Flory exponents for generalized polymer problems

Abstract

We use Flory's approximation to calculate the upper critical dimension, dc, below which mean field theory breaks down. We also calculate the exponent ν controlling the dependence of the radius of gyration, R, of a polymer on the degree of polymerization N. In particular, we treat linear and branched polymers in dilute good solvents and in monodisperse melts and linear and branched polyelectrolytes in dilute solutions. New results include ν = 5/2(d + 2) for dilute branched polymers, d c = 10 for dilute branched polyelectrolytes, and a modified Flory derivation of the exact result ν = 2/d - 2 for dilute linear polyelectrolytes