Rheology of gelling polymers in the Zimm model

TL;DR

This paper studies the rheological behavior of gelling polymers using the Zimm model, analyzing how cluster topology affects viscosity and normal stresses, and compares numerical results with experimental data.

Contribution

It introduces a numerical analysis of the Zimm model with random cluster topologies, revealing the independence of scaling exponents from hydrodynamic interactions and challenging existing scaling relations.

Findings

Scaling exponents are independent of hydrodynamic interaction strength.

Numerical exponents agree with experimental data for branched polymers.

The traditional model cannot produce a critical divergence of viscosity at the gel point.

Abstract

In order to study rheological properties of gelling systems in dilute solution, we investigate the viscosity and the normal stresses in the Zimm model for randomly crosslinked monomers. The distribution of cluster topologies and sizes is assumed to be given either by Erd\H os-R\'enyi random graphs or three-dimensional bond percolation. Within this model the critical behaviour of the viscosity and of the first normal stress coefficient is determined by the power-law scaling of their averages over clusters of a given size $n$ with $n$. We investigate these Mark--Houwink like scaling relations numerically and conclude that the scaling exponents are independent of the hydrodynamic interaction strength. The numerically determined exponents agree well with experimental data for branched polymers. However, we show that this traditional model of polymer physics is not able to yield a critical divergence at the gel point of the viscosity for a polydisperse dilute solution of gelation clusters. A generally accepted scaling relation for the Zimm exponent of the viscosity is thereby disproved.