Shear wave dispersion in mechanically self-similar gel networks

Abstract

A study of viscoelastic shear wave dispersion in a simulated gelation process involving mechanically self-similar nodal networks is reported. The network formed at the gel point (the infinite network cluster, or `critical gel') shares a common structural feature of smaller network clusters and the onset of a recognizably `gel-like' feature is shown to occur when the characteristic wavelength of the network cluster becomes twice that of an individual node. It is shown that, during gelation, the dispersion of shear waves can be exploited to assess the proximity of a system to an equivalent `critical gel' state at any single frequency, thereby identifying the smallest length scale at which gel-like characteristics are established prior to the gel point. In this way, and for the first time, a rheometrical basis is established for examining the gel-like, self-similar characteristics of pre-gel point viscoelastic liquid systems, in terms of the gel equation but in the absence of a frequency-independent loss tangent. Experiments are reported for a critical gel in which the high-frequency wave dispersion is in good agreement with theory.