Effects of the size of fillers on viscoelasticity in the glassy state of poly(styrene--butadiene) reinforced by carbon black

Watanabe, Yuki*; Kumagawa, Daiki*; Karitani, Shu*; Inoue, Tadashi*; Iwabuki, Hitoshi*; Nakanishi, Yohei*; Shibata, Motoki*; Motokawa, Ryuhei   ; Sugita, Tsuyoshi   ; Ueda, Yuki   ; Kumada, Takayuki   ; Yamamoto, Katsuhiro*; Mita, Kazuki*; Miyazaki, Tsukasa*; Takenaka, Mikihito*

We investigated how the particle size of carbon black (CB) affects the reinforcement of CB to vulcanized poly(styrene-co-butadiene) (SBR) in the glassy region. When the average diameter of CB d is larger than 100 nm, the enhancement of modulus can be expressed by the Eshelby/Mori-Tanaka model, which agrees with the results obtained for an SBR/silica system. On the other hand, at d 100nm, the volume fraction dependence of the enhancement becomes stronger than the theory's prediction. The scattering studies on the SBR/CB systems revealed that the aggregates of CB at d 100nm consist of densely packed CB, while the aggregates of CB at d 100nm exhibit branch structures. At d 100nm, the voids or the occluded region in the packed CB increase the volume fraction, resulting in a stronger volume fraction dependence of the enhancement.