Rate of Binary Free-Radical Copolymerization

In deriving an expression for the rate of copolymerization in binary systems the following assumptions (Walling, 1949) will be made (a) rate constants for the reactions of a growing chain depend only upon the monomer unit at the chain end, and not on other units preceding the end unit (b) steady-state conditions apply both to the total radical concentration and to the separate concentrations of the two radicals (c) chain termination is by bimolecular radical reaction. 

If the cross-termination rate constant, that is, the rate constant for termination of radical Mi with radical M2 is A /i2, 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 ri2, that is, 

Equation (7.52) can also be derived from Eq. (7.43) by eliminating radical concentrations with the help of two steady-state assumptions written as Eqs. (7.44) and (7.47) and then using the definitions of ri and r2. Equation (7.52) represents a one-parameter model for the copoly merization rate (Melville et al., 1947) containing the parameter (p. Statistically, (p is expected to equal unity. However, the values of (p obtained in practice by inserting experimental copolymerization rates into Eq. (7.52) are frequently greater than unity. (For styrene-methylmethacrylate, for 

Problem 7.13 Show that if reaction probabilities of radicals depend only on encounter rates and are independent of the nature of the radicals, p should equal unity. 

For simplicity consider a reaction mixture in which [Mi ] = [M2 ]. Since Mi radicals will collide with M2 and Ml radicals with equal frequency and since the same applies to M2 radicals, the frequency of Ml - M2 encounters is twice that of Mi - Mi or M2 -M2 collisions. If the reaction probabilities depend only on encounter rates, 

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