Dynamic Mechanical Properties for Carbon Black-in-Oil; Analysis of Frequency and Temperature Dependence
Authors: Fitzgerald Edwin R. , Ferry John D. 
Published: February 2011

Abstract
None of the viscoelastic data on complex compliance vs. frequency reported by Fitzgerald for a sample of carbon black-in-oil can be reduced to a common reference temperature by horizontal shifting of the frequency scale. At temperatures from 25.2 to 50.6°C, the elastic compliance, J′, and the elastic modulus, G′, can be superposed quite well by magnitude (vertical) shift factors, ST−1 and ST, respectively. The same values of ST bring curves for the loss compliance, J″, and the loss modulus, G″, near each other but not into coincidence. The factor ST decreases with increasing temperature; log ST is not linear in the reciprocal absolute temperature, but at 25°C, the slope of such a plot corresponds to a van't Hoff energy of 41.9 kJ (10 kcal) which, on the basis of a reversible dissociation of a network of carbon black agglomerates with increasing temperature, may be interpreted as some measure of the agglomeration energy of the carbon black network. The frequency dependence of the viscoelastic functions was characterized by relatively little change in J′ and G′ at low frequencies, with a loss tangent of the order of 0.4, contrasted with a very abrupt increase in both modulus components (decrease in both compliance components) at the upper end of the frequency range. At temperatures below 25.2°C, the shapes of the compliance and modulus functions change with temperature and cannot be superposed by vertical shifts. G′ increased and J′ decreased more rapidly with decreasing temperature. At the lowest temperatures, the frequency dependence of the viscoelastic functions was quite different from that at high temperatures. The loss tangent was near unity; G′ and G″ were both approximately proportional to ω1/2 and J′ and J″ were both proportional to ω1/2, where ω is the circular frequency. This difference at low temperatures may be associated with a much higher viscosity of the oil (pour point 4.4°C). However, an analysis of the properties of this composite system in terms of its components was not attempted at the present time. In particular, a determination of the dynamic mechanical properties of the process oil alone is needed in order to judge its contribution to the mechanical response of the combined oil-black system. The above evidence cited for two distinct temperature regimes for the viscoelastic behavior of the carbon black-in-oil is strengthened by the loss tangent vs. circular frequency curves which as measured, without shifting, cluster quite closely together at temperatures from 25.2 to 50.6°C as expected for equal temperature-magnitude shifts for each component of compliance or modulus. However, at 14.0 and 5.5°C the loss tangent curves are distant from the high temperature cluster of curves and at −4.2 and −12.2°C are of completely different shapes than those at the other temperatures. From the initial analysis and the partial success of the temperature-magnitude superposition of the dynamic mechanical data on this sample of carbon black-in-oil, we conclude that measurements of this kind, on other blacks, in other oils, and in other concentrations will prove to be valuable in gaining an increased quantitative understanding of the role that carbon black agglomeration networks play in modifying the mechanical properties of vulcanized rubber stocks.