Elasticity of high-volume-fraction fractal aggregate networks: A thermodynamic approach

The elastic modulus of a colloidal aggregate network is dependent on the am ount and spatial distribution of mass, as well as particle properties inclu ding size, shape, and particle-particle interactions. At high volume fracti ons, the elastic properties of a network of close-packed particle Aocs is d ependent on the strength of the interfloc links. A previously developed wea k-link fractal scaling theory relates the elastic constant (K) of the netwo rk to the volume fraction of solids (Phi), namely K similar to Phi (1/(3-D) ). In this paper, we extend this theory to include a pre-exponential factor and obtain an exact expression for relationship between the Young's modulu s and the volume fraction of solids.