Dynamics of gelling liquids: a short survey

TL;DR

This survey reviews models of gelling liquids' dynamics, analyzing their critical behavior near sol-gel transition, and explores both equilibrium and non-equilibrium properties, highlighting inconsistencies in traditional scaling arguments.

Contribution

It provides a comparative analysis of Rouse- and Zimm-type models with different crosslink statistics, revealing new insights into critical dynamics and rheology of gelling liquids.

Findings

Critical behavior of scattering functions near sol-gel transition

Anomalous stress relaxation in shear flow

Contradictions in traditional scaling arguments

Abstract

The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse-type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium, its critical behaviour near the sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by looking at stress relaxation in a simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the results contradict long-standing scaling arguments, which are shown to be flawed by inconsistencies.