2022-08-09T05:20:49Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000136042021-08-03T01:28:19ZDimensionality and Hierarchy of Liquid Crystalline Phases: X-ray Structural Analysis of the Dimensional Assemblies液晶相の次元性と階層性：その次元性集合体のX 線構造解析太田, 和親液晶相の種類liquid crystalline phase types液晶相のX線構造解析X-ray structure analysis of liquid crystalline phases結晶格子の段階的崩壊stepped degradation of crystalline latticesX線反射線の次元性dimensionalities of X-ray reflection lines液晶相の次元性dimensionalities of liquid crystalline phases部分空間linear subspace液晶構造解析の黄金則Four Golden Rules for Mesophase Structural Analysis逆格子reciprocal latticeFirst of all, the author describes a great variety of liquid crystalline phases (=mesophases) and their classifications from a classical viewpoint of the molecular shapes. The classical classification is unable to rationally overview the whole liquid crystalline phases. Therefore, the author adopts universal linear algebra to overview dimensionalities of all the liquid crystalline phases, and he explains his useful theory of "Stepped Degradation of Dimensionality" from the equations of original three-dimensional crystal structures. For example, on heating or adding solvent, a three-dimensional orthogonal lattice stepwise degrades into a sum of two-dimensional rectangular lattice and one-dimensional lattice, and, on further heating or adding more solvent, the two-dimensional lattice vanishes and one-dimensional lattice only remains, and then the one-dimensional lattice finally degrades into zero dimensionality: i. e., 3D → (2⊕1)D → 1D → 0D. Hereupon, (2⊕1)D means not 3D but a direct sum of two-dimensional subspace and one-dimensional subspace from the viewpoint of linear algebra. Hence, the mesophases having (2⊕1)D are not crystalline phases having 3D. By using a temperature-dependent X-ray diffractometer, we can realize the stepped degradation of dimensionality from three-dimension to 0-dimension on the stepped phase transitions of liquid crystalline materials. We can categorize all the liquid crystalline phases from the dimensionalities irrespective of molecular shapes, which are very useful for a simple systematic classification of all kinds of liquid crystals. Finally, the author explains his developed method of X-ray structural analysis of the dimensional assemblies from his original “Four Golden Rules for Mesophase Structural Analysis”. For reader’s understanding, representative mesophase structures are practically analyzed from his method by using reciprocal lattices, in this textbook.Articlearticle2013-05-11application/pdf128https://soar-ir.repo.nii.ac.jp/record/13604/files/Dimensionality_and_Hierarchy_of_Liquid_Crystalline_Phases.pdfjpn