Compositions of Feed and Copolymer

The copolymer equation (7.11) can be converted to a more useful form by expressing concentrations in terms of mole fractions. Let fi and /2 be the mole fractions of monomers Mi and M2 in the feed, that is. 

Equation (7.18), which is also called the copolymer equation, gives the mole fraction of monomer Mi in the copolymer whose feed contained fi mole fraction of monomer Mi. It is more convenient to use than its previous form [Eq. (7.11)]. 

It should be noted that Fi gives the instantaneous copolymer composition and both fi and Fi change as the polymerization proceeds. The composition of the copolymer as a function of conversion can be derived by integration ofEq. (7.18). 

Equation (7.18) may be used to calculate the instantaneous composition of copolymer as a function of feed composition for various monomer reactivity ratios. A series of such curves are shown in Fig. 7.1 for ideal copolymerization, i.e., r r2 = 1. The term ideal copolymerization is used to show the analogy between the curves in Fig. 7.1 and Aose for vapor-liquid equilibria in ideal liquid mixtures. The vapor-liquid composition curves of ideal binary mixtures have no inflection points and neither do the polymer-composition curves for random copolymerization in which riV2 = 1. Such monomer systems are therefore called ideal. It does not in any sense imply an ideal type of copolymerization. 

It is evident from Fig. 7.1 that only a small range of feed compositions give copolymers containing appreciable amounts of both components unless monomers have very similar reactivities. Suppose, for example, that it is desired to synthesize an ideal copolymer with 60 mol% Mi in a system where r = 0.5. From Fig. 7.1 it is seen that a feed composition of about 75% Ml is required. However, since F 7 /1, there occurs a drift in monomer composition as copolymer is formed. Therefore copolymer composition changes with conversion. To obtain a constant copolymer composition of 60% Ml, it would be necessary to maintain a constant feed composition of 75%, such as by adding fresh Mi to the feed. For cases in which r = T2 = 1, the composition of the copolymer F ) will always be the same as the feed composition (/i). For this copolymer system obviously there occurs no drift in composition with conversion. 

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