New techniques in sol–gel characterisation – mechanical measurements and fractal characteristics

We report theoretical and experimental work which demonstrates how the viscoelastic dispersion of shear waves may be exploited in studies of the rheological properties of systems such as `critical-gelsʹ – systems at the gel point. At the gel point a material undergoing gelation changes, from one in which only short range connectivity is present, to one in which structural self-similarity is sample-spanning. Experiments are described in which marked changes in high-frequency shear-wave dispersion are recorded during the viscoelastic-liquid to viscoelastic solid transition about the gel point. The results accord with theoretical treatments of the sol–gel transition, based on a modified form of the Gross–Marvin network model. We report how this modified model has been used to investigate the interdependence of the high- and low-frequency features of the evolving relaxation time spectra associated with the growth of discrete, mechanically self-similar nodal networks. An analysis of the growth of the networks reveals a scale-invariant characteristic of the underlying gel microstructure and an associated fractal dimension, df, in the range 1<df<1.8, the maximum value of which corresponds to that reported in computer simulations of `cluster–clusterʹ aggregation processes. The limitations of conventional rheometry in identifying the inner `cut-offʹ length scale of such a fractal characteristic are discussed. Shear wave dispersion measurements are also reported for aqueous dispersions of a synthetic clay colloid which, like the simulated viscoelastic networks, combines the characteristics of high-shear elasticity and low-wave attenuation with a maximum fractal dimension of 1.8.