Rate Expression for Radical Chain Polymerization

Equations (6.3) through (6.12) constitute the detailed mechanism of a free-radical initiated chain polymerization. According to this scheme, the initiator I first decomposes into a pair of primary (free) radicals, R, as in Eq. (6.3), the rate of radical generation being then given by 

The rate of propagation is the sum of many individual propagation steps [Eqs. (6.6a)-(6.6c)]. It is, however, assumed that the propagation rate constant kp is independent of the size or the number of monomer units in the propagating radical. One can therefore express the rate of propagation by 

The termination rates Rt corresponding to the different modes of termination are 

The factor of 2 is used in the above expressions for the simple reason that for each incidence of a termination reaction, two chain radicals disappear from the system. It is important to note that as radicals are generated in pairs, they are also destroyed in pairs. 

In order to obtain a kinetic expression for the overall rate of polymerization, it is necessary to assume that both kp and kt are independent of the size of the radical. [This assumption is inherent in Eqs. (6.15) through (6.18).] It may be recalled that the same type of assumption was also employed in deriving the kinetics of step polymerization (Chapter 5). There is, however, ample experimental evidence which indicates that although radical reactivity depends on molecular size, the effect of the size vanishes after the dimer or trimer [Ij. 

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