The strain dependence of rubber viscoelasticity. Part II. The influence of carbon black

Abstract

In Part I of this series it was shown how variations in the dynamic Young's modulus with extension could be represented by linear relations for gum rubbers in the region of 0 to 100% extension.' The present work uses a similar treatment to examine how the viscoelastic behavior of natural rubber within this extension region is affected by the incorporation of two carbon blacks of widely differing colloidal activity. One of these materials, MT black, consists substantially of spherical particles with a mean diameter of about 0.4 microns: electron microscopy of cut surfaces of the black-rubber compound showed that the individual particles were welldispersed. The finer material, HAF black, has a mean particle diameter of about 0.04 microns but exists in the rubber compound in a flocculated condit,ion with aggregates up to about 0.3 microns in diameter.The rubber containing the coarse, &IT black yielded linear strain relations enabling a direct comparison to be made with the behavior of the gum: the HAF material did not give linear relations for either the dynamic or the equilibrium Young's modulus. To facilitate discussion of this behavior it is desirable to set out more explicitly than in Part I the model underlying the analysis. Figure 1 shows the model used to formalize the c. -dependence of dynamic behavior upon extension. The series modulus E , represents the normal Hookean elasticity of a solid. This will be a slowly decreasing function of temperature and probably a slowly increasing function of strain12 but its magnitude will generally be well in excess of 1Olo dyne/ so that the deformation in this element will be relatively small under conditions where there is an appreciable rubberlike contribution to the elasticity. The rest of the model comprises an equilibrium modulus Eo in parallel with a number of Maxwellian elements typified by the modulus Er damped by the series viscosity T~ES, T , being the relaxation time of the element.It is now supposed that the system is stretched to a finite extension ratio X and allowed to relax at this extension so that Em, Eo, E,, and T , all take up equilibrium values dependent on X and, in general, differing from their values in the unstrained stat,e. In the present work the frequency and temperature are such that the dynamic Young's modulus E*( = E' + iE") is always much smaller than Em, and under this conditionwhere w / 2~ is the frequency and the other variables all relate to the extension ratio X.In amorphous viscoelasticity theory the moduli Eo and E , are treated as rubberlike moduli, being directly proportional to the absolute temperature and to the density. If it is now assumed that these moduli all have the same strain dependence, viz : Eo(X) = Eo(l)f(X)Et(X) = Et(l)f(X) for all i

Chain and Segmental Dynamics of Poly(2-vinylpyridine) Nanocomposites

“…The most interesting question becomes: why do oxide NPs have rather weak effect on segmental dynamics in our case? Numerous studies of the interfacial effects on segmental mobility present a wide array of conflicting experimental resultssome with large changes in T g − ,− and others with negligible changes. A comprehensive review on the subject has been compiled by Robertson and Roland .…”

The effect of filler surface energy on the Tg of silica—polydimethylsiloxane composites

“…He calculated from the Williams, Landel, and Ferry equation (WLF) an increase in glass transition temperature of 2, 6, and 7OC for systems filled with 8.68, 20.3, and 36.7 vol % glass beads. On the other hand, Mason (2) found no change in the glass transition temperature of rubber loaded with 18 vol % of a reinforcing black. According to Landel's calculations, at this loading the increase should have amounted to a 4.5OC rise in T,.…”

Glass Transition and Interfacial Segmental Dynamics in Polymer-Particle Composites

“…Accurate volume measurements are more difficult than calorimetry and thus only a few studies 64,[75][76][77] have reported the glass transition of filled polymers by dilatometry (Table VI). The earliest was by Mason,75 who found no T g shift in natural rubber filled with either a larger particle MT carbon black or a tenfold-smaller HAF carbon black at filler concentrations up to 18% by volume. Since this was unexpected, Mason prepared other compositions, which exhibited the same T g invariance.…”