Average Property Relations for Nonlinear Polymerization with Unequal Reactivity

This paper extends the authors' method of calculating average physical properties of ideal nonlinear, stepwise polymerizations to systems with nonequally reactive functional groups. Two special cases are considered in detail: Af+A2+B2, where the two B units comprising a B2 monomer react at different rates; and Af+A2+B2, where one or two A units on the Af monomer may react at different (slower) rates than the remaining A's. Weight average molecular weight, the gel point, weight fraction solubles, and cross-link density are derived. These properties are calculated for several systems with unequal, first-order reaction rates and are compared to the corresponding properties for the analogous ideal systems. It is indicated how to extend this approach to other systems with unequal reactivity.