Dynamics of gelling liquids: a short survey
arXiv:cond-mat/0412101 · doi:10.1088/0953-8984/17/20/002
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.
arXiv comment21 pages, 3 figures; Dedicated to Lothar Schaefer on the occasion of his 60th birthday; Changes: added comments on the gel phase and some references
References in corpus (20)
- Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State
- Stress Relaxation of Near-Critical Gels
- Viscoelasticity near the gel-point: a molecular dynamics study
- Universality and its Origins at the Amorphous Solidification Transition
- Critical Exponents for Diluted Resistor Networks
- Critical Dynamics of Gelation
- Elastic critical behaviour in a 3d model for polymer gels
- Shear viscosity of a crosslinked polymer melt
- Scaling of Entropic Shear Rigidity
- Elasticity near the vulcanization transition
- Renormalization-Group Approach to the Vulcanization Transition
- Dynamical signatures of the vulcanization transition
- Goldstone fluctuations in the amorphous solid state
- Towards finite-dimensional gelation
- Critical behaviour of the Rouse model for gelling polymers
- The amorphous solid state: a locally stable thermodynamic phase of randomly constrained systems
- Anomalous stress relaxation in random macromolecular networks
- Normal stresses at the gelation transition
- A model for gelation with explicit solvent effects: Structure and dynamics
- Rheology of gelling polymers in the Zimm model