Integrated Binary Copolymer Equation

It should be noted that the copolymer equations, Eqs. (7.11) and (7.17), give only the instantaneous copolymer composition, i.e., the composition of the copolymer that is formed instantly at a given feed composition at very low degrees of conversion (approximately 5%) such that the composition of the monomer feed may be considered to be essentially unchanged from its initial value. For all copolymerizations except when the feed composition is an azeotropic mixture or where ri = rz = 1, the copolymer product compositions are different from monomer feed compositions. Thus there occurs a drift in the comonomer composition, and correspondingly a drift in the copolymer composition, as the degree of conversion increases. It is important to be able to calculate the course of such changes. 

Problem 7.4 A monomer pair with r = 0.2 and ro = 5.0 is copolymerized beginning with a molar monomer ratio [Mi]/[M2] = 60/40. Assuming that the copolymer composition within a 10 mol% conversion interval is constant, calculate instantaneous monomer and copolymer compositions and cumulative average copolymer compositions at 10 mol% conversion intervals up to 100% total conversion. Show the results graphically as change in composition of the copolymer and the monomer mixture during copolymerization. 

The results obtained by proceeding in this way are tabulated below  

The data in column 3 represent the instantaneous values at the beginning of different intervals. The values are assumed to be constant within the respective intervals. The composition data in column 5 relate to mixtures of different copolymers and, at higher conversions, to mixtures of copolymers and some Mj homopolymer. The results are shown graphically in Fig. 7.3. 

Comment If one malces the conversion interval smaller and smaller, this corresponds to an integration of the copolymer equation (see below). 

Problem 7,4 A monomer pair with rj = 0.2 and rz = 5.0 is copolymerized beginning with a molar monomer 

---

The monomer reactivity ratios r and r2 can be determined from the experimental conversion-composition data of binary copolymerization using both the instantaneous and integrated binary copolymer composition equations, described previously. However, in the former case, it is essential to restrict the conversion to low values (ca. < 5%) in order to ensure that the feed composition remains essentially unchanged. Various methods have been used to obtain monomer reactivity ratios from the instantaneous copolymer composition data. Several procedures for extracting reactivity ratios from the differential copolymer equation [Eq. (7.11) or (7.17)] are mentioned in the following paragraphs. Two of the simpler methods involve plotting of r versus r2 or F versus f. ... 

For a detailed analysis of monomer reactivity and of the sequence-distribution of mers in the copolymer, it is necessary to make some mechanistic assumptions. The usual assumptions are those of binary, copolymerization theory their limitations were discussed in Section III,2. There are a number of mathematical transformations of the equation used to calculate the reactivity ratios and r2 from the experimental results. One of the earliest and most widely used transformations, due to Fineman and Ross,114 converts equation (I) into a linear relationship between rx and r2. Kelen and Tudos115 have since developed a method in which the Fineman-Ross equation is used with redefined variables. By means of this new equation, data from a number of cationic, vinyl polymerizations have been evaluated, and the questionable nature of the data has been demonstrated in a number of them.116 (A critique of the significance of this analysis has appeared.117) Both of these methods depend on the use of the derivative form of,the copolymer-composition equation and are, therefore, appropriate only for low-conversion copolymerizations. The integrated... 

---