Studies of shearwave dispersion in critical-gel systems

The viscoelastic dispersion of shearwaves in a gelling system about the gel-point is examined from the viewpoint of rheometrically exploitable features. Marked changes in the wave dispersion occur due to the changing pattern of frequency dependence of the complex shear modulus G in the viscoelastic-liquid to viscoelastic-solid transition. These changes are compared with theoretical predictions of the shearwave dispersion characteristics of critical-gel systems at the gel-point, where G has a frequency dependence described by the Chambon-Winter Gel Equation, in which G',G'~ ωn (0 < n < 1). An Oldroyd rheological model is used to simulate the propagation of a transitional viscoelastic liquid-like to viscoelastic solid-like behaviour from high- to low-frequencies, a notion consistent with the macroscopic gel-like characteristics presented by growing molecular clusters to high-frequency shearwaves in cross-linking systems. The results of this treatment are in good agreement with critical-gel behaviour for n in the range predicted by theoretical treatments of gel- point. The latter are based on self-similar connectivity of branched macromolecules and a scaling theory of fractal correlations, in which n is in the range 0.67 < n < 1. The measured wave dispersion between 400 Hz and 1.2 kHz in a system for which n lies within this range at gel-point, is in good agreement with the theoretical prediction