Effect of Carbon Black on Hysteresis of Rubber Vulcanizates: Equivalence of Surface Area and Loading

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Abstract
We have developed an empirical correlation between the loss tangent (tan δ) and the product of the volume fraction (ϕ) of carbon black in the composite and the total filler-polymer interfacial area per unit volume of composite (ψ). This correlation was applied to vulcanizates based on SBR-1500, SBR-1712, and NR with various compounding procedures and under different deformation conditions, including forced vibration nonresonant dynamic test machines, and the Goodyear-Healey pendulum rebound. The functional form of the correlation was qualitatively similar in all instances ; however, quantitative aspects of the correlation are dependent upon the particular experimental conditions. Tan δ is a weak function of the deformation amplitude over the region of practical interest. This is in contrast to hysteretic energy loss, which is proportional to the square of the amplitude. The validity of the correlation over wide ranges of amplitude, temperature, and frequency indicates that the viscoelastic relaxation or loss processes are similar over the range of conditions studied. Since the combined parameter, ϕψ, is proportional to ϕ2 multiplied by the specific surface area of the carbon black, this relation implies an equivalence between surface area and loading, with regard to tan 5. It has previously been shown that the elastic modulus depends on structure and loading. Thus, the dynamic properties, including hysteresis under various conditions, can be predicted from the carbon black properties, and compounds can be designed for desired dynamic properties by independent adjustment of loading, structure and surface area.

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