Abstract: | 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 ? (fw ? 1)(μA,A ? 1) ? (gw ? 1)(μ B,B ? 1) + (fw ? 1)(gw ? 1)Dμ = 0, where fw and gw 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 Dμ ≡ (μA,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 |