Hierarchically Self-Organized Dissipative Structures of Filler Particles in Poly(styrene-ran-butadiene) Rubbers

We elucidated the spatial distribution of filler particles in cross-linked poly­(styrene-ran-butadiene) rubbers (SBR) developed under a typical fillers/rubbers compounding process as one of dissipative structures formed under a stress field imposed on the given system. Two types of fillers and two types of SBR were used to prepare four kinds of the fillers/rubbers composites to investigate effects of specific polymer/filler interactions on the hierarchically self-organized dissipative structures under a given processing condition. The dispersion structures of the filler particles were explored by using the combined small-angle scattering (CSAS) method, which enables the exploration of the structures existing over the wide length scale ranging from ∼6 nm to ∼20 μm. The measured CSAS profiles were analyzed by using a newly developed scattering theory on fractal structures built up by the “cluster” as their lower cutoff objects. This cluster is composed of a few aggregates, defined as the fused primary filler particles, bound by the SBR chains. The scattering from the cluster having characteristic internal structures built up by the fillers and the SBR chains was theoretically formulated by generalizing the Debye–Bueche fluctuation theory for infinite space to the theory for a “confined space” relevant to the cluster size. The dispersion state of the fillers in SBR was clarified on the basis of hierarchical structures consisting of five structure levels as detailed in the text. More specifically, it has the following characteristics depending on the specific interactions: Small, compact clusters build up compact mass-fractal structures, while large, loose clusters build up open mass-fractal structures.