Carbon-black-filled rubber stress concentration

The response of unvulcanized black-filled polymers (in the rubbery zone) to oscillating shear strains (151) is characterized by a strong dependence of the dynamic storage modulus, G, on the strain amplitude or the strain work (product of stress and strain amplitudes). The same behavior is observed in cross-linked rubbers and will be discussed in more detail in connection with the dynamic response of filled networks. It is clearly established that the manyfold drop of G, which occurs between double strain amplitudes of ca. 0.001 and 0.5, is due to the breakdown of secondary (Van der Waals) filler aggregation. In fact, as Payne (102) has shown, in the limit of low strain amplitudes a storage modulus of the order of 10 dynes/cm2 is obtained with concentrated (30 parts by volume and higher) carbon black dispersions made up from low molecular liquids or polymers alike. Carbon black pastes from low molecular liquids also show a very similar functional relationship between G and the strain amplitude. At lower black concentrations the contribution due to secondary aggregation becomes much smaller and, in polymers, it is always sensitive to the state of filler dispersion. 

---