International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B. ch. 4.4, p. 455
Section 4.4.3.2. Modulated smectic-A and smectic-C phases
aDivision of Engineering and Applied Science and The Physics Department, Harvard University, Cambridge, MA 02138, USA |
Previously, we mentioned that, although the reciprocal-lattice spacing for many smectic-A phases corresponds to , where L is the molecular length, there are a number of others for which is between and (Leadbetter, Frost, Gaughan, Gray & Mosley, 1979; Leadbetter et al., 1977). This suggests the possibility of different types of smectic-A phases in which the bare molecular length is not the sole determining factor of the period d. In 1979, workers at Bordeaux optically observed some sort of phase transition between two phases that both appeared to be of the smectic-A type (Sigaud et al., 1979). Subsequent X-ray studies indicated that in the nematic phase these materials simultaneously displayed critical fluctuations with two separate periods (Levelut et al., 1981; Hardouin et al., 1980, 1983; Ratna et al., 1985, 1986; Chan, Pershan et al., 1985, 1986; Safinya, Varady et al., 1986; Fontes et al., 1986) and confirmed phase transitions between phases that have been designated smectic- with period , smectic- with period and smectic- with period . Stimulated by the experimental results, Prost and co-workers generalized the De Gennes mean-field theory by writing where 1 and 2 refer to two different density waves (Prost, 1979; Prost & Barois, 1983; Barois et al., 1985). In the special case that the free energy represented by equation (4.4.2.3) must be generalized to include terms like that couple the two order parameters. Suitable choices for the relative values of the phenomenological parameters of the free energy then result in minima that correspond to any one of these three smectic-A phases. Much more interesting, however, was the observation that even if the two order parameters could still be coupled together if and were not collinear, as illustrated in Fig. 4.4.3.1(a), such that . Prost et al. predicted the existence of phases that are modulated in the direction perpendicular to the average layer normal with a period . Such a modulated phase has been observed and is designated as the smectic-A (Hardouin et al., 1981). Similar considerations apply to the smectic-C phases and the modulated phase is designated smectic-; (Hardouin et al., 1982; Huang et al., 1984; Safinya, Varady et al., 1986).
References
Barois, P., Prost, J. & Lubensky, T. C. (1985). New critical points in frustrated smectics. J. Phys. (Paris), 46, 391–399.Google ScholarChan, K. K., Pershan, P. S., Sorensen, L. B. & Hardouin, F. (1985). X-ray scattering study of the smectic-A1 to smectic-A2 transition. Phys. Rev. Lett. 54, 1694–1697.Google Scholar
Chan, K. K., Pershan, P. S., Sorensen, L. B. & Hardouin, F. (1986). X-ray studies of transitions between nematic, smectic-A1, -A2, and -Ad phases. Phys. Rev. A, 34, 1420–1433.Google Scholar
Fontes, E., Heiney, P. A., Haseltine, J. H. & Smith, A. B. III (1986). High resolution X-ray scattering study of the multiply reentrant polar mesogen DB9ONO2. J. Phys. (Paris), 47, 1533–1539.Google Scholar
Hardouin, F., Levelut, A. M., Achard, M. F. & Sigaud, G. (1983). Polymorphisme des substances mésogenes à molécules polaires. I. Physico-chimie et structure. J. Chim. Phys. 80, 53–64.Google Scholar
Hardouin, F., Levelut, A. M., Benattar, J. J. & Sigaud, G. (1980). X-ray investigations of the smectic A1–smectic A2 transition. Solid State Commun. 33, 337–340.Google Scholar
Hardouin, F., Sigaud, G., Tinh, N. H. & Achard, M. F. (1981). A fluid smectic A antiphase in a pure nitro rod-like compound. J. Phys. (Paris) Lett. 42, L63–L66.Google Scholar
Hardouin, F., Tinh, N. H., Achard, M. F. & Levelut, A. M. (1982). A new thermotropic smectic phase made of ribbons. J. Phys. (Paris) Lett. 43, L327–L331.Google Scholar
Huang, C. C., Lien, S. C., Dumrongrattana, S. & Chiang, L. Y. (1984). Calorimetric studies near the smectic-A1–smectic-Ã phase transition of a liquid crystal compound. Phys. Rev. A, 30, 965–967.Google Scholar
Leadbetter, A. J., Durrant, J. L. A. & Rugman, M. (1977). The density of 4-n-octyl-4′-cyano-biphenyl (8CB). Mol. Cryst. Liq. Cryst. 34, 231–235.Google Scholar
Leadbetter, A. J., Frost, J. C., Gaughan, J. P., Gray, G. W. & Mosley, A. (1979). The structure of smectic A phases of compounds with cyano end groups. J. Phys. (Paris) Colloq. 40, C3–375–C3–380.Google Scholar
Levelut, A. M., Tarento, R. J., Hardouin, F., Achard, M. F. & Sigaud, G. (1981). Number of SA phases. Phys. Rev. A, 24, 2180–2186.Google Scholar
Prost, J. (1979). Smectic A to smectic A phase transition. J. Phys. (Paris), 40, 581–587.Google Scholar
Prost, J. & Barois, P. (1983). Polymorphism in polar mesogens. II. Theoretical aspects. J. Chim. Phys. 80, 65–81.Google Scholar
Ratna, B. R., Nagabhushana, C., Raja, V. N., Shashidhar, R. & Chandrasekhar, S. (1986). Density, dielectric and X-ray studies of smectic A–smectic A transitions. Mol. Cryst. Liq. Cryst. 138, 245–257.Google Scholar
Ratna, B. R., Shashidhar, R. & Raja, V. N. (1985). Smectic-A phase with two collinear incommensurate density modulations. Phys. Rev. Lett. 55, 1476–1478.Google Scholar
Safinya, C. R., Varady, W. A., Chiang, L. Y. & Dimon, P. (1986). X-ray study of the nematic phase and smectic-A1 to smectic-Ã phase transition in heptylphenyl nitrobenzoyloxybenzoate (DB7NO2). Phys. Rev. Lett. 57, 432–435.Google Scholar
Sigaud, G., Hardouin, F., Achard, M. F. & Gasparoux, H. (1979). Anomalous transitional behaviour in mixtures of liquid crystals: a new transition of SA–SA type? J. Phys. (Paris) Colloq. 40, C3–356–C3–359.Google Scholar