Variation of Copolymer Composition with Conversion

A useful method for analyzing copolymer composition as a function of conversion is that developed by Skeist [1946], Consider a system initially containing a total of M moles of the two monomers and in which the copolymer formed is richer in monomer Mi that is the feed (i.e., F /i). When dM moles of monomers have been copolymerized, the polymer will contain F dM moles of monomer 1 and the feed will contain (M — dM)(f — df ) moles of monomer 1. A material balance for monomer 1 requires that the moles of Mi copolymerized equal the difference in the moles of Mi in the feed before and after reaction, or 

Equation 6-32 can be rearranged (neglecting the df dM term, which is small) and converted to the integral form 

Equation 6-15 allows the calculation of F as a function of/i for a given set of r and r2 values. These can then be employed as (F — f ) to allow the graphical or numerical integration of Eq. 6-33 between the limits of (/i)0 and f. In this manner one can obtain the 

Equation 6-33 has been integrated to the useful closed form 

Equation 6-34 or its equivalent has been used to correlate the drift in the feed and copolymer compositions with conversion for a number of different copolymerization systems [Capek et al., 1983 O Driscoll et al., 1984 Stejskal et al., 1986 Teramachi et al., 1985], The larger the difference in the t and r2 values of a comonomer pair, the greater is the variation in copolymer composition with conversion [Dadmun, 2001]. 

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Since most polymers prepared fw practical purposes are copolymers, it is important to consider the effects of having more than one monomer present in a batch emulsion polymerization. Obviously, the introduction of a second monomer brings with it the need to take into account the effects of differences in monomer reactivity on the composition of the copolymer formed and the variation of copolymer composition with conversion. For a bulk or solution polymerization, the copolymer composition equation can be applied directly (Equations (1.33) and (1.34) in Section 1.6.1). However, for emulsion polymerizations, the situation is... 

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