Variational bounds for the shear viscosity of gelling melts

TL;DR

This paper derives bounds on the shear viscosity divergence at the gel transition in gelling melts, highlighting the importance of excluded-volume interactions and establishing a relation for isolated cluster viscosity.

Contribution

It introduces a lower bound for shear viscosity divergence in gelling melts, incorporating excluded-volume effects and connecting critical exponents.

Findings

Shear viscosity diverges algebraically with a critical exponent k ≥ 2ν - β.

Divergence is stronger than in the Rouse model, emphasizing excluded-volume interactions.

Exact results at the critical point relate shear viscosity to cluster size via a Mark-Houwink relation.

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.