Linear algebraic proof and examples of composite-lattice-based liquid crystalline phases

References

• Satake, I. (2007). Linear Algebra (Senkei Daisu in Japanese), Kyoritsu: (Tokyo): ISBN 4-320-01554-1.
   Google Scholar
• Sakurai, T. (1995). Guidebook for X-ray Crystal Analysis (X-sen Kozo Kaiseki no Tebiki in Japanese), Shokabo: (Tokyo); ISBN-13:978-4785324025.
   Google Scholar
• Jhambre, P. Weiss and Miller indices, https://www.youtube.com/watch?v=e0Rm3RELwqo
   Google Scholar
• Proof of Weiss zone law: See page AH123 in the following pdf document: Midgley, P. (2013). Materials Science ”, University of Cambridge. http://pramodkumarsingh.weebly.com/uploads/2/6/4/4/26446137/ah.pdf.
   Google Scholar
• See Figure 2.2-1 and Supplementary Table I in Ref. 2 for Bravais lattices and 230 space groups, respectively.
   Google Scholar
• Ohta, K. (2013). Dimensionality and Hierarchy of Liquid Crystalline Phases: X-ray Structural Analysis of the Dimensional Assemblies, The depository of Shinshu University, submitted on 11 May, http://hdl.handle.net/10091/17016.
   Google Scholar
• See Equation (2.5-5) in p. 43 of Ref. 2.
   Google Scholar
• For block-out of matrix and reduction of representation, see Ref. 1 and the following review: Tanimura, S. (2007). Introduction of Group Theory for Liquid Crystal Scientists, Ekisho, 11(4), 365–372 .
   Google Scholar
• SL, SG, SH, SJ and SK are hard liquid crystalline phases having a little bit three-dimensionality: see Table I in the following book: Gray, G. W., & Goodby, J. W. G. (1984). Smectic Liquid Crystals-Textures and Structures, Leonard Hill: (Grasgow and London): ISBN 0-249-44168-3.
   Google Scholar
• Alami, E., Levy, H., Zana, R., Weber, P., & Skoulious, A. (1993). Liq. Cryst., 13, 201.
   Web of Science ®Google Scholar
• Ohta, K., Sugiyama, T., & Nogami, T. (2000). J. Mater. Chem., 10, 613.
   Web of Science ®Google Scholar
• Goossens, K., Lava, K., Nockemann, P., van Hecke, K., van Meervelt, L., Driesen, K., Görller-Walrand, C., Binnemans, K., & Cardinaels, T. (2009). Chem. Eur. J., 15, 656.
   PubMed Web of Science ®Google Scholar
• See Figure 10.10 and Table I in Ref. 9.
   Google Scholar
• Billard, J. (1984). C. R. Acad. Sc. Paris, t. 299, Serie II, n° 14, 905.
   Google Scholar
• Ohta, K., Ishii, A., Yamamoto, I., & Matsuzaki, K. (1984). J. Chem. Soc., Chem. Commun., 1099.
   Google Scholar
• Ohta, K., Muroki, H., Takagi, A., Hatada, K., Ema, H., Yamamoto, I., & Matsuzaki, K. (1986). Mol. Cryst. Liq. Cryst., 140, 131.
   Web of Science ®Google Scholar
• Sakashita, H., Nishitani, A., Sumiya, Y., Terauchi, H., Ohta, K., Yamamoto, I. (1988). Mol. Cryst. Liq. Cryst., 163, 211.
   Web of Science ®Google Scholar
• Méry, S., Haristoy, D., Nicoud, J.-F., Guillon, D., Diele, S., Monobe, H., & Shimizu, Y. (2002). J. Mater. Chem., 12, 37.
   Web of Science ®Google Scholar
• See the X-ray diffraction pattern of the compound P0-17 in Fig. 5 of the following paper: Pressner, D., Göltner, Chr., Spieß, H. W., & Müllen, K. (1993). Ber. Bunsenges. Phys. Chem., 97, 1362.
   Web of Science ®Google Scholar
• El-ghayoury, A., Douce, L., Skoulios, A., & Ziessel, R. (1998). Angew. Chem. Int. Ed., 37, 1255.
   PubMed Web of Science ®Google Scholar
• See Figure 7 and Table III in the following paper: Belarbi-Massouras, Z., Takagi, A., Ema, H., Hasebe, H., Ohta, K., Massouras, G., Fujimoto, T., & Yamamoto, I. (1991). Mol. Cryst. Liq. Cryst., 201, 147.
   Web of Science ®Google Scholar
• See Figure 4 (a) and (b) in Ref. 21.
   Google Scholar
• See Figures 2, 3 and 4 in Page 22–23 in the following book: Helfrich, W., & Heppke, G. ed., Springer Series in Chemical Physics 11, Liquid Crystals of One- and Two-Dimensional Order”, Springer-Verlag, 1980(Berlin);
   Google Scholar
  Richter, L., Demus, D., Sackman, H. (1976). J. Phys. Colloques., 37, C3–41.
   Google Scholar
• See Figures 2 and 3 in the following paper: Horie, H., Takagi, A., Hasebe, H., Ohta, K., Yamamoto, I. (2001). J. Mater. Chem., 11, 1063.
   Web of Science ®Google Scholar
• See Figures 14 and 16 in the following paper: Lindner, N., Kölbel, M., Sauer, C., Diele, S., Jokiranta, J., & Tschierske, C. (1998). J. Phys. Chem. B, 102, 5261.
   Web of Science ®Google Scholar
• Kutsumizu, S., Morita, K.., Ichikawa, T., Yano, S., Nojima, S., Yamaguchi, T. (2002). Liq. Cryst., 29, 1447.
   Web of Science ®Google Scholar
• Ichikawa, T., Yoshio, M., Hamasaki, A., Mukai, T., Ohno, H., Kato, T. (2007). J. Am. Chem. Soc., 129, 10662.
   PubMed Web of Science ®Google Scholar
• Ichihara M., Suzuki A, Hatsusaka, K., Ohta, K. (2007). Liq. Cryst., 34, 555.
   Web of Science ®Google Scholar
• Mukai, H., Yokokawa, M., Ichihara, M., Hatsusaka, K., Ohta, K. (2010). J. Porphyrins Phthalocyanines, 14, 188.
   Web of Science ®Google Scholar