1. Variational bounds for the shear viscosity of gelling melts
- Author
-
Köhler, Claas H., Löwe, Henning, Müller, Peter, and Zippelius, Annette
- Subjects
Condensed Matter - Statistical Mechanics ,Condensed Matter - Disordered Systems and Neural Networks ,Condensed Matter - Soft Condensed Matter - 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 $k\ge 2\nu-\beta$. 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., Comment: 5 pages; CHANGES: typos corrected, some references added; version as published
- Published
- 2007
- Full Text
- View/download PDF