Experimental Evaluation of Monomer Reactivity Ratios

Various methods have been used to obtain monomer reactivity ratios from the copolymer composition data. The most often used method involves a rearrangement of the copolymer composition equation into a form linear in the monomer reactivity ratios. Mayo and Lewis [1944] rearranged Eq. 6-12 to 

Data for the feed and copolymer compositions for each experiment with a given feed are substituted into Eq. 6-36 and r2 is plotted as a function of various assumed values of r. Each experiment yields a straight line and the intersection of the lines for different feeds gives the best values of r and r2. Any variations observed in the points of intersection of various lines are a measure of the experimental errors in the composition data and the limitations of the mathematical treatment (see below). The composition data can also be treated by linear least-squares regression analysis instead of the graphical analysis. 

The experimental composition data are unequally weighted by the Mayo-Lewis and Fineman-Ross plots with the data for the high or low compositions (depending on the equation used) having the greatest effect on the calculated values of r and r2 [Tidwell and Mortimer, 1965, 1970]. This often manifests itself by different values of r and r2 depending on which monomer is indexed as Mi. 

Kelen and Tudos [1975] refined the linearization method by introducing an arbitrary positive constant a into Eq. 6-37 to spread the data more evenly so as to give equal weight to all 

Plotting T against q gives a straight line that yields rijr). and r as intercepts on extrapolation to q — 0 and tq — I, respectively. The value of a, chosen as a = (FmFM) 2 where Fm and Fm are the lowest and highest F values, respectively, distributes the experimental data symmetrically on the plot. 

---