Rate constants free radical addition polymerization

Solution. Using the rate constants from Example 9.1 along with [M = M and [/] = [7]o from above in Equation 9.39 gives q = 0.9954. This illustrates the point made above that q 1 right from the beginning of a typical free-radical addition polymerization. 

In order to be able to predict the degree and rate of polymerization for a particular free radical addition polymerization system it is necessary to know the individual rate constants A , kp and kt. Also in order to determine Xn, the mechanism of termination must be known. This can be done using radioactively labelled initiator molecules. The rate constant for the breakdown of initiator ki can be determined from measurements upon the initiator alone. However, ki, so determined, may be different from that in the presence of monomer molecules. So far we have developed two equations that can be used to determine the three rate constants. The equations are... 

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

The addition of carbon-centered radicals to C-C double bonds (for a review see Giese 1983) is the key reaction in the free-radical-induced polymerization. In general, the rate constants of these reactions are only moderately high, but this process becomes fast and efficient, because in technical applications the polymerizing olefin is usually present at high concentrations. In aqueous solutions, the rate constant of the addition of the hydroxyethyl radical to ethene [reaction (29)], a non-activated C-C double bond, has been determined at 3 x 104 dm3 mol1 s1 (Soylemez and von Sonntag 1980). 

Equation (l) shows the rate of polymerization is controlled by the radical concentration and as described by Equation (2) the rate of generation of free radicals is controlled by the initiation rate. In addition. Equation (3) shows this rate of generation is controlled by the initiator and initiator concentration. Further, the rate of initiation controls the rate of propagation which controls the rate of generation of heat. This combined with the heat transfer controls the reaction temperature and the value of the various reaction rate constants of the kinetic mechanism. Through these events it becomes obvious that the initiator is a prime control variable in the tubular polymerization reaction system. 

Addition of phosphonyl radicals onto alkenes or alkynes has been known since the sixties [14]. Nevertheless, because of the interest in organic synthesis and in the initiation of free radical polymerizations [15], the modes of generation of phosphonyl radicals [16] and their addition rate constants onto alkenes [9,12,17] has continued to be intensively studied over the last decade. Narasaka et al. [18] and Romakhin et al. [19] showed that phosphonyl radicals, generated either in the presence of manganese salts or anodically, add to alkenes with good yields. 

Transfer constants for polystyrene chain radicals at 60° and 100°C, obtained from the slopes of these plots and others like them, are given in the second and third columns of Table XIII. Almost any solvent is susceptible to attack by the propagating free radical. Even cyclohexane and benzene enter into chain transfer, although to a comparatively small extent only. The specific reaction rate at 100°C for transfer with either of these solvents is less than two ten-thousandths of the rate for the addition of the chain radical to styrene monomer. A fifteenfold dilution with benzene was required to halve the molecular weight, i.e., to double l/xn from its value (l/ rjo for pure styrene (see Fig. 16). Other hydrocarbons are more effective in lowering the degree of polymerization through chain transfer. 

Reaction (49) can be suppressed by addition of [Cr(OH2)6]2+, or it can be driven at the limiting rate by adding a scavenger to eliminate [Cr(OH2)6]2+ or -R. As a consequence, the first-order rate constant for (49) remains independent of the nature and concentration of the scavenger. Thus, these organochromium(III) alkyls can be regarded as a source of stored free radicals, but practical applications such as polymerization initiation are only in their infancy. 

Stereocontrol of free radical polymerization is influenced by monomer constitution, solventy and temperature. Most polymerizations seem to follow at least a Markov first-order one-way mechanism. Ratios of the four possible rate constants ki/iy ki/8, k8/i, and k8/8 can be calculated from the experimentally accessible concentrations of configurational triads and diads. With increasing temperature, more heterotactic triads are formed at a syndiotactic radical whereas the monomer addition at an isotactic radical favors isotactic and not heterotactic triads. Compensation effects exist for the differences of activation enthalpies and activation entropies for each of the six possible combinations of modes of addition. The compensation temperature is independent of the mode of addition whereas the compensation enthalpies are not. 

Baxendale, Evans and coworkers reported in 1946 that the polymerization of methyl methacrylate (MMA) in aqueous solution was characterized by homogeneous solution kinetics, i.e. where mutual termination of free radicals occurred, in spite of the fact that the polymer precipitated as a separate phase. Increases in the rates of polymerization upon the addition of the surfactant cetyl trimethyl ammonium bromide (CTAB) were attributed to the retardation of the rate of coagulation of particles, which was manifested in a reduction in the effective rate constant for mutual termination,... 

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. 

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