Dynamics of gelling liquids: a short survey

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 Erdős-Rényi 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.

Variational bounds for the shear viscosity of gelling melts

“…On the other hand, if excluded-volume interactions were absent, the geometric fractal dimension d f would take on p-3 the Gaussian or ideal Rouse value d (G) f ≈ 4. The resulting lower bound for k would then coincide with the exact result in the phantom case that was computed previously [22][23][24].…”

“…for the viscosity of the Rouse model for gelling polymers [22][23][24] in terms of the cluster-weighted sum of the squared radii of gyration…”

Chain Dynamics in Microgels: Poly(N-vinylcaprolactam-co-N-vinylpyrrolidone) Microgels as Examples

“…The translational diffusion coefficient is a macroscopic transport coefficient, but DLS is actually a technique that records all types of motions excited by thermal fluctuations. If the measurements are made in the limit of small q values such that qR g < 1, the whole particle is seen. 11a− On the other hand, scattering measurements made under conditions of qR g ≫ 2 probe distances in a particle which are much smaller than the particle diameter. For most colloidal particles there will be no difference in the result for the diffusion coefficient when the experiments are made at any angle.…”

“…In contrast, macromolecules are composed of mostly flexible linear, branched, or cross-linked chains. Now, segmental modes of motion are superimposed upon the translational motion. 11a,b …”

Mean first passage time for random walk on dual structure of dendrimer

“…Besides, the major difference between the structures of dendrimer and Husimi cactus is that the former is a tree while the latter contains loops. The previous research showed that the existence of loops has strong correlation with the dynamics of polymer networks [54][55][56], so that we also analyze the influence of loop structure on trapping process by comparing the results of Husimi cactus with dendrimer.…”