Statistics of « starburst » polymers

We discuss the growth of completely branched polymer, based on tertiary amine branch points conected by flexible linear portions (« spacers ») each of P monomers. The method is a modified version of the Edwards self consistent fields. We find that ideal « starburst » growth (without any residual secondary amine functions) is restricted to a number of generations m ≤ m1 where m1 ≅ 2.88(ln P + 1.5). This corresponds in space to a limiting radius R1 which increases linearly with P. Well below this limit, the polymer radius R(M), plotted as a function of molecular weight M, should increase like M0.2. Above the limit (R > R 1) we expect compact structures (R ∼ M0.33).