Formation Mechanism of Triply Periodic Minimal Surface as a Thermodynamic Equilibrium Structure

对热致性和溶致性液晶进行了热力学和结构研究，特别关注了与三周期极小表面密切相关的复杂结构的自发形成原因。在热致性和溶致性体系中，tpms相关的立方相通常比邻近的液晶相热容量小。这种趋势可以通过考虑TPMS三维连通性所抑制的波动来理解。通过对片层相（近晶相）和立方相相变熵的分析，提出了在“表面”的基础上构建“热力学”的可能性，其中立方相的单元胞将起到基本单元的作用。通过一个新的例子BABH系列证明了多元立方相随烷基链长而出现。基于具有i3d对称的立方相（旋相）反射强度与烷基链长的关系，首次揭示了分子水平上的聚集结构。BABH分子的烷基链末端位于旋回线上，分子核聚集形成棒状聚集体组成的“攀爬架”。即使烷基链的体积大于分子核的体积，这种聚集模式仍然存在。这与嵌段共聚物和溶致液晶的情况形成强烈对比，在这些情况下，聚集模式转变为逆相。在它们的体积大致相等的区域，另一种具有Im3m对称性的立方相在BABH和ANBC中常见。这表明，澄清该Im3m相的分子聚集模式及其稳定性将是解决低质量热致性体系与溶致性体系和嵌段共聚物有何不同的关键，这两种体系的物理表面都很容易想象。

Thermodynamic and structural study was conducted on thermotropic and lyotropic liquid crystals paying special attention on why so complex structures closely related to triply periodic minimal surfaces (TPMS) are spontaneously formed. Smaller heat capacity than neighboring liquid crystalline phases is common to TPMS-related cubic phases both in thermotropic and lyotropic systems. This trend can be understood by considering the suppressed fluctuation due to three-dimensional connectivity of TPMS. The analysis of the phase transition entropy between lamellar (smectic) and cubic phases suggests the possible construction of "thermodynamics" on the basis of "surfaces", where a unit cell of cubic phase would play a role of a basic unit. Appearance of plural cubic phases depending on the alkyl chain length was proved through putting a new example, BABH series. On the basis of the alkyl chain length dependence of the reflection intensities from a cubic phase having Ia3d symmetry (gyroid phase), the aggregation structure at the molecular level was, for the first time, revealed. The ends of alkyl chain of BABH molecules are located on the gyroid while the molecular cores aggregated to form a "jungle gym" consisting of rod-like aggregates. This aggregation mode survives even if the volume of the alkyl chain becomes larger than that of the molecular core. This is in a strong contrast to the cases of block copolymer and lyotropic liquid crystals, where the aggregation mode changes into the inverse phase. In the region where their volumes are roughly equal to each other, the other cubic phase with Im3m symmetry appears commonly in BABH and ANBC. This suggests that the clarification of the molecular aggregation mode in this Im3m phase and of its stability would be a key to solve the issue how different are low-weight thermotropic system from lyotropic system and block copolymers, in both of which physical surface can easily be imagined.