Elasticity of a percolation system: silica smoke

Abstract

Cab-O-Sil powder is a cluster aggregate of silica spheres formed from silica smoke. The fractal dimension of clusters of 14 nm diameter spheres is determined to be [Formula: see text], in good agreement with that calculated for the cluster-aggregate model, [Formula: see text]. Measurements of Young's modulus (Y) of packed 7 nm Cab-O-Sil powder, with an occupied volume fraction in the range 0.035 < f < 0.3, are well described by the percolation threshold fc = 0.017 ± 0.002 and an elasticity exponent τ = 2.9 ± 0.2. The measured exponent is larger than the calculated scalar Born (balls and springs) result, τ = 2.0, but smaller than the more realistic bond-bending result, τ > 3.55. The measured result is attributed to bond bending within a complex percolation structure.