Generality of product probability values in unifying and predicting relationships among monomers in copolymerization

It is shown that a knowledge of the reactivity ratios for the binary systems A–B and B–C allows reactivity ratios for the copolymer system A–C to be calculated from the relationship: PabPbcPca = PacPcbPba = (a constant). The various probabilities include the possibilities of adding A, B, or C monomers to any of the corresponding radicals and can be expressed in terms of binary reactivity ratios. At equimolar concentrations it is shown that for systems of three conjugated or three unconjugated monomers approximates 0.037. Similarly, for systems of two conjugated and one unconjugated monomers or two unconjugated and one conjugated monomers approximates 0.006. Once the appropriateness of these constants is established, it is shown how the relationship may be used to assess the most probable values among widely varying reported reactivity ratios. It is shown that the values of the constant for different combinations of monomers allow the assessment of the reactivity of conjugated monomers compared with unconjugated monomers for conjugated or unconjugated radicals. It develops that the reactivity of unconjugated monomers is between 5 and 10% of that of conjugated monomers for unconjugated radicals. For more precise assessment of unknown reactivity ratios it is suggested that is a product function of unique reactivity parameters characteristic of the individual monomers involved.