Fractal aggregate networks elasticity

Marangoni, A.G. 2000. Elasticity of high-volume-fraction fractal aggregate networks A thermodynamic approach. Phys. Rev. B. 62, 13951-13955. 

Elasticity of Fractal Aggregate Networks Mechanical Arguments... 

Accordingly, we expect a power law behavior G,0 (O/Op)3 5 of the small strain elastic modulus for 0>0. Thereby, the exponent (3+df [j)/(3—df)w3.5 reflects the characteristic structure of the fractal heterogeneity of the filler network, i.e., the CCA-clusters. The strong dependency of G 0 on the solid fraction Op of primary aggregates reflects the effect of structure on the storage modulus. 

In 1992, Vreeker et al. presented rheological data for aggregated fat networks in the framework of previous fractal theories. These authors indicated that the elastic modulus varied with particle concentration according to a power law, in keeping with the proposed models for the elasticity of colloidal gels. 

Marangoni s group has since advanced the fractal theory applying Shih et al. s weak link regime with Vreeker s rheological findings to develop a fractal theory for fat crystal networks. Fat crystal networks are considered as cross-linked fractal clusters formed by aggregating fat crystals. Self-similarity is assumed to exist within the clusters, from the primary fat crystals to the clusters. If the force-constant of the links between micro structures was expressed as k/, then the macroscopic elastic constant K (in one dimension) of the network could be modeled as ... 

Flocculation occurs when the net force between the particles is attractive. At low volume fractions, aggregation results in clusters, or floes, which have a fractal structure (7). For most systems, the properties of the aggregating suspension changes drastically at a certain critical particle concentration, 0g, which corresponds to the formation of a space-filling particle network. In dilute suspensions, at 0 < 0g, suspensions have no yield stress and the discrete clusters will settle more or less independently. Above 0g, the suspension can sustain a stress before yielding the elasticity may be significant, and the rate of settling is very slow. 

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