Relationship between the bulk modulus and the conductivity on a fractal

Abstract

De Gennes has shown by an explicit calculation that the conductivity, conductance, and bulk modulus of a percolating network (a simple model for gelation without solvent) are related. We use recent scaling results on fractals to demonstrate that the bulk modulus on a fractal scales with the conductivity, while the force constant scales with the conductance. Our treatment is applicable to all fractal geometries, of which the percolating network is a special example.