Rate constants in free-radical polymerization

Table II - Rate constants in free radical polymerizations at 30°C.

Where kp is the rate constant, R, is the rate of initiation, and kt is the termination rate constant. In free radical polymerization initiated by thermal decomposition of... 

The use of organometallic compounds as chain-transfer catalysts in free-radical polymerization has been widely studied. One objective is the production of polymers with terminal vinyl groups and lower molecular weight components compared with polymerization in the absence of chain-transfer catalysts. Gomplexes of cobalt(ii) have been used as effective catalysts, but the instability of the intermediate cobalt hydride does not permit firm establishment of the reaction mechanism. To address this issue, several chromium compounds have been applied as catalysts for the polymerization of methylmethacrylate (MMA) and styrene. The temperature dependence of the rate constant for free-radical polymerization of MMA for catalyzed chain transfer by (GsPh5)Gr(GO)3 has been determined using the Mayo equation. ... 

The theory of radiation-induced grafting has received extensive treatment [21,131,132]. The typical steps involved in free-radical polymerization are also applicable to graft polymerization including initiation, propagation, and chain transfer [133]. However, the complicating role of diffusion prevents any simple correlation of individual rate constants to the overall reaction rates. Changes in temperamre, for example, increase the rate of monomer diffusion and monomer... 

Once least squares values of the /3 s were obtained, it was desirable to extract from them as much information as possible about the original parameters. To do so, we make one further statement concerning the relations between the rate constants for mutual termination of polymeric radicals of different size. It has been shown (2) that termination rates in free radical polymerizations are determined by diffusion rates rather than chemical factors. The relative displacement of two radicals undergoing Brownian motion with diffusion coefficients D and D" also follows the laws of Brownian diffusion with diffusivity D = D -J- D" (11). It... 

In contrast, recent kinetic investigation of the polymerization of spacerless G2 dendron-substi-tuted styrene and methylmethacrylate, respectively, in solution lead to the unexpected conclusion that above a certain critical monomer concentration a strong increase in the rate of the free radical polymerization is observed [21]. The results can be explained by self-organization of the growing polymer chain to a spherical or columnar superstructure in solution, depending on the degree of polymerization (DP, Fig. 2). The rate constants and low initiator efficiency lead one to conclude that the self-assembled... 

The reactivities of various chemical species are usually assessed by comparing rate constants for selected reactions. This is not a convenient procedure in free-radical polymerizations, however, because absolute rate constant measurements are rare. More convenient and plentiful parameters in free-radical systems are functions of more than one rate constant as in the factor, reactivity ratios, and chain... 

The steps in free-radical polymerization reaction and the corte- spending rate laws are summarized in Table 7-3. For the polymexiza-tion of styrene at 80°C initiated by 2,2-azobkisobutyromtrile the rate constants are... 

The reactivity ratios rj and T2 can be determined from the composition of the copolymer product. However, a serious complication exists because the propagation rate constants, k j, are composite rate constant, being composed of free-ion contributions and ion-pair contributions, and hence the reactivity ratios also will be composite quantities, having contributions from both ion pairs and free ions. Because the relative abundances of free ions and ion pairs are strongly dependent on the reaction conditions, the reactivity ratios will also depend on these conditions and they can be applied only to systems identical to those for which they were determined. Therefore the utility of such ratios is much more limited in anionic than in free-radical polymerization. 

Note that Equation 7.21 predicts that rate of polymer formation in free-radical polymerization is first order in monomer concentration and half order in initiator concentration. This assumes, of course, that the initiator efficiency is independent of monomer concentration. This is not strictly valid. In fact, in practice Equation 7.21 is valid only at the initial stage of reaction its validity beyond lOto 15% requires experimental verification. Abundant experimental evidence has confirmed the predicted proportionality between the rate of polymerization and the square root of initiator concentration at low extents of reaction (Figure 7.2). If the initiator efficiency, f, is independent of the monomer concentration, then Equation 7.21 predicts that the quantity Rp/[I] [M] should be constant. In several instances, this ratio has indeed been found to show only a small decrease even over a wide range of dilution, indicating an initiator efficiency that is independent of dilution. This confirmation of first-order kinetics with respect to the monomer concentration suggests an efficiency of utilization of primary radicals, f, near unity. Even where the kinetics indicate a decrease in f with dilution, the decreases have been invariably small. For undiluted monomers, efficiencies near unity are not impossible. 

The collection of data and critical evaluation of possible influences of parameters on the CLD (as was carried out by Heuts et al. ) might help to elucidate the current question of the true nature of chain length dependence of the rate constant of propagation in free radical polymerization. Therefore, the investigation of the polymerization behaviour of monomers other than styrene and methyl methacrylate is necessaryf and the use of the correction procedures should eliminate the error introduced by the effect of BB. Thus, comparison of data obtained from either different research groups and/or with the aid of different techniques (MALDI, SEC) should be better feasible. 

In free-radical polymerization, the initiator fragment moves away from the growing chain and therefore can influence chain growth and termination during only the first few monomer insertion steps. Consequently, the values of the polymerization kinetic parameters depend mainly on the monomer type, thus permitting the creation of tables of rate constants and activation energies as a function of monomer type, independently of the type of initiator used during polymerization. 

Rate constants for termination kx may be of the order of 10 liter/mol sec in free-radical polymerizations. Consider the polymerization of styrene initiated by di-t-butyl peroxide at 60°C. For a solution of 0.01 M peroxide and 1.0 M styrene in benzene, the initial rate of polymerization is 1.5 x 10 mol/liter sec and of the polymer produced is 138,000. 

Olaj OF, Schnoll-Bitai I. Solvent effects on the rate constant of chain propagation in free radical polymerization. Monatsh Chem 1999 130 731-740. 

TABLE 2.6 Some typical values for the rate constants for propagation and termination in free-radical polymerization... 

Assuming that in free-radical polymerization the rate constants can be replaced by the appropriate Arrhenius expressions ... 

Rate constants for displacement reactions are also included in the so-called transfer constants of free radical polymerization. These transfer constants have, however, not been included in this compilation, since a complete collection has already been published in the Polymer Handbook , Second Edition, J. Brandrup and E.H. Immergut, (eds.), John Wiley and Sons, New York etc., 1975. 

In free radical polymerization the propagation tion rate constants describe the reactions and termina-... 

Free-radical polymerization processes are used to produce virtually all commercial methacrylic polymers. Usually free-radical initiators (qv) such as azo compounds or peroxides are used to initiate the polymerizations. Photochemical and radiation-initiated polymerizations are also well known. At a constant temperature, the initial rate of the bulk or solution radical polymerization of methacrylic monomers is first-order with respect to monomer concentration, and one-half order with respect to the initiator concentration. Rate data for polymerization of several common methacrylic monomers initiated with 2,2 -azobisisobutyronitrile [78-67-1] (AIBN) have been deterrnined and are shown in Table 8. 

Photoinitiation is an excellent method for studying the pre- and posteffects of free radical polymerization, and from the ratio of the specific rate constant (kx) in non-steady-state conditions, together with steady-state kinetics, the absolute values of propagation (kp) and termination (k,) rate constants for radical polymerization can be obtained. 

As the polymerization reaction proceeds, scosity of the system increases, retarding the translational and/ or segmental diffusion of propagating polymer radicals. Bimolecular termination reactions subsequently become diffusion controlled. A reduction in termination results in an increase in free radical population, thus providing more sites for monomer incorporation. The gel effect is assumed not to affect the propagation rate constant since a macroradical can continue to react with the smaller, more mobile monomer molecule. Thus, an increase in the overall rate of polymerization and average degree of polymerization results. 

---