The Rate of Addition Copolymerization

The rate of copolymerization in a binary system depends not only on the rates of the four propagation steps but also on the rates of initiation and termination reactions. To simplify matters the rate of initiation may be made independent of the monomer composition by choosing an initiator which releases primary radicals that combine efficiently with either monomer. The spontaneous decomposition rate of the initiator should be substantially independent of the reaction medium, as otherwise the rate of initiation may vary with the monomer composition. 2-Azo-bis-isobutyronitrile meets these requirements satisfactorily. The rate Ri of initiation of chain radicals of both types Ml and M2 is then fixed and equal to 2//Cd[7], or twice the rate of decomposition of the initiator I if the efficiency / is equal to unity (see Chap. IV). The relative proportion of the two types of chain radicals created at the initiation step is of no real importance, for they wall be converted one into the other by the two cross-propagation reactions of the set (1). Melville, Noble, and Watson presented the first complete theory of copolymerization suitable for handling the problem of the rate. The theory was reduced to a more concise form by Walling, whose procedure is followed here. 

Two steady state conditions apply one to the total radical concentration and the other to the concentrations of the separate radicals Ml- and M2-. The latter has already appeared in Eq. (2), which states that the rates of the two interconversion processes must be equal (very nearly). It follows from Eq. (2) that the ratio of the radical population, Mi - ]/ [M i ], is proportional to the ratio k i/ki of the cross propagation reaction rate constants. The steady-state condition as applied to the total radical concentration requires that the combined rate of termination shall be equal to the combined rate of initiation, i.e., that 

The total rate of polymerization, obtained by adding Eqs. (3) and (4) and then eliminating [ilf2 ] through the use of Eq. (2), is 

Results derived from copolymerization rate studies are summarized 

In thermal polymerization where the rate of initiation may also vary with composition, an abnormal cross initiation rate may introduce a further contribution to nonadditive behavior. The only system investigated quantitatively is styrene-methyl methacrylate, rates of thermal copolymerization of which were measured by Walling. The rate ratios appearing in Eq. (26) are known for this system from studies on the individual monomers, from copolymer composition studies, and from the copolymerization rate at fixed initiation rate. Hence a single measurement of the thermal copolymerization rate yields a value for Ri. Knowing hm and ki22 from the thermal initiation rates for either monomer alone (Chap. IV), the bimolecular cross initiation rate constant kii2 may be calculated. At 60°C it was found to be 2.8 times that 

---