Supporting Information Conformations of Ring Polystyrenes in Semidilute Solutions and in Linear Polymer Matrices Studied by SANS

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1 Supporting Information Conformations of Ring Polystyrenes in Semidilute Solutions and in Linear Polymer Matrices Studied by SANS Takuro Iwamoto, Yuya Doi,, Keita Kinoshita, Atsushi Takano,*, Yoshiaki Takahashi, Eunhye Kim, Tae-Hwan Kim, Shin-ichi Takata, Michihiro Nagao #,% and Yushu Matsushita*, S-1. SEC profiles of h/d-random linear PS samples Figure S1 shows size exclusion chromatography (SEC) profiles of three random linear polystyrene (PS) samples consisting of hydrogenous/deuterium styrene monomers at the volume ratio of 50/50 with different molar masses of (20, 80 and 270) kg/mol. All three samples have M w/m n less than Although ran-lps-80 shows a small peak-tail at shorter elution time, i.e., higher molecular weight side, the fraction of this tail is not much large (less than 5 %). Hence, this sample was used as it was. The molecular characteristics of these samples are summarized in Table 2 of the main text. Figure S1. SEC profiles of (a) ran-l-20, (b) ran-l-80 and (c) ran-l-270. S1

2 S-2. Scattering profiles of R-70 measured at NIST and HANARO Raw SANS data of the bulk R-70 sample measured at NIST and HANARO are shown together in Figure S2. The profiles exhibit a good overlap each other, and hence in this study we can fairly treat and compare the data obtained at the two instruments. Figure S2. Raw SANS profiles for the bulk R-70 sample measured at NIST and HANARO. Error bars of the data are within symbol sizes. S-3. Determination of background scattering intensities Accurate estimation of background scattering intensities is important to correctly evaluate the information of ring chain conformations in solutions and in solid solutions. In this study, we need to subtract two kinds of background scatterings from raw data, I(q) raw, i.e., one is the incoherent scattering intensities originating from hydrogenous polymers in R-70 (or L-70), and the other is scatterings from solvents and matrices, i.e., d 8-toluene and h/d-ran-lps. Here, we denote these two terms as I incoh and I solv, and the coherent scattering intensity I(q) coh is represented as the following relationship: I(q) coh = I(q) raw I incoh (1 Φ P) I solv (S1) where Φ P represents the volume fraction of R-70 (or L-70). First, to estimate I incoh of the solution and solid solution samples, we adopted the method reported by Shibayama et al. 1 as I incoh K exp( Kt) 1 (S2) 4 t d N m A s H (S3) where t is the sample thickness, d is the density of a hydrogenous polymer (1.05 g/cm 3 ), N A is the Avogadro s number, m is the molar mass of monomer ( g/mol), σ s is the scattering cross section per monomer ( cm 2 ), Φ H is the volume fraction of the hydrogenous polymer (= 0.5 Φ p). We confirmed S2

3 that I incoh for bulk R-70 and L-70 samples (i.e., Φ p = 1) are (0.20 ± 0.01) cm -1, 2 and those for solutions and ring/linear blends regularly decrease with decreasing Φ P. Second, the contribution of I solv for solutions and ring/linear solid solution samples is determined by directly measuring the solvent and matrices samples, i.e., d 8-toluene and three ran-lps. Figure S3 shows the raw I(q) data of d 8-toluene and three ran-lps samples. We confirmed that the intensities of the solvent and matrices are almost q-independent at q 0.02 Å -1, and they are sufficiently lower than those for the solution and ring/linear blend samples measured in this study. By using I incoh and I solv, we successfully estimated the I(q) coh, for all of the solution and solid solution samples, and the data obtained are shown in the main text. Figure S3. Raw SANS profiles of d 8-toluene and three ran-lps samples. S-4. Estimation of the contribution of intermolecular correlation term To estimate the contribution of intermolecular correlations in solution samples, SANS measurements for L-70 and R-70 solutions with Φ P ~ 0.1 dissolved in h- and d 8-toluene mixtures were conducted. Theoretically, the coherent scattering intensity I(q) for solution samples consisting of h-polymer, d-polymer and solvent is described as: 3-6 I(q) = (ρ hp ρ S) 2 S HH(q) + (ρ dp ρ S) 2 S DD(q) + 2 (ρ hp ρ S) (ρ dp ρ S) S HD(q) (S4) where ρ hp, ρ dp and ρ S are the scattering length densities for hydrogenous polymer, deuterated polymer and solvent, respectively, S HH(q) and S DD(q) are the scattering factors for a pair of hydrogenous polymers and a pair of deuterated polymers, respectively, and S HD(q) is the cross term. This relationship can be rewritten as: 5-6 I(q) = (ρ hp ρ dp) 2 S S(q) + (ρ P ρ S) 2 S T(q) (S5) where ρ P (= ρ hpφ hp/φ P + ρ dpφ dp/φ P) is the scattering length density for the hydrogenous/deuterated polymer mixture. S S(q) represents the single-chain scattering factor, while S T(q) denotes the total chain scattering S3

4 factor including both intrachain and interchain contributions. When measuring the solution samples without any consideration for the scattering contrast, I(q) inevitably contains the contribution of S T(q) in addition to that of S S(q). In contrast, when matching the scattering contrast of solute polymer (ρ P) with that of solvent (ρ S), i.e., ρ P = ρ S, the second term on the right side of eq. S5 can vanish. 5-6 Here, ρ hp = cm 2 for h-ps, ρ dp = cm 2 for d-ps, ρ hs = cm 2 for h-toluene and ρ ds = cm 2 for d 8-toluene are used. For the solutions of h-ps/d-ps (volume ratio of 50/50) dissolved in d 8-toluene, their S T(q) terms do not vanish, while for the solutions of h-ps/d-ps (volume ratio of 50/50) dissolved in h-/d 8-toluene mixture (volume ratio of ~50/50) their S T(q) term should be theoretically disappeared. Moreover, the ratio S S(q)/S T(q) is known to become larger as the concentration of solutions becomes higher. 7 Based on the above backgrounds, we performed the SANS measurements of R-70 and L-70 solutions with Φ P ~ 0.1 dissolved in d 8-toluene and in h-/d 8-toluene mixture (volume ratio of 50/50), and evaluated the contribution from S T(q). SANS measurements were performed using the time-of-flight small- and wide-angle neutron scattering instrument, TAIKAN, installed on the BL15 beamline at the Material and Life Science Experimental Facility (MLF) in the Japan Proton Accelerator Research Complex (J-PARC). 8 The range of the neutron wavelength λ was from 4.2 to 11.4 Å, and the sample-to-detector distance was 5.65 m, covering the q-range of q/å Figure S4a and S4b show the raw SANS profiles of R-70 and L-70 solutions, respectively, with Φ P ~ 0.1 dissolved in d 8-toluene and h/d 8-toluene (volume fraction of 50/50). To normalize the intensity, I(q) was divided by Φ P. For both R-70 and L-70 solutions, the data at low q ( 0.02 Å -1 ) show a good agreement between the solutions in d 8-toluene and h/d 8-toluene. In contrast, I(q) at high q ( 0.02 Å -1 ) for h/d 8-toluene solutions are much higher than those for d 8-toluene ones. We conceive this difference at high q mainly originates from the background scattering of solvents. Figure S4. Raw SANS profiles for (a) R-70 and (b) L-70 solutions with Φ P ~ 0.1 dissolved in d 8-toluene (red circles) and h/d 8-toluene (with the volume fraction of 50/50; blue diamonds). Error bars of the data are within a symbol size. S4

5 Then, the background scattering is subtracted from the raw I(q) data following the manner as described in the previous section (S-3) of the Supporting Information, and the results are shown in Figure S5. It is found from Figure S5 that the I(q) profiles for both R-70 and L-70 solutions in d 8-toluene and in h/d 8-toluene show a good overlap covering a whole q range after subtraction of the background. In particular, the data at low q ( 0.02 Å -1 ), which are used for the Guinier s approximation to estimate R g in the main text, are almost completely overlapped, irrespective of the isotopes of the solvent. Therefore, for semi-dilute solutions with Φ P 0.1 of R-70 and L-70, we can conclude that the R g values are correctly estimated from d 8-toluene solutions without any further consideration of S T(q). At high q regime with 0.02 q/å , a small difference in I(q) for both R-70 and L-70 solutions is observed, i.e., I(q) for d 8-toluene solutions are slightly higher than those for h/d 8-toluene ones. We conceive this difference originates from the small but non-negligible contribution of S T(q). However, it is probably difficult to accurately estimate this S T(q) term for the solutions with Φ P ~ 0.1. If we treated the toluene solution samples of R-70 and L-70 having much lower Φ P, we would have to consider the contribution of the S T(q) term more carefully. Figure S5. Coherent SANS profiles of (a) R-70 and (b) L-70 solutions with Φ P ~ 0.1 dissolved in d 8-toluene (red circles) and h/d 8-toluene (with the volume fraction of 50/50; blue diamonds) after subtraction of the background scattering, i.e., I incoh and I solv. Error bars of the data are within a symbol size. We would like to emphasize that solutions dissolved in h/d 8-toluene mixtures exhibit the relatively strong background scattering from solvents as shown in Figure S4, although it should be probable to vanish the S T(q) term by the contrast matching method. We actually prepared the solute polymer samples, R-70 (and L-70), by blending h- and d-homopolymers with the volume fraction of 50/50 to obtain the scattering intensity as high as possible (see eq. 11 in the main text.) Nevertheless, the intensity of the h/d 8-solvent mixture is non-negligibly high compared with the particle scattering of R-70 (and L-70). The I(q) data of samples with lower scattering power such as more diluted solutions tend to be more uncertain. Thus, we concluded that in this study the preparation of the samples, i.e., R-70 (and L-70) simply dissolved in d 8-toluene, is the best way to obtain the accurate I(q) data with small contribution from the solvent, at least S5

6 for the concentrated region with Φ P 0.1 treated in this study. Finally, we need to make a comment for R-70/ran-LPS solid solutions. For these samples, we do not need to consider the correlation term S T(q) at any solute polymer concentration Φ P since the solute R-70 and the matrix ran-lps have exactly the same scattering length density (i.e., ρ P = ρ S), and hence the S T(q) term in eq. S5 should always vanish. S-5. Guinier plots for d8-toluene solutions of L-70 Figure S6 shows the Guinier plots for L-70 solutions with various Φ L dissolved in d 8-toluene. These plots show a good linearity in each adequate q range. The R g values obtained from these plots are summarized in Table 3 in the main text. Figure S6. Guinier plots (ln I(q) vs q 2 ) for L-70 solutions in d 8-toluene. The black solid lines indicate the best fit lines for the Guinier s methods (eq. 1 in the main text). S6

7 S-6. SANS profile analyses for d8-toluene solutions in the Kratky form. Figure S7 and S8 display the Kratky s form (q 2 I(q) vs q) of the fitting results for L-70 and R-70 solutions in d 8-toluene, respectively. It was confirmed from Figure S7 and S8 that the fittings show a good agreement with experimental data for both L-70 and R-70 solutions as described in the main text. Figure S7. Comparison of the experimental SANS profiles for L-70/d 8-toluene solutions (symbols) and the fitting (solid curves) in the Kratky representation (q 2 I(q) vs q). Figure S8. Comparison of the experimental SANS profiles for R-70/d 8-toluene solutions (symbols) and the fitting (solid curves) in the Kratky representation (q 2 I(q) vs q). S7

8 References: 1. Shibayama, M.; Nagao, M.; Okabe, S.; Karino, T. Evaluation of Incoherent Neutron Scattering from Softmatter. J. Phys. Soc. Jpn. 2005, 74, Iwamoto, T.; Doi, Y.; Kinoshita, K.; Ohta, Y.; Takano, A.; Takahashi, Y.; Nagao, M.; Matsushita, Y. Conformations of Ring Polystyrenes in Bulk Studied by SANS. Macromolecules 2018, 51, Benoit, H.; Koberstein, J.; Leibler, L. Small Angle Neutron Scattering from Mixture of Labelled and Unlabelled Chains and from Partially Labelled Chains. Makromol. Chem. Suppl. 1981, 4, Quan, X.; Koberstein, J. T. Theoretical Aspects of Small-Angle Neutron Scattering from Multiphase Polymers. J. Polym. Sci., Part B: Polym. Phys. 1987, 25, Hammouda, B. SANS from Homogenous Polymer Mixtures: A Unified Overview. Adv. Polym. Sci. 1993, 106, Hammouda, B.; Jia, D.; Cheng, H. Single-Chain Conformation for Interacting Poly(N-isopropylacrylamide) in Aqueous Solution. Open Access J. Sci. Technol. 2015, 3, King, J. S.; Boyer, W.; Wignall, G. D.; Ullman, R. Radii of Gyration and Screening Lengths of Polystyrene in Toluene as a Function of Concentration. Macromolecules 1985, 18, Takata, S.; Suzuki, J.; Shinohara, T.; Oku, T.; Tominaga, T.; Ohishi, K.; Iwase, H.; Nakatani, T.; Inamura, Y.; Ito, T.; Suzuya, K.; Aizawa, K.; Arai, M.; Otomo, T.; Sugiyama, M. The Design and q Resolution of the Small and Wide Angle Neutron Scattering Instrument (TAIKAN) in J-PARC. JPS Conf. Proc. 2014, 8, S8

2.1 Traditional and modern applications of polymers. Soft and light materials good heat and electrical insulators

2.1 Traditional and modern applications of polymers. Soft and light materials good heat and electrical insulators . Polymers.1. Traditional and modern applications.. From chemistry to statistical description.3. Polymer solutions and polymer blends.4. Amorphous polymers.5. The glass transition.6. Crystalline polymers.7.