The necessary and sufficient conditions for the existence of critical points (azeotropic compositions) in multicomponent copolymerization are defined, and the preferred method for calculating critical points for a given set of reactivity ratios is provided. This method offers considerable advantages in both simplicity and computation speed over methods already in the literature. A computer program for performing the calculation on systems with up to 10 components is briefly described. Approximate probabilities for the existence of critical points in ternary and quaternary systems have been evaluated as a function of whether binary critical points exist for pairs of the monomers involved. These data show that, contrary to the widely held view, in systems of three or more components all rij > 1 or all rij < 1is neither a necessary nor a sufficient condition for the existence of a critical point. Those systems which always and those systems which never give rise to critical points are indicated.
Australian Journal of Chemistry,
Vol. 39, no. 11 (1986), pp. 1877-1881