Does an Intermediate Structure Exist in an Ordered Bicontinuous Double Diamond-Double Gyroid Transition? Singular Value Decomposition of Small-Angle X-ray Scattering

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  • 特異値分解法を用いた共連続ダブルダイアモンド-ダブルジャイロイド転移における小角X線散乱の解析 中間体構造は存在するのか？
  • トクイチ ブンカイホウ オ モチイタ キョウ レンゾク ダブルダイアモンド-ダブルジャイロイド テンイ ニ オケル ショウカク Xセン サンラン ノ カイセキ : チュウカンタイ コウゾウ ワ ソンザイ スル ノ カ?

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Abstract

<p>Microdomain structures formed in the mixture of polystyrene-b-polyisoprene (SI) diblock copolymer, whose number-averaged molecular weight, Mn, and volume fraction, ƒPS are, respectively, 45,000 and 0.70, with a polyisoprene homopolymer (PI, Mn = 18,000) and dioctyl phthalate (DOP) were studied by the singular value decomposition (SVD) of small-angle X-ray scattering. The volume ratio of SI/PI/DOP was 43.7/16.3/40 vol.%. SAXS measurement was performed on the mixture every 20 ℃ from 130 to 30 ℃ in a cooling cycle and successively every 20 ℃ from 30 to 130 ℃ in a heating cycle. The scattering observed at the corresponding temperatures in both of the cycles were in good agreement. The scattering measured at 130 ℃ had multiple peaks; the relative peak position ratios to the primary peak was close to 1 : √8/6 : √14/6 : √16/6 : √20/6 : √22/6 that are typical to an ordered bicontinuous double gyroid (OBDG) structure, while the one at 30 ℃ had multiple peaks; the relative peak position ratios to the primary peak were 1 : √3/2 : √4/2 : √6/2 : √8/2 typical to an ordered bicontinuous double diamond (OBDD) structure. The scattering at the intermediate temperatures from 50 to 110 ℃ showed more complex multiple peaks. The SVD was conducted on the set of the SAXS profiles: The rank was 6 but the first two singular values were significantly larger than the rest of the four values. Thus, the low-rank approximation with the first two singular values was employed. All of the temperature dependent SAXS were successfully rebuilt with the first two basis functions obtained by SVD. The weighting functions used to reconstruct the profiles relate to the first two singular values; the second weighting function relating to the temperature change of the SAXS showed only one drastic change between 70 and 90 ℃. This means that no intermediate structure between OBDD and OBDG exists. The fraction of OBDD was also calculated by the temperature change in SAXS: 0.98, 0.85, 0.28 and 0.11 at 50, 70, 90 and 110 ℃, respectively.</p>

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