Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 4.4, pp. 464-465   | 1 | 2 |

Section 4.4.7.  Notes added in proof to first edition

P. S. Pershana*

aDivision of Engineering and Applied Science and The Physics Department, Harvard University, Cambridge, MA 02138, USA
Correspondence e-mail:

4.4.7. Notes added in proof to first edition

| top | pdf | Phases with intermediate molecular tilt: smectic-L, crystalline-M,N

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Following the completion of this manuscript, Smith and co-workers [G. S. Smith, E. B. Sirota, C. R. Safinya & N. A. Clark (1988). Phys. Rev. Lett. 60, 813–816; E. B. Sirota, G. S. Smith, C. R. Safinya, R. J. Plano & N. A. Clark (1988). Science, 242, 1406–1409] published an X-ray scattering study of the structure of a freely suspended multilayer film of hydrated phosphatidylcholine in which the phase that had been designated [\hbox{L}_{B'}] in the literature on lipid phases [M. J. Janiak, D. M. Small & G. G. Shipley (1979). J. Biol. Chem. 254, 6068–6078; V. Luzzati (1968). In Biological Membranes: Physical Fact and Function, Vol. 1, edited by D. Chapman, pp. 71–123; A. Tardieu, V. Luzzati & F. C. Reman (1973). J. Mol. Biol. 75, 711–733] was shown to consist of three separate two-dimensional phases in which the positional order in adjacent layers is uncoupled. The three phases are distinguished by the direction of the alkane-chain tilt relative to the nearest neighbours, and in one of these phases the orientation varies continuously with increasing hydration. At the lowest hydration, they observe a phase in which the tilt is towards the second-nearest neighbour; in analogy to the smectic-F phase, they designate this phase [\hbox{L}_{\beta {\rm F}}]. On increasing hydration, they observe a phase in which the tilt direction is intermediate between the nearest- and next-nearest-neighbour directions, and which varies continuously with hydration. This is a new phase that was not previously known and they designate it [\hbox{L}_{\beta {\rm L}}]. On further hydration, they observe a phase in which the molecular tilt is towards a nearest neighbour and this is designated [\hbox{L}_{\beta {\rm I}}]. At maximum hydration, they observe the phase with long-wavelength modulation that was previously designated [\hbox{P}_{\beta}] [M. J. Janiak, D. M. Small & G. G. Shipley (1979). J. Biol. Chem. 254, 6068–6078]. J. V. Selinger & D. R. Nelson [Phys. Rev. Lett. (1988), 61, 416–419] have subsequently developed a theory for the phase transitions between phases with varying tilt orientation and have rationalized the existence of phases with intermediate tilt. To be complete, both Fig.[link] and Table[link] should be amended to include this type of hexatic order which is now referred to as the smectic-L. Extension of the previous logic suggests that the crystalline phases with intermediate tilt should be designated M and N, where N has `herringbone' type of intermolecular order. Nematic to smectic-A phase transition

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At the time this manuscript was prepared, there was a fundamental discrepancy between theoretical predictions for the details of the critical properties of the second-order nematic to smectic-A phase transition. This has been resolved. W. G. Bouwan & W. H. de Jeu [Phys. Rev. Lett. (1992), 68, 800–803] reported an X-ray scattering study of the critical properties of octyloxyphenylcyanobenzyloxybenzoate in which the data were in good agreement with predictions of the three-dimensional xy model [T. C. Lubensky (1983). J. Chim. Phys. 80, 31–43; J. C. Le Guillou & J. Zinn-Justin (1985). J. Phys. Lett. 52, L-137–L-141]. The differences between this experiment and others that were discussed previously, and which did not agree with theory, are firstly that this material is much further from the tricritical point that appears to be ubiquitous for most liquid-crystalline materials and, secondly, that they used the Landau–De Gennes theory to argue that the critical temperature dependence for the [{\bf Q}_{\perp}^{4}] term in the differential cross section given in equation ([link] is not that of the [c\xi_{\perp}^{4}] term but rather should vary as [[(T - T_{\rm NA})/T]^{-\gamma/4}], where [\gamma] is the exponent that describes the critical-temperature dependence of the smectic order parameter [|\Psi |^{2}\simeq [(T - T_{\rm NA})/T]^{-\gamma}]. The experimental results are in good agreement with the Monte Carlo simulation of the N–SA transition that was reported by C. Dasgupta [Phys. Rev. Lett. (1985), 55, 1771–1774; J. Phys. (Paris), (1987), 48, 957–970].


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