Volume 78, Number 4, May 2007
|Number of page(s)||5|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||03 May 2007|
Variational bounds for the shear viscosity of gelling melts
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
Accepted: 4 April 2007
We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity , which implies that it diverges algebraically with a critical exponent . Here, ν and 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
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