Shear elasticity and yield stress of silica–silicone physical gels: Fractal approach

Abstract

The elastoplastic behavior of silica–silicone compounds has been characterized by a yield stress σ s and an elastic modulus G 0 . Scaling laws have been established for the changes in rheometrical parameters with the volume fraction Φ v of silica: σ s ∝(Φ v ) 3.3 and G 0 ∝(Φ v ) 4.2 and single master curves have been obtained whatever the silica type used. The mesoscopic structure of the compounds has been studied using x-ray and light scattering and a semidilute fractal structure has been observed, with a fractal dimension D≈1.8 and a characteristic length scale 4 μm. In this paper, a formulation of the nonfluctuating semidilute fractal concept allows us to relate the fractal dimension to the rheological scaling laws: σ s ∝(Φ v ) 4/( 3−D ) and G 0 ∝(Φ v ) 5/( 3−D ) .