Using a combined ultra-small-angle and small-angle scattering (CSAS) method of neutrons and X-rays, we investigated hierarchical structures of carbon black (CB) highly loaded in polyisoprene (PI) and poly-(styrene-random-butadiene) copolymer (SBR) under mechanical field (defined respectively as CB/PI and CB/ SBR) as well as in toluene under a sonic field (defined as CB/toluene). In order to analyze each structure level comprising the hierarchical structures of CB from the CSAS profiles, we employed the unified Guinier/powerlaw approach proposed by Beaucage (J. Appl. Cryst. 1995, 28, 717). Furthermore, in order to extract not only sizes but also shapes of the structure elements, we developed a modified approach, in which the Guinier scattering function utilized in the Beaucage approach was replaced by a form factor of the corresponding structure. Comparison of the scattering profiles from CB/PI and CB/SBR with CB/toluene clarified that (i) the smallest structure elements of CB (that further form mass-fractal objects) in PI and SBR were not an unbreakable unit of the CB filler which resulted after sonification in toluene but were instead composed of the several unbreakable units bounded together by polymer chains (defined as "dispersible units") and (ii) sizes and shapes of the dispersible units depended on the polymer matrix: Its size was larger in PI than in SBR. (iii) Moreover, the enlarged size of the dispersible unit in PI was found to enlarge the upper cutoff length of the mass-fractal structure in PI, while the mass-fractal dimensions themselves remained unchanged between PI and SBR. Hence, the detailed characterizations of the hierarchical structures by using CSAS shed new light on the dispersion process of the filler compound in the polymer matrix.

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