title: Power law polydispersity and fractal structure of hyperbranched polymers.
abstract: Using the complementary approaches of Flory theory and the overlap function, we study the molecular weight distribution and conformation of hyperbranched polymers formed by the melt polycondensation of A-R(N)(0)-B(f - 1) monomers in their reaction bath close to the mean field gel point p(A) = 1, where p(A) is the fraction of reacted A groups. Here f > or = 3, N(0) is the degree of polymerisation of the linear spacer linking the A group and the f-1 B groups and condensation occurs exclusively between the A and B groups. For Epsilon tripe bond (1-pA) <<1, we assume that the number density of hyperbranched polymers with degree of polymerisation N generally obeys the scaling form n(N) =N(- tau)f(N/Nl) and we explicitly show that this scaling assumption is correct in the mean field regime (here Nl is the largest characteristic degree of polymerisation and the function f (N/Nl) cuts off the power law sharply for N>Nl). We find the upper critical dimension for this system is d(c) = 4, so that for d> or = dc the mean field values for the polydispersity exponent and fractal dimension apply: tau=3/2, d(f) = 4. For d = 3, mean field theory is still correct for Epsilon > Epsilon G where Epsilon G approximately equal N -1 0 is the Ginzburg point; for Epsilon < Epsilon G, mean field theory applies on small mass scales N< N c but breaks down on larger mass scales N> N c where N c approximately equal N 3 0 is a cross-over mass. Within the Ginzburg zone (i.e., d< d(c) < Epsilon G), we show that the hyperbranched chains on mass scales N> N(c) are non-Gaussian with fractal dimension given by d(f) = d (for d = 2,3,4). Our results are qualitatively different from those of the percolation model and indicate that the polycondensation of AB(f-1), unlike polymer gelation, is not described by percolation theory. Instead many of our results are similar to those for a monodisperse melt of randomly branched polymers, a consequence of the fact that tau < 2 so that polydispersity is irrelevant for excluded volume screening in hyperbranched polymer melts.
authors.affiliation: Polymer IRC, Department of Physics & Astronomy, University of Leeds, LS2 9JT, Leeds, UK. d.m.a.buzza@leeds.ac.uk
authors.forename: D M A
authors.initials: DM
authors.lastname: Buzza
mesh_terms: D015233:Models, Statistical; D008962:Models, Theoretical; D016011:Normal Distribution; D011108:Polymers / Q000737:chemistry*
chemical_list: D011108:Polymers