Application of the Christensen‐Lo Model to the Reinforcement of Elastomers by Fractal Fillers

This paper is concerned with the development of a hydrodynamic model for the reinforcement of rubber by colloidal fillers such as silica and carbon black. Each fractal aggregate is replaced by an equivalent effective sphere, and the reinforcing ability of the latter is estimated using the Christensen-Lo solution of the “three-phase composite sphere model”. With a single adjustable parameter, the model allows a quantitative interpretation of the small-strain modulus of rubber loaded with up to 50 PHR of N234 carbon black, which falls just below the filler overlap concentration. No additional contributions to the small-strain modulus by filler–filler “interactions” are needed to interpret the data. A branched filler aggregate made up of spherical primary particles (black) and the effective sphere replacing it (gray).