k_t* (the average rate coefficient of termination derived from the rate of polymerization in a PLP system) and its chain length dependence.     

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

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

Investigation of autoacceleration effects during the solution polymerization of styrene

The possibility of obtaining increases in the rate and degree of polymerization through a decrease in the termination rate in nonviscous, homogeneous solution polymerizations of styrene has been investigated. Decreases in the termination rate were achieved through decreasing segmental diffusion of the propagating macroradical by greater occlusion, on the average, of the radical in the coiled polymeric chain. Coiling of the polymeric chain was effected by polymerizing styrene in thermodynamically poor (θ) solvents near the θ temperature for polystyrene. Examples of such systems are diethyl oxalate at 51.5°C. and cyclohexane at 34.6°C. Polymerization under these conditions did lead to a decrease in the k_t/k_p² kinetic ratio; this decrease resulted in increases in the degree of polymerization, but changes in the rate of polymerization, in contrast to the marked increases noted in viscous solution or heterogeneous polymerizations, were not observed. Possible explanations for the latter observations are discussed.     

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     

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.     

Emulsion polymerization. V. Lowest theoretical limits of the ratio kt/kp

It is assumed that the propagating polymeric radicals have no diffusive mobility in the very highly viscous medium within latex particles. Chain growth takes place on a lattice when the polymeric radical reacts with a monomer present on a lattice site adjacent to that occupied by the reactive chain end. For termination, two radical chain ends must be positioned on adjacent lattice sites at the same instant. The k_t/k_p ratios calculated with this model are either similar to or somewhat lower than the values determined in emulsion polymerization experiments. A minimum value of k_t/k_p can be calculated with the aid of the rate equation of Part III by assuming that only “living” polymer is produced during emulsion polymerization. This value of k_t/k_p is significantly lower than that calculated by the lattice model. Since the value corresponding to the lattice model gives the slowest practically achievable termination rate, it is concluded from these calculations that emulsion polymerization cannot be carried out under conditions in which chain termination is completely suppressed.     

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

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

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.