Kinetics of Chain Propagation in Copolymerization

Radicals of type Mi- are formed by primary initiation and by reaction (2,1) above. They are destroyed by the reaction (1,2) and in termination reactions. At the steady state, the rates of generation and of disappearance of these radicals are practically equal. If the chains are long, initiation and termination are of exceedingly rare occurrence compared with the reactions (1), and it suffices therefore to consider the latter only for the present where we are concerned merely with the relative concentrations of the two types of chain radicals. The steady-state condition reduces in this approximation to 

The same equation may, of course, be derived by similar application of the steady-state condition to radicals of type M2 . The rates of consumption of monomers Mi and M2 are 

Thus ri represents the ratio of the rate constants for the reaction of a radical of type 1 with monomer Mi and with monomer M2, respectively. The monomer reactivity ratio similarly expresses the relative reactivity of an M2 radical toward an M2 compared with an Ml monomer. The quantity d[M /d M given by Eq. (5) represents the ratio of the two monomers in the increment of polymer formed when the ratio of unreacted monomers is The former ratio 

The compositions of the monomer feed and of the polymer formed may be expressed as mole fractions instead of the mole ratios used above. To this end we let Fi represent the fraction of monomer Mi in the increment of copolymer formed at a given stage in the polymerization. Then 

Letting/] and/2 represent the mole fractions of unreacted monomers Ml and M2 in the feed, i.e. 

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