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 phi(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 similar to phi(0)(3.9), in agreement with predictions, and with direct mechanical measurements.