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，特别关注为什么自发形成与三重周期极小表面（TPMS）密切相关的复杂结构。在热致和溶致体系中，与TPMS相关的立方相的热容比相邻液晶相小是常见的。这种趋势可以通过考虑TPMS的三维连通性所抑制的波动来理解。层状（近晶）和立方相之间的相变熵的分析表明，可能的“热力学”的基础上的“表面”，其中立方相的晶胞将发挥作用的基本单位的建设。以BABH系列为例，证明了多立方相的出现依赖于烷基链的长度。的基础上的烷基链长度的反射强度从立方相具有Ia3d对称性（螺旋相）的依赖性，在分子水平上的聚集结构，为第一次，揭示。BABH分子的烷基链末端位于螺旋体上，而分子核心聚集成由棒状聚集体组成的“爬架”。即使烷基链的体积变得大于分子核心的体积，这种聚集模式也会存在。这与嵌段共聚物和溶致液晶的情况形成强烈对比，其中聚集模式变为反相。在它们的体积彼此大致相等的区域中，在BABH和ANBC中通常出现具有Im 3m对称性的另一立方相。这表明，在该Im3m相中的分子聚集模式及其稳定性的澄清将是解决低重量热致体系与溶致体系和嵌段共聚物有何不同的问题的关键，在这两种体系中，可以容易地想象物理表面。

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.