International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 4.4, pp. 463-464   | 1 | 2 |

Section 4.4.6. Other phases

P. S. Pershana*

aDivision of Engineering and Applied Science and The Physics Department, Harvard University, Cambridge, MA 02138, USA
Correspondence e-mail: pershan@deas.harvard.edu

4.4.6. Other phases

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We have deliberately chosen not to discuss the properties of the cholesteric phase in this chapter because the length scales that characterize the long-range order are of the order of micrometres and are more easily studied by optical scattering than by X-rays (De Gennes, 1974[link]; De Vries, 1951[link]). Nematic phases formed from chiral molecules develop long-range order in which the orientation of the director [\langle {\bf n}\rangle] varies in a plane-wave-like manner that can be described as [{\bf x} \cos (2 \pi z/ \lambda) + {\bf y} \sin (2 \pi z/ \lambda)], where x and y are unit vectors and [\lambda/2] is the cholesteric `pitch' that can be anywhere from 0.1 to 10 µm depending on the particular molecule. Even more interesting is that for many cholesteric systems there is a small temperature range, of the order of 1 K, between the cholesteric and isotropic phases for which there is a phase known as the `blue phase' (Coates & Gray, 1975[link]; Stegemeyer & Bergmann, 1981[link]; Meiboom et al., 1981[link]; Bensimon et al., 1983[link]; Hornreich & Shtrikman, 1983[link]; Crooker, 1983[link]). In fact, there is more than one `blue phase' but they all have the property that the cholesteric twist forms a three-dimensional lattice twisted network rather than the plane-wave-like twist of the cholesteric phase. Three-dimensional Bragg scattering from blue phases using laser light indicates cubic lattices; however, since the optical cholesteric interactions are much stronger than the usual interactions between X-rays and atoms, interpretation of the results is subtler.

Gray and Goodby discuss a `smectic-D' phase that is otherwise omitted from this chapter (Gray & Goodby, 1984[link]). Gray and co-workers first observed this phase in the homologous series of 4′-n-alkoxy-3′-nitrobiphenyl-4-carboxylic acids (Gray et al., 1957[link]). In the hexadecyloxy compound, this phase exists for a region of about 26 K between the smectic-C and smectic-A phases: smectic-C (444.2 K) smectic-D (470.4 K) smectic-A. It is optically isotropic and X-ray studies by Diele et al. (1972[link]) and by Tardieu & Billard (1976[link]) indicate a number of similarities to the `cubic–isotropic' phase observed in lyotropic systems (Luzzati & Riess-Husson, 1966[link]; Tardieu & Luzzati, 1970[link]). More recently, Etherington et al. (1986[link]) studied the `smectic-D' phase of 3′-cyano-4′-n-octadecyloxybiphenyl-4-carboxylic acid. Since this material appears to be more stable than some of the others that were previously studied, they were able to perform sufficient measurements to determine that the space group is cubic P23 or [Pm3] with a lattice parameter of 86 Å. Etherington et al. suggested that the `smectic-D' phase that they studied is a true three-dimensional cubic crystal of micelles and noted that the designation of `smectic-D' is not accurate. Guillon & Skoulios (1987[link]) have proposed a molecular model for this and related phases.

Fontell (1974[link]) has reviewed the literature on the X-ray diffraction studies of lyotropic mesomorphic systems and the reader is referred there for more extensive information on those cubic systems. The mesomorphic structures of lyotropic systems are much richer than those of the thermotropic and, in addition to all structures mentioned here, there are lyotropic systems in which the smectic-A lamellae seem to break up into cylindrical rods which seem to have the same macroscopic symmetry as some of the discotic phases. On the other hand, it is also much more difficult to prepare a review for the lyotropic systems in the same type of detail as for the thermotropic. The extra complexity associated with the need to control water concentration as well as temperature has made both theoretical and experimental progress more difficult, and, since there has not been very much experimental work on well oriented samples, detailed knowledge of many of these phases is also limited. Aside from the simpler lamellae systems, which seem to have the same symmetry as the thermotropic smectic-A phase, it is not at all clear which of the other phases are three-dimensional crystals and which are true mesomorphic structures. For example, dipalmitoylphosphatidylcholine has an [{\rm L}_{\beta}] phase that appears for temperatures and (or) water content that is lower than that of the smectic-A [{\rm L}_{\alpha}] phase (Shipley et al., 1974[link]; Small, 1967[link]; Chapman et al., 1967[link]). The diffraction pattern for this phase contains sharp large-angle reflections that may well correspond to a phase that is like one of the crystalline phases listed in Tables 4.4.1.1[link] and 4.4.1.2[link], and Fig. 4.4.1.1[link]. On the other hand, this phase could also be hexatic and we do not have sufficient information to decide. The interested reader is referred to the referenced articles for further detailed information.

References

Bensimon, D., Domany, E. & Shtrikman, S. (1983). Optical activity of cholesteric liquid crystals in the pretransitional regime and in the blue phase. Phys. Rev. A, 28, 427–433.
Chapman, D., Williams, R. M. & Ladbrooke, B. D. (1967). Physical studies of phospholipids. VI. Thermotropic and lyotropic mesomorphism of some 1,2-diacylphosphatidylcholines (lecithins). Chem. Phys. Lipids, 1, 445–475.
Coates, D. & Gray, G. W. (1975). A correlation of optical features of amorphous liquid–cholesteric liquid crystal transitions. Phys. Lett. A, 51, 335–336.
Crooker, P. P. (1983). The cholesteric blue phase: a progress report. Mol. Cryst. Liq. Cryst. 98, 31–45.
De Gennes, P. G. (1974). The physics of liquid crystals. Oxford: Clarendon Press.
De Vries, H. L. (1951). Rotary power and other optical properties of liquid crystals. Acta Cryst. 4, 219–226.
Diele, S., Brand, P. & Sackmann, H. (1972). X-ray diffraction and polymorphism of smectic liquid crystals. II. D and E modifications. Mol. Cryst. Liq. Cryst. 17, 163–169.
Etherington, G., Leadbetter, A. J., Wang, X. J., Gray, G. W. & Tajbakhsh, A. (1986). Structure of the smectic D phase. Liq. Cryst. 1, 209–214.
Fontell, K. (1974). In Liquid crystals and plastic crystals, Vol. II, edited by G. W. Gray & P. A. Winsor, pp. 80–109. Chichester, England: Ellis Horwood.
Gray, G. W. & Goodby, J. W. (1984). Smectic liquid crystals: textures and structures. Glasgow: Leonard Hill.
Gray, G. W., Jones, B. & Marson, F. (1957). Mesomorphism and chemical constitution. Part VIII. The effect of 3′-substituents on the mesomorphism of the 4′-n-alkoxydiphenyl-4-carboxylic acids and their alkyl esters. J. Chem. Soc. 1, 393–401.
Guillon, D. & Skoulios, A. (1987). Molecular model for the R smectic DS mesophase. Europhys. Lett. 3, 79–85.
Hornreich, R. M. & Shtrikman, S. (1983). Theory of light scattering in cholesteric blue phases. Phys. Rev. A, 28, 1791–1807.
Luzzati, V. & Reiss-Husson, F. (1966). Structure of the cubic phase of lipid–water systems. Nature (London), 210, 1351–1352.
Meiboom, S., Sethna, J. P., Anderson, P. W. & Brinkman, W. F. (1981). Theory of the blue phase of cholesteric liquid crystals. Phys. Rev. Lett. 46, 1216–1219.
Shipley, C. G., Hitchcock, P. B., Mason, R. & Thomas, K. M. (1974). Structural chemistry of 1,2-diauroyl-DL-phosphatidylethanolamine: molecular conformation and intermolecular packing of phospholipids. Proc. Natl Acad. Sci. USA, 71, 3036–3040.
Small, D. (1967). Phase equilibria and structure of dry and hydrated egg lecithin. J. Lipid Res. 8, 551–557.
Stegemeyer, H. & Bergmann, K. (1981). In Liquid crystals of one- and two-dimensional order. Springer Series in Chemical Physics 11, edited by W. Helfrich & G. Heppke, pp. 161–175. Berlin/Heidelberg/New York: Springer-Verlag.
Tardieu, A. & Billard, J. (1976). On the structure of the `smectic D modification'. J. Phys. (Paris) Colloq. 37, C3-79–C3-81.
Tardieu, A. & Luzzati, V. (1970). Polymorphism of lipids: a novel cubic phase – a cage-like network of rods with enclosed spherical micelles. Biochim. Biophys. Acta, 219, 11–17.








































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