The effects of degree of mixing and concentration of carbon black on the tensile properties of filled elastomers

Based on the concept of entropy of mixing, a new method for determining the degree of mixing of the filler in a polymer matrix has been established. The measurement used in this method is based on a new variable, the effective volume fraction of the filler, ϕ′, which is a function of the mixing index, A, and the volume fraction of the filler, ϕ. The mixing index can be determined from the tensile modulus data of filled elastomers. Excellent agreement is obtained between the mixing index and the dispersion of the filler as determined by a morphological study of cryogenically fractured surfaces of filled elastomers. Using the new variable, the effective volume fraction of the filler, useful relationships for the tensile modulus and the ultimate stretch ratio of filled elastomer have been established. Experimental data confirm that these relationships can well describe the effects of concentration and degree of mixing on the two tensile properties of filled elastomers.