Power law polydispersity and fractal structure of hyperbranched polymers

Buzza, D. M.A.

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-RN0-Bf - 1monomers in their reaction bath close to the mean field gel point pA= 1, where pAis the fraction of reacted A groups. Here f ≥ 3 , N0is 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 ε ≡ (1-pA), ≪ we assume that the number density of hyperbranched polymers with degree of polymerisation N generally obeys the scaling form n (N) = N-τf (N/Nl) and we explicitly show that this scaling assumption is correct in the mean field regime (here Nlis 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 dc= 4, so that for d≥ dcthe mean field values for the polydispersity exponent and fractal dimension apply: τ = 3/2 , df= 4. For d = 3, mean field theory is still correct for ε > εGwhere εG≅ N0-1is the Ginzburg point; for ε < εG, mean field theory applies on small mass scales NNcwhere Nc≅ N03is a cross-over mass. Within the Ginzburg zone (i.e., dNcare non-Gaussian with fractal dimension given by df= d (for d = 2,3,4). Our results are qualitatively different from those of the percolation model and indicate that the polycondensation of ABf-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 τ

Citation

Buzza, D. M. (2004). Power law polydispersity and fractal structure of hyperbranched polymers. European Physical Journal E, 13(1), 79-86. https://doi.org/10.1140/epje/e2004-00042-3

• Journal Article Type: Article
• Acceptance Date: Dec 15, 2003
• Online Publication Date: Mar 2, 2004
• Publication Date: Jan 1, 2004
• Deposit Date: Jul 11, 2018
• Journal: The European Physical Journal E
• Print ISSN: 1292-8941
• Electronic ISSN: 1292-895X
• Publisher: EDP Sciences
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 1
• Pages: 79-86
• DOI: https://doi.org/10.1140/epje/e2004-00042-3
• Keywords: Fractal Dimension; Polycondensation; Mass Scale; Molecular Weight Distribution; Critical Dimension
• Public URL: https://hull-repository.worktribe.com/output/923083
• Publisher URL: https://link.springer.com/article/10.1140%2Fepje%2Fe2004-00042-3