Temperature Dependence of Viscoelastic Properties of Carbon-Black-Filled Rubbers in Small Shearing Deformations

Measurements of dynamic storage and loss shear moduli G′ and G″ (0.12 to 2 Hz) and shear relaxation modulus G(t) (up to 104 s) have been made on six vulcanized and one unvulcanized carbon-black-filled rubber compounds over a temperature range from −22.5° to 63°C. The maximum shear strain in the oscillatory deformations was less than 0.005 and in the stress relaxation measurements, 0.015. The temperature dependence of viscoelastic properties could not be fully described in terms of horizontal shifts (αT) of logarithmic time or frequency scales. It could, however, be largely described by vertical shifts (ST) corresponding to uniform temperature dependence of the magnitudes of contributions to modulus from a spectrum of relaxation mechanisms. There were some departures from this behavior, especially in a blend containing two rubber species and in the unvulcanized compound at long times. The temperature dependence of the ST shift factors followed the van't Hoff equation with values of ΔH from 5.9 to 14.7 kJ/mole, attributable to a heat of dissociation of contacts between particle aggregates. The slow relaxation over many logarithmic decades of time scale in the rubbery zone of viscoelastic behavior is attributed to adjustments of such contacts by Brownian motion, which leave the density of the structure unchanged as shown by constancy of the differential dynamic modulus measured by superposed small oscillating deformations.