Significance of Monomer Reactivity Ratios

As defined by Eq. (7.10), the monomer reactivity ratio can be looked upon as the relative tendency for homopropagation and cross-propagation. If for a given monomer pair, ri = 0 and hence k =0, it would mean that Mi does not ho-mopolymerize in the presence of M2. Similarly, ri 1, i.e., A n 12 means that M preferentially adds Mi instead of M2 and ri 1, i.e., k 2 11 means that M preferentially adds M2. For example, an ri value of 0.5 would mean that M adds M2 twice as fast as Mi. 

It is evident from Eq. (7.10) that the values of ri and r2 refer only to a pair of monomers undergoing copolymerization. Thus the same monomer can have different values of ri in combination with different monomers, e.g., acrylonitrile has (ri, r2) values of (0.35,1.15), (0.02,1.8), (1.5,0.84), and (4.2,0.05) at 50°C in free-radical copolymerization with acrylic acid, isobutylene, methyl acrylate, and vinyl acetate, respectively, each being designated as M2 and the other monomer, acrylonitrile, as Mi. 

Problem 7.1 The above derivation of the copolymer composition equation [Eq. (7.11)] involves the steady-state assumption for each type of propagating species. Show that the same equation can also be derived from elementary probability theory (Melville et al., 1947 Vollmert, 1973 Odian, 1991) without invoking steady-state conditions. 

P 1 = probability that M will add Mi rather than M2. (Here the first subscript designates the active center and the second the monomer.) 

In the formation of high polymer, the termination occurs rarely. So neglecting it in the present case, one may write 

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