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A linear relation is found between tan δ and a loading-interfacial-area parameter, ϕψ, for NR vulcanisates with six untreated carbon blacks at several loadings. In IIR, a better linear relation is found between tan δ and a modified parameter ( ϕ1.5ψ0.5 ), indicating that the dependence on loading is relatively stronger than on interfacial area. In both polymers, a graphitized black gives high tan δ and an oxidized black gives low tan δ (at the appropriate value of the loading-interfacial-area parameter). The data suggest a slight effect of aggregate morphology, in that carbon blacks of more compact, less open aggregate structure tend to give lower tan δ; however, the results are on the borderline of experimental error. The value of tan δ at high amplitude is a linear function of ΔE′ , where ΔE′ is the difference between the elastic modulus at low and high amplitudes. This indicates that tan δ depends on the number and strength of interaggregate interactions, as proposed by Payne. Reduced rubber-black interaction, as with the graphitized black, gives more interaggregate interaction, leading to higher ΔE′ and tan δ; and conversely with the oxidized black. With the graphitized black in IIR, tan δ is even higher than expected from the value of ΔE′ ; thus it appears that in the virtual absence of polymer-filler interaction, molecular slippage may make an additional contribution to hysteresis.
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Medalia et al. (1978) studied this question.
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