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

The elastic modulus of a colloidal aggregate network is dependent on the amount and spatial distribution of mass, as well as particle properties including size, shape, and particle-particle interactions. At high volume fractions, the elastic properties of a network of close-packed particle flocs is dependent on the strength of the interfloc links. A previously developed weak-link fractal scaling theory relates the elastic constant (K) of the network to the volume fraction of solids ({Φ}), namely K~Φ^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 modulus and the volume fraction of solids.