Internal Dynamics and Elasticity of Fractal Colloidal Gels

The dynamic structure factor of fractal colloidal gels is shown to exhibit a stretched exponential decay to a finite plateau with an exponent of about 0.7. The value of the plateau depends on both initial particle volume fraction ${\ensuremath{\varphi}}_{0}$ and scattering wave vector. We show that this behavior results from the contribution of internal elastic modes of many length scales, and present a model which accounts for the data. From the observed plateau we determine that the very small elastic modulus scales as $G\ensuremath{\sim}{\ensuremath{\varphi}}_{0}^{3.9}$, in agreement with predictions, and with direct mechanical measurements.