我們使用小角度X光散射實驗研究聚丙烯-聚苯乙烯 (isotactic polypropylene-block- polystyrene, iPP-b-PS) 所形成的雙連續奈米結構，分別為ordered bicontinuous double diamond (OBDD) 結構及ordered bicontinuous double gyroid (OBDG) 結構。我們由小角度X光散射圖譜可得知此嵌段共聚物在升溫過程中會形成OBDG結構，當繼續升溫至有序-無序轉化溫度 (order-disorder temperature) 時則轉變為無序結構;而在初步降溫過程中會漸漸發展出無序結構與OBDG結構的共存相，最終，OBDG結構經由有序-有序轉化 (order-order transition, OOT) 轉變為OBDD結構。
此實驗結果顯示低溫狀態時OBDD較OBDG結構穩定，為比較兩結構的熱力學穩定性，我們分別探討界面自由能(interfacial free energy) 及iPP與PS兩鏈段之packing frustration熵的損失。在界面自由能方面，雙曲面分布的OBDD結構擁有較高的比表面積 (specific surface area, S/V)；而iPP與PS兩鏈段的packing frustration則是互相競爭的關係，若假設兩結構轉換過程中體積守恆，且結構的幾何形狀為圓柱而非雙曲面分布，我們可得知每單位體積的OBDD結構擁有較小的iPP鏈段packing frustration，但會增加PS鏈段的packing frustration；反之，OBDG結構則擁有較低的PS鏈段packing frustration。
綜合實驗結果及熱力學計算，我們推論在高溫狀態中，減緩PS鏈段的packing frustration為主導因素，進而使OBDG成為穩定結構；而在低溫狀態下則是由iPP鏈段的packing frustration主導，造成OBDD成為低溫時的穩定結構。

We have investigated the formation of ordered bicontinuous nanostructures in a diblock copolymer composed of a stereoregular block, isotactic polypropylene-block- polystyrene (iPP-b-PS). The ordered bicontinuous double diamond (OBDD) and ordered bicontinuous double gyroid (OBDG) nanostructures in iPP-b-PS were revealed by temperature-dependent small angle x-ray scattering (SAXS) experiments. The OBDG structure developed at the temperature above the melting point of iPP block upon heating from the as-cast state. The OBDG structure transformed into disordered state as further heating to the order-disorder transition (ODT) temperature. The subsequent cooling from the disordered state resulted in the formation of OBDG phase which coexisted with the disordered phase. Further cooling induced the development of the OBDD structure. Eventually, OBDD became the dominant structure, indicating that there was an order-order transition (OOT) from OBDG to OBDD and the OBDD was more stable at the lower temperature. We further discussed the thermodynamic stabilities of OBDG and OBDD by comparing the interfacial free energy and packing frustration of iPP and PS blocks in these two phases. The OBDG constructed by the tripods of iPP prescribed lower packing frustration for the PS block, while the OBDD constructed by the tetrapod iPP domains offered smaller packing frustration for the iPP block chains. In the case of the interfacial free energy, OBDD was found to exhibit a slightly higher specific interface (S/V) than OBDG if the iPP domains exhibit hyperbolic surface. However, as the iPP domains approach cylinder in geometry, (i.e., the domain with constant mean curvature) OBDG displays a slightly higher (S/V). Therefore, we proposed that the stabilities of OBDG and OBDD were governed by the packing frustration of PS and iPP blocks constituting the matrix phase and microdomains, respectively. At high temperature, the release of packing frustration of PS block dominated, such that OBDG was more stable. On the other hand, the relief of iPP packing frustration became increasingly important with decreasing temperature, and when the temperature was sufficiently low, this thermodynamic driving force dominated, such that OBDD became the stable structure. The relief of the packing frustration of iPP block was probably relevant to its strong tendency to form helical segments at lower temperature.

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