Modified fractal model and rheological properties of colloidal networks

The scaling relationship between the storage modulus (G(')) and the volume fraction of solids (Phi) in fat crystal networks has been explained by the fractal model developed by our group. However, many experimental results and simulation studies suggest that the stress distribution within a colloidal network is dramatically heterogeneous, which means that a small part of the network carries most of the stress, while the other part of the network does not contribute much to the elastic properties of the system. This concept was introduced into a modified fractal model. The volume fraction of solids term (Phi) in the original fractal model was replaced by Phi(e), the effective volume fraction of solids, in the modified fractal model, which represents the volume fraction of stress-carrying solids. A proposed expression for Phi(e) is given and a modified expression for the scaling relationship between G(') and Phi is obtained. The modified fractal model fits the experiment data well and successfully explains the sometimes observed nonlinear log-log behavior between the storage modulus of colloidal networks and their volume fraction of solids.