Free radical polymerization propagation rate constants

As indicated earlier, G=0.7 for free radical initiation and about 0.1 for the free ions. The termination rate constants are 3 X 10 M sec for free radicals and 2 x 10 M sec for the free ions. The propagation rate constants have been determined to be 30, 4 X 10 and about 10 sec for free radical, cationic and anionic polymerization, respectively. 

Rate constants of free radical polymerization (propagation, termination and transfer constants) See corresponding chapter of this Handbook ... 

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. 

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... 

As mentioned in Section 9.3, Jackson (141) has obtained estimates of the chain-transfer coefficient of the growing radical with polymer in the free-radical polymerization of ethylene, C,p, by choosing the value so as to fit the MWD. As the polymerization conditions for the polymers mentioned in Table 10.1 are not disclosed, it is necessary to choose typical conditions 220° C and 2000 atm will be selected. Under these conditions Ctp, the ratio of the rate constant for attack on polymer (per monomer unit) to that for propagation, in a homogeneous phase, was found to be about 4.0 x 10 3. This is in good agreement with the known transfer coefficients for the lower alkanes (160), when allowance is made for the differences in pressure and temperature (100). The relation between Ctp and k is ... 

Acrylonitrile (AN) is a particular case among vinjd monmners reprding the solvent dependence of the propagation rate constant (kp) in homogeneous free radical polymerization. Whereas in dimethylformamide and dimethylsulfoxide kp has values which might be expected from a comparison with other monomers and from the reactivity of the growing radical (400 and 1910 1 mol s , respectively, at 25 the propagation rate constant is considerably hig ier in water... 

Comprehensive Models. This class of detailed deterministic models for copolymerization are able to describe the MWD and the CCD as functions of the polymerization rate and the relative rate of addition of the monomers to the propagating chain. Simha and Branson (3) published a very extensive and rather complete treatment of the copolymerization reactions under the usual assumptions of free radical polymerization kinetics, namely, ultimate effects SSH, LCA and the absence of gel effect. They did consider, however, the possible variation of the rate constants with respect to composition. Unfortunately, some of their results are stated in such complex formulations that they are difficult to apply directly (10). Stockmeyer (24) simplified the model proposed by Simha and analyzed some limiting cases. More recently, Ray et al (10) completed the work of Simha and Branson by including chain transfer reactions, a correction factor for the gel effect and proposing an algorithm for the numerical calculation of the equations. Such comprehensive models have not been experimentally verified. 

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. 

The purpose of this review article is to summarize the historical development of the solvent effect on free radical polymerization and to point out possibilities of specific interactions of the propagating radical with solvent. The effect of metal salts on the propagation process will not be described. Emphasis will be laid on the interpretation of experimental results, relating to the influence of aromatic solvents on propagation rate constants, and on the discussion for the molecular interpretation. 

Schulz et al.12,13 estimated the elementary rate constants for methyl methacrylate in solvents whose viscosities varied by a factor of 170, indicating that the termination rate constants were inversely proportional to the viscosity of the solvents. The variation of propagation rate constants was much less than that of termination rate constants. They have also obtained similar results in the free radical polymerization of benzyl methacrylate. 

Turning to the comparison between the rate constants for the chain propagation in the free radical polymerization of methyl and butyl acrylayes, it can be observed that both these reactions should occur with the same entropy decrease, because identical double bonds are involved. From the experimental data by Melville and Bickel (1 3) and by Bengough and Melville (14) relative to butyl acrylate, 4 pairs of activation energy and entropy can be calculated, which are collected in Table IV. It is evident that the experimental activation entropy which is closest to the calculated ASp for alkyl acrylates (i.e. the ASp value reported for methyl acrylate in Table III) is -12.+. f j/mol K, whereas all the other activation entropies seem to be too high. The rate constant calculated at JO°C from... 

Table IV - Experimental activation energy and entropy and rate constant at 30°C for the chain propagation in the free radical polymerization of butyl acrylate.

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