Rate of Free-Radical Copolymerization

In the derivation of copolymer composition equation, Eq. (7.11), we considered only the rates of the four possible propagation steps in a binary system. However, the overall rate of copolymerization depends also on the rates of Initiation and termination. In deriving an expression for the rate of copolymerization in binary systems the following assumptions will be made [25] (a) rate constants for the reaction of a growing chain depend only 

If the cross-termination rate constant, that is, the rate constant for termination of radical Mi with radical M2 is ktvi-, then the steady-state for the total concentration of radicals can also be written as 

If we define mole fractions of the respective radicals as ni and TI2, that is, 

Equation (7.64) can also be derived from Eq. (7.55) by eliminating radical concentrations with the help of two steady-state assumptions written as Eqs. (7.56) and (7.59). Equation (7.64) represents a one-parameter model for the copolymerization rate [8] containing the parameter f . Statistically, f is expected to equal unity. 

Problem 7.15 Show that if reaction probabilities of radicals depend only on encounter rates and are independent of the nature of the radicals, j should equal 

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