Overall reaction rate of ideal polymerization

The rate of monomer consumption in polymerizations proceeding according to reactions (13)—(19) is given by 

In writing eqn. (20), the assumption is made that the reactivities of radical M of various degrees of polymerization n is equal. Let us introduce the further hypothesis that the reactivities of the radicals R and T are equal to that of M i. e. k = kj tr = k. Equation (20) is then simplified to as 

The concentration [M ] is, of course, unknown but for stationary conditions it can be calculated (remembering that an error is introduced by neglect of the changes in termination rate with the length of the interacting radicals) with 

The assumptions under which eqn. (23) has been derived are very stringent, and they are rarely fulfilled. Nevertheless, the situation described does exist. An example is the polymerization of butyl-1-chloroacrylate, which is first order with respect to monomer (see Fig. 1). 

Experimental results of the studies of polymerization kinetics can often be explained by the reversible character of eqn. (13) and by the relatively slow generation rate of the radicals M. Again assuming equal reactivity of radicals of various length we have 

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