Micromechanical modeling of the linear viscoelasticity of carbon-black filled styrene butadiene rubbers: The role of the filler–rubber interphase

Abstract

Micromechanics modeling of the linear viscoelasticity of carbon-black filled styrene butadiene rubbers (SBR) shows that a simple representation of a spherical rigid-phase surrounded by rubber gum and embedded in an homogeneous equivalent medium provides access to the effective volume fraction of fillers. This simple representation is successful for a significant range of filler amount, and for materials in the glassy state. For materials in the rubbery state, experimental results support the existence of a filler-rubber interphase with reduced mobility due to confinement. The 4-phase micromechanics model, which accounts for a bounded rubber layer coating the fillers, provides satisfactory estimates of the linear viscoelasticity of filled rubbers from the rubbery state to the glassy state. It also provides access to the fillerrubber interphase behavior that appears viscoelastic, and to an estimate of the interphase thickness.

Using a pattern-based homogenization scheme for modeling the linear viscoelasticity of nano-reinforced polymers with an interphase

“…Therefore, the latter contain some gum trapped between filler subparticles, and an effective volume content of particles can be defined that we denote f 1 . As explained by Diani et al (2013), the values that are used here are consistent with experimental measures based on the experimental procedure of Medalia (1972). In addition to a volume fraction and an average size, these particles may also have a size distribution, and the distance between nearest neighbors may also be distributed around an average value.…”

“…Then, assuming that the viscoelastic shear modulus of the interphase is enhanced compared to the viscoelastic shear modulus of the bulk gum shown in Fig. 3, because of a reduced molecular mobility, and assuming the carbon black is elastic and incompressible, with G 1 = 70 GPa, Diani et al (2013) experiment is shown in Fig. 4 for the SBR filled with 40 per hundred rubber (phr) carbon black, where a 30% effective volume fraction of filler could be evaluated.…”

“…In order to investigate the impacts of a possible effect of dispersing the particles more or less uniformly and of a probable particle size distribution on the estimate of the viscoelastic behavior of filled rubbers, the MRP selfconsistent model is applied assuming that the behavior of the interphase estimated by Diani et al (2013) is reasonable. Therefore, in the following, phase 1 consists of incompressible elastic spherical particles with G 1 = 70 GPa, with a radius of 30 nm (except when a radius distribution is defined) and with a volume fraction of f 1 = 0.3.…”

“…In a recent work (Diani et al, 2013), the present authors studied the viscoelastic behavior of several carbon-black filled styrene butadiene rubbers (SBRs). The experimental data showed evidences in favor of the existence of an interphase at the rubber-filler interface, with enhanced viscoelastic properties compared to the bulk matrix viscoelasticity.…”

Physical interpretation of the Mullins softening in a carbon-black filled SBR

“…As a consequence, in order to understand how the degradation of the rubber-filler interface may have such a drastic impact on the mechanical response of the filled rubbers, another explanation must be taken into account. Actually, the micromechanics analysis of the linear viscoelasticity of carbon-black filled rubbers is in favor of the existence of a layer at the rubber-filler interface significantly stiffer than the rubber matrix due to restrained mobility [9]. A degradation of this layer, by desorption for instance, may have a significant impact on the material stiffness.…”