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Eugene Andrews
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1 Supporting Information for Hierarchically Self-organized Dissipative Structures of Filler Particles in Poly(styrene-ran- butadiene) Rubbers Daisuke Yamaguchi 1, Takeshi Yuasa 2, Takuo Sone 2, Tetsuo Tominaga 2, Yohei Noda 1, 3, Satoshi Koizumi 1, 3 1, 4, 5,*, and Takeji Hashimoto 1 Quantum Beam Science Center, Japan Atomic Energy Agency, Tokai, Naka, Ibaraki , Japan 2 Yokkaichi Research Center, JSR Corporation, 100 Kawajiri-cho, Yokkaichi, Mie , Japan 3 Faculty of Engineering, Ibaraki University, Nakanarusawa-cho , Hitachi-shi, Ibaraki , Japan 4 Kyoto University, Kyoto , Japan 5 National Tsing Hua University, Hsinchu 30013, Taiwan * to whom correspondence should be addressed: hashi2@pearl.ocn.ne.jp S1

2 S-1. Comparisons between the SAXS and CSANS Profiles from the Composites with the Fillers (Si/SBR and CB/SBR) and Those from the Composites without the Fillers (SBR). Figure S1 presents comparisons between the scattering profiles from Si/f-SBR and those from f-sbr without Si (part a) and comparisons between those from Si/n-SBR and those from n-sbr without Si (part b), while Figure S2 presents corresponding comparisons between CB/f-SBR and f-sbr (part a) and those between CB/n-SBR and n- SBR (part b). More precisely, in each part of each figure the top two profiles numbered (1) and (2) compare the CSANS profiles from the composites with and without the fillers, respectively, while the other top two profiles numbered (4) and (5) compare the SAXS profiles from the composites with and without the fillers, respectively. The scattering powers of the particles of Si, CB, and ZnO, which significantly contribute to the net scattering, are given by the square of the difference in SLD between each particle and SBR,!b 2 P, i, (i = n or X for the neutron and X-ray beam, respectively) where!b P, i is defined by!b P, i = b P, i " b SBR, i (see Table 3 for the values). Here the subscript P designates the particle, Si, CB or ZnO. Figure S3 presents the reduced scattering power of the particle P in the matrix of the SBR for the neutron or X-ray, reduced with respect to the scattering power of Si or CB in the matrix of the for X-ray, (!b P, i ) 2 / (!b Si, X or!b CB, X ) 2 in the logarithmic scale where the subscript X denotes X-ray. In Figures S1 and S2, each of the CSANS and SAXS profiles from the composites with the fillers [the profiles (1) and (5), respectively] has the scattered intensity higher than those without the fillers [the profiles (2) and (4), respectively] in the whole q range covered. These results are natural because of the extra contribution of the fillers to the scattering. However, the difference in the intensity between the two cases for SAXS is much smaller than that for CSANS; S2

3 In the case of the SAXS the difference becomes small at q q C, X as indicated by the arrow marked by q C, X in Figures S1 and S2, commonly for all the four composites, while in the case of CSANS, the difference becomes small only near q C, n also marked by the arrow marked by q C, n in those figures. These differences in the scattering intensity can be accounted for on the basis of the differences in the scattering powers between!b 2 ZnO, n and!b2 Si, n!b 2 ZnO, n and!b2 CB, n for neutron and those between!b2 ZnO, X and!b2 Si, X or those between or those between!b 2 ZnO, X and!b2 CB, X for X-ray as calculated from Table 3 and shown in Figure S3. In fact, the ratio (!b 2 / ZnO, n!b2 Si, n ) / (!b 2 / ZnO, X!b2 Si, X) 1/7 suggests that the contribution of ZnO relative to that of Si to the net CSANS intensity is much less than that to the net SAXS intensity: The ratio (!b 2 / ZnO, n!b2 CB, n ) / (!b 2 / ZnO, X!b2 CB, X) 1/40 suggests the same conclusion as given above with the qualification that the relative contribution of ZnO becomes even smaller in the case of CB compared with Si. S-2. Extraction of CSANS and SAXS Profiles Arising from the Spatial Distribution of the Fillers (Si or CB) Only. We treated the scattering from the SBR composites without the fillers (but with ZnO) as the background scattering for the net scattering from the filler/sbr composites. We subtracted the background scattering (profiles 2 and 4) from the net scattering (profiles 1 and 5, respectively) from the composites with the fillers containing ZnO by the same amount (see Table 2). The profiles (3) and (6) shown by the solid lines in parts (a) and (b) in Figures S1 and S2 present the CSANS and SAXS profiles, respectively, corrected for the background scattering. The corrected profiles (3) for CSANS and (6) for SAXS shown by the solid lines were respectively compared with the uncorrected net scattering profiles (1) for CSANS and (5) for SAXS shown by the symbols in parts S3

4 (a) and (b) in Figure S1 and S2. The results clearly revealed that ZnO hardly contributes to the net CSANS scattering from the compounds in the whole q-range covered, which is common for all the four composites with the fillers (as shown in Figures S1 and S2). It was also elucidated that the ZnO contribution to the net SAXS results is negligible at q q c, X. Moreover, the corrected CSANS and SAXS profiles are superposable each other only by the vertical shift in the double logarithmic plot commonly for all the four composites. This revealed an important conclusion that the corrected CSANS and corrected SAXS profiles are essentially described by the two-phase structure having the dispersed Si and CB fillers in the homogeneous matrix composed of the SBR polymer and the other ingredients shown in Table 3, respectively. S-3. Comparison of CSANS Profiles for Si/CB/K-SBR (K = f and n) Composites with the Theoretical Scattering Profiles for Model C. We analyzed the scattering profiles for the Si/CB/K-SBR = 50/4/100 (K = f or n) composites, which form currently major commercial products due to their specific merits, e.g., the wet grip property for Si and the tear and abrasion resistance properties for CB, on the basis of the theoretical scattering profiles, I av, theor, K -SBR (K = f or n), for Model C given by eq 32. The result indicates that the agreement between I exp and I av, theor, K -SBR is fine in the high q region at q > ~ (nm 1 ) both for Si/CB/n-SBR and for Si/CB/f-SBR but poor at q < ~ (nm 1 ) for Si/CB/n-SBR and at q < ~ nm 1 for Si/CB/f-SBR. The fine agreement in the high q-range is natural, because the scattering arises from the independent scattering from the fillers and thereby depends only on the total amount of Si and CB. Thus, the fine agreement in the high q range emphasizes and makes sure the disagreement in the low q-range. This further implies that Model C cannot account for the spatial distribution of Si and CB in K-SBR and hence the hierarchical S4

5 structures of the fillers at the structure level higher than level 3(clusters and fractal agglomerate of the clusters). Hence, the alternative fitting procedure based on Model A and Model B was conducted in Figure 13. S5

6 Figure S1. CSANS and SAXS profiles from (a) Si/f-SBR and (b) Si/n-SBR. In each part, the profiles (1) and (2) are for the CSANS profiles with and without the fillers, respectively, while the profiles (4) and (5) are for the SAXS profiles with and without the fillers, respectively. The profile (3) is the CSANS profile corrected for the scattering from the ZnO particles obtained by subtracting profile (2) from profile (1), while the profile (6) is the SAXS profile corrected for the scattering from the ZnO particles [the profile (5) the profile (4)]. The CSANS and SAXS profiles should be referred to the left-hand-side ordinate scale and the right-hand-side ordinate scale, respectively. S6

7 Figure S2. CSANS and SAXS profiles from (a) CB/f-SBR and (b) CB/n-SBR. The profiles (1) to (6) have the same meaning as those specified in Figure S1 with the replacement of Si by CB. S7

8 Figure S3. The reduced scattering power of the particle P (= CB, ZnO, Si), " # (!b P, i ) 2 /!b Si, X ( ) 2 or (!b CB, X ) 2 $ %, for the neutron (i =n) or X-ray (i =X) beam in the matrix of the SBR polymer. The number in the parenthesis in the figure shows the value for the reduced scattering power. Note that!b Si, X =!b CB, X. S8

9 Figure S4. Experimental CSANS profiles, I exp ( q), for the binary filler systems: The top two profiles present those for Si/CB/n-SBR (filled blue circles) and Si/CB/f-SBR (filled red circles), while the profiles shown by unfilled blue circles marked with ( 2) and unfilled red circles marked with ( 3) are the corresponding profiles vertically shifted by 10 2 and 10 3, respectively. These experimental profiles, I exp ( q), for Si/CB/K-SBR (K = f and n) composites are compared with the theoretical scattering profiles, I av, theor, f-sbr and I av, theor, n-sbr for Model C, shown by green and purple solid lines, respectively. S9

Space-Filling Fractal Description of Ion-induced. Local Thermal Spikes in Molecular Solid of ZnO

Space-Filling Fractal Description of Ion-induced Local Thermal Spikes in Molecular Solid of ZnO Shoaib Ahmad 1,2,* and Muhammad Yousuf 1 1 CASP, Church Road, Government College University, Lahore 54000,