Gel formation with multiple interunit junctions. II—mixture of different functional molecules

Number‐ and weight‐average molecular weight of condensation polymers formed in the mixture of primary molecules carrying different species of functional groups A and B are derived by the cascade theory. These functional groups are allowed to form multiple junctions of arbitrary multiplicity k. From the weight average, the gel point condition is found to be given by 1 ? (f_w ? 1)(μ_A,A ? 1) ? (g_w ? 1)(μ _B,B ? 1) + (f_w ? 1)(g_w ? 1)D_μ = 0, where f_w and g_w are average functionality of the primary molecules, μ _αβ the average multiplicity of β groups in the junctions where a path of an α‐group enters, and D_μ ≡ (μ_A,A ? 1)(μ _B,B ? 1) ? μ _A,Bμ _B,A the multiplicity determinant. Possible applications to thermoreversible gelation are suggested. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2413–2421, 2003