Variational bounds for the shear viscosity of gelling melts

Details Variational bounds for the shear viscosity of gelling melts Variational bounds for the shear viscosity of gelling melts

2007-02-26

arxiv.org/abs/cond-mat/0702590v2

Europhys. Lett. 78, 46002 (2007)

Physics

Condensed Matter

Statistical Mechanics

5 pages; CHANGES: typos corrected, some references added; version as published

Scientific paper

10.1209/0295-5075/78/46002

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.

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