Free radical copolymerization rate constants

Note that this inquiry into copolymer propagation rates also increases our understanding of the differences in free-radical homopolymerization rates. It will be recalled that in Sec. 6.1 a discussion of this aspect of homopolymerization was deferred until copolymerization was introduced. The trends under consideration enable us to make some sense out of the rate constants for propagation in free-radical homopolymerization as well. For example, in Table 6.4 we see that kp values at 60°C for vinyl acetate and styrene are 2300 and 165 liter mol sec respectively. The relative magnitude of these constants can be understod in terms of the sequence above. 

Monomer concentrations Ma a=, ...,m) in a reaction system have no time to alter during the period of formation of every macromolecule so that the propagation of any copolymer chain occurs under fixed external conditions. This permits one to calculate the statistical characteristics of the products of copolymerization under specified values Ma and then to average all these instantaneous characteristics with allowance for the drift of monomer concentrations during the synthesis. Such a two-stage procedure of calculation, where first statistical problems are solved before dealing with dynamic ones, is exclusively predetermined by the very specificity of free-radical copolymerization and does not depend on the kinetic model chosen. The latter gives the explicit dependencies of the instantaneous statistical characteristics on monomers concentrations and the rate constants of the elementary reactions. 

Currently this model is one of the most commonly used in the theory of free-radical copolymerization. The formation of a donor-acceptor complex Ma... iVlbetween monomers Ma and in some systems is responsible for a number of peculiarities absent in the case of the ideal model. Such peculiarities are due to the fact that besides the single monomer addition to a propagating radical, a possibility also exists of monomer addition in pairs as a complex. Here the role of kinetically independent elements is played by ultimate units Ma of growing chains as well as by free (M ) and complex-bound (M ) monomers, whose constants of the rate of addition to the macroradical with a-th ultimate unit will be... 

The obtained value of a indicates the proximity of the rate constant values of the addition of TBSM to the macroradicals MA and of MA to TBSM This can be explained by a similar influence of intermolecular coordination on chain propagation. The values of pt and p2 indicate that in free-radical copolymerization of TBSM with MA both free and complex-bound monomers are involved in chain propagation with a higher contribution of the latter. 

The effect of temperature on reactivity ratios in free radical copolymerization is small. We can reasonably assume that the propagation rate constants in the reactions (7-2)-(7-5) can be represented by Arrhenius expressions over the range of temperatures of interest, such as... 

Now, according to the transition-state theory of chemical reaction rates, the pre-exponential factors are related to the entropy of activation, A5 , of the particular reaction [A = kT ere k and h are the Boltzmann and Planck constants, respectively, and An is the change in the number of molecules when the transition state complex is formed.] Entropies of polymerization are usually negative, since there is a net decrease in disorder when the discrete radical and monomer combine. The range of values for vinyl monomers of major interest in connection with free radical copolymerization is not large (about —100 to —150 JK mol ) and it is not unreasonable to suppose, therefore, that the A values in Eq. (7-73) will be approximately equal. It follows then that... 

The Q-e scheme is an attempt to express free radical copolymerization data on a quantitative basis by separating reactivity ratio data for monomer pairs into parameters characteristic of each monomer. Under this scheme, radical-monomer reaction rate constant k, is written as ... 

Anionic copolymerization of macromonomers with low molecular weight monomers could offer an interesting alternative to access graft copolymers of well-controlled structural parameters and composition. Provided that no deactivation takes place, quantitative copolymerization yields are to be expected. Compared to free-radical copolymerization, the rate constants are higher (due to the higher selectivity of carbanions over radicals). As a result, it should be easier to determine the influence of the parameters quoted on the macromonomer reactivity. Another problem is that it is not always easy to purify the macromonomers, since distillation is not possible. 

Table 22-7. Copolymerization Rates Propagation Rate Constants kp, and Factors for the Free Radical Copolymerization of Methyl Methacrylate with Styrene at 60 C...

Cross termination n. In free radical copolymerization, termination by reaction of two radicals terminated by monomer units of the opposite type, i.e., termination, by combination or disproportionation with rate constant /cab Crosstermination is often favored over termination by reaction between two like radicals due to polar effects. 

Copolymerization. In free-radical copolymerization (qv), the composition of the copolymer is controlled by the comonomer reactivity ratios (23). The monomer reactivity ratio is defined as the quotient of the rate constants for chain homopropagation to the rate constant for chain cross-propagation. 

In contrast to the free-radical copolymerization, the lack of termination in living ionic copol5mierization enables the direct determination of the rate coefficients of the cross-propagation step. The reaction rate of monomer B with the living chain end a is directly accessible via the concentration decrease of a , which may be traced via a suitable spectroscopic method. Alternatively, the concentration of B can be determined as a function of time with the concentration of a being held constant. The latter experimental technique requires extrapolation of time toward zero, because the cross-propagation step is immediately followed by homopropagation of B. 

Gilbert et al. [133] employed EPR spectroscopy to monitor the initial stages in the free-radical copolymerization of carbohydrates and methacrylic acid, initiated by a metal-peroxide redox couple. The authors aimed to understand the behavior of mixed carbohydrate-monomer systems in the presence of radical initiators by gaining knowledge of the rate constants and their dependence on radical structure and different substitution patterns. 

Vinyl chloride (VC) readily copolymerizes with MA (see table in the appendix to this chapter) maleates and maleimides, using free-radical initiators to give random copolymers.The effect of MA on the chain-transfer constant (C ) during polymerization of vinyl chloride has been studied at 40-70°C. At 60°C, the MA Cs was 7.7 x 10, compared to a styrene Cs of 72.2 X 10. Melville and Burnett determined the copolymerization rate constant for the VC-MA pair to be 2.1 x 10" liter moF s Several studies have shown that equimolar copolymers may also be obtained for the monomer pair (see Chapter 10). It has been observed that the presence of MA enhanced the polymerization rate of vinyl chloride. As shown in the table in this chapter s appendix, vinylidene chloride also undergoes free-radical copolymerization with MA. ... 

Free-radical copolymerization of cyclopentene with MA has also been studied at pressures up to 6 000 kg/cm. At 60°C, the rate of copolymerization increased with pressure and the conversion at 6 000 kg/cm attained a maximum constant value in a short time. For a given monomer feed, the content of cyclopentene in the copolymer increased with pressure. A maximum rate of copolymerization was observed at about 0.6 mol fraction cyclopentene. No pressure dependence of the molecular weight was noted for the copolymers... 

The problem of free-radical copolymerization kinetics is not nearly in such good shape. In addition to the four propagation reactions, there are three possible termination reactions (Fx- H- Fj-, Fx -H Fx-, Pz +- Fj-), each with its own rate constant. A general rate equation has been developed, but because of a lack of... 

The terms kp, k, and so forth, are the rate constants for the respective reactions. The kinetic scheme resembles that of a free-radical copolymerization between the monomer M and the thiuram disulfide (RSSR) considered as a second monomer, and a kinetic expression for a conventional radical copolymerization can be suitably applied to this system when the termination is chemically controlled (as it is for low conversion). Thus, the rate of polymerization can be written as follows ... 

We saw in the last chapter that the stationary-state approximation is apphc-able to free-radical homopolymerizations, and the same is true of copolymerizations. Of course, it takes a brief time for the stationary-state radical concentration to be reached, but this period is insignificant compared to the total duration of a polymerization reaction. If the total concentration of radicals is constant, this means that the rate of crossover between the different types of terminal units is also equal, or that R... 

The basic reaction scheme for free-radical bulk/solution styrene homopolymerization is described below. A complete description of copolymerization kinetics involving styrene is not given here however, the homopolymerization kinetic scheme can be easily extended to describe copolymerization using the pseudo-kinetic rate constant method [6]. Such practice has been used by many research groups [7-10] and has been used extensively for modelling of copolymerization involving styrene by Gao and Penlidis [11]. In this section, all rate constants are defined as chemically controlled, i.e. they are only a function of temperature. 

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. 

---