Variational bounds for the shear viscosity of gelling melts

C. H. Köhler; H. Löwe; P. Müller; A. Zippelius

doi:doi:10.1209/0295-5075/78/46002

EPL, 78 (2007) 46002
DOI: 10.1209/0295-5075/78/46002

Variational bounds for the shear viscosity of gelling melts

C. H. Köhler¹, H. Löwe², P. Müller¹ and A. Zippelius¹

¹ Institut für Theoretische Physik, Georg-August-Universität - D-37077 Göttingen, Germany
² Swiss Federal Institute for Snow and Avalanche Research - Flüelastr. 11, CH-7260 Davos Dorf, Switzerland

received 26 February 2007; accepted in final form 4 April 2007; published May 2007
published online 3 May 2007

Abstract
We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $\eta$ , which implies that it diverges algebraically with a critical exponent $k\geqslant 2\nu -\beta$ . Here, $\nu$ and $\beta$ are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact results imply a Mark-Houwink relation for the shear viscosity of isolated clusters of fixed size.

PACS
64.60.Ht - Dynamic critical phenomena.
61.25.Hq - Macromolecular and polymer solutions; polymer melts; swelling.
61.20.Lc - Time-dependent properties; relaxation.

© Europhysics Letters Association 2007