Rheology and molecular weight distribution of hyperbranched polymers

We study the melt rheology and molecular weight distribution of four short chain branched hyperbranched polyesters with different molecular weights and containing branched monomers of various alkyl chain lengths n (2 → 4; n is the number of CH₂ groups in the alkyl chain). We find that the molecular weight distribution for all our samples obeys the static scaling form n(M) ∼ M^{- τ}exp(-M/M_char) where n(M) is the number density of hyperbranched polymers with mass M, M_char is the largest characteristic molecular weight, and τ is the polydispersity exponent. The values of τ for all our samples (either 1.35 or 1.55) are close to but not the same as the mean field value of τ = 1.5, a consequence of the fact that our polymers were synthesized under non-mean-field polycondensation conditions. For all our samples, we found that the rheology at low and intermediate frequencies could be modeled accurately using a dynamic scaling theory based on the Rouse model. This confirms that these hyperbranched polymers behave as polymeric fractals which are essentially unentangled. For these polymers, the fractal dimension in the melt was found to be consistent with the hyperscaling relation for hyperbranched polymers d_f = 3, although we found rheology to be rather insensitive to d_f for our system.