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

International Tables for Crystallography (2006). Vol. B, ch. 4.4, pp. 458-460   | 1 | 2 |

Section 4.4.4.2.2. Smectic-F, smectic-I

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

4.4.4.2.2. Smectic-F, smectic-I

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In contrast to the hexatic-B phase, the principal reciprocal-space features of the smectic-F phase were clearly determined before the theoretical work that proposed the hexatic phase. Demus et al. (1971[link]) identified a new phase in one material, and subsequent X-ray studies by Leadbetter and co-workers (Leadbetter, Mazid & Richardson, 1980[link]; Leadbetter, Gaughan et al., 1979[link]; Gane & Leadbetter, 1981[link]) and by Benattar and co-workers (Benattar et al., 1978[link], 1980[link], 1983[link]; Guillon et al., 1986[link]) showed it to have the reciprocal-space structure illustrated in Fig. 4.4.4.4(b)[link]. There are interlayer correlations in the three-dimensional smectic-F phases, and as a consequence the reciprocal-space structure has maxima along the diffuse rods. Benattar et al. (1979[link]) obtained monodomain smectic-F samples of the liquid crystal N,N′-(1,4-phenylenedimethylene)bis(4-n-pentylaniline) by melting a single crystal that was previously precipitated from solution. One of the more surprising results of this work was the demonstration that the near-neighbour packing was very close to what would be expected from a model in which rigid closely packed rods were simply tilted away from the layer normal. In view of the facts that the molecules are clearly not cylindrical, and that the molecular tilt indicates that the macroscopic symmetry has been broken, it would have been reasonable to expect significant deviations from local hexagonal symmetry when the system is viewed along the molecular axis. The fact that this is not the case indicates that this phase has a considerable amount of rotational disorder around the long axis of the molecules.

[Figure 4.4.4.4]

Figure 4.4.4.4 | top | pdf |

Scattering intensities in reciprocal space from three-dimensional tilted hexatic phases: (a) the smectic-I and (b) the smectic-F. The variation of the intensity along the [Q_{L}] direction indicates interlayer correlations that are absent in Figs. 4.4.4.1(d)[link] and (e)[link]. The peak widths [\Delta {\bf Q}_{L1,2}] and [\Delta {\bf Q}_{H1,2}] correspond to the four inequivalent widths in the smectic-F phase. Similar inequivalent widths exist for the smectic-I phase. The circle through the shaded points in (a) indicates the reciprocal-space scan that directly measures the hexatic order. A similar scan in the smectic-C phase would have intensity independent of [\chi].

Other important features of the smectic-F phase are, firstly, that the local molecular packing is identical to that of the tilted crystalline-G phase (Benattar et al., 1979[link]; Sirota et al., 1985[link]; Guillon et al., 1986[link]). Secondly, there is considerable temperature dependence of the widths of the various diffuse peaks. Fig. 4.4.4.4(b)[link] indicates the four inequivalent line widths that Sirota and co-workers measured in freely suspended films of the liquid crystal N-[4-(n-heptyloxy)benzylidene]-4-n-heptyl aniline (7O.7). Parenthetically, bulk samples of this material do not have a smectic-F phase; however, the smectic-F is observed in freely suspended films as thick as ∼200 layers. Fig. 4.4.4.5[link] illustrates the thickness–temperature phase diagram of 7O.7 between 325 and 342 K (Sirota et al., 1985[link]; Sirota, Pershan & Deutsch, 1987[link]). Bulk samples and thick films have a first-order transition from the crystalline-B to the smectic-C at 342 K. Thinner films indicate a surface phase above 342 K that will be discussed below. Furthermore, although there is a strong temperature dependence of the widths of the diffuse scattering peaks, the widths are independent of film thickness. This demonstrates that, although the free film boundary conditions have stabilized the smectic-F phase, the properties of the phase are not affected by the boundaries. Finally, the fact that the widths [\Delta {\bf Q}_{L1}] and [\Delta {\bf Q}_{L2}] along the L direction and [\Delta {\bf Q}_{H1}] and [\Delta {\bf Q}_{H2}] along the in-plane directions are not equal indicates that the correlations are very anisotropic (Brock et al., 1986[link]; Sirota et al., 1985[link]). We will discuss one possible model for these properties after presenting other data on thick films of 7O.7. From the fact that the positions of the intensity maxima for the diffuse spots of the smectic-F phase of 7O.7 correspond exactly to the positions of the Bragg peaks in the crystalline-G phase, we learn that the local molecular packing must be identical in the two phases. The major difference between the crystalline-G and the tilted hexatic smectic-F phase is that, in the latter, defects destroy the long-range positional order of the former (Benattar et al., 1979[link]; Sirota et al., 1985[link]). Although this is consistent with the existing theoretical model that attributes hexatic order to a proliferation of unbounded dislocations, it is not obvious that the proliferation is attributable to the same Kosterlitz–Thouless mechanism that Halperin & Nelson and Young discussed for the transition from the two-dimensional crystal to the hexatic phase. We will say more on this point below.

[Figure 4.4.4.5]

Figure 4.4.4.5 | top | pdf |

The phase diagram for free films of 7O.7 as a function of thickness and temperature. The phases ABAB, AAA, [OR_{m1}], [OR_{m2}], [OR'_{m1}], M and ABAB are all crystalline-B with varying interlayer stacking, or long-wavelength modulations; CrG, SmF and SmI are crystalline-G, smectic-F and smectic-I, respectively (Sirota et al., 1985[link]; Sirota, Pershan & Deutsch, 1987[link]; Sirota, Pershan, Sorensen & Collett, 1987[link]).

The only identified difference between the two tilted hexatic phases, the smectic-F and the smectic-I, is the direction of the molecular tilt relative to the near-neighbour positions. For the smectic-I, the molecules tilt towards one of the near neighbours, while for the smectic-F they tilt between the neighbours (Gane & Leadbetter, 1983[link]). There are a number of systems that have both smectic-I and smectic-F phases, and in all cases of which we are aware the smectic-I is the higher-temperature phase (Gray & Goodby, 1984[link]; Sirota et al., 1985[link]; Sirota, Pershan, Sorensen & Collett, 1987[link]).

Optical studies of freely suspended films of materials in the nO.m series indicated tilted surface phases at temperatures for which the bulk had uniaxial phases (Farber, 1985[link]). As mentioned above, X-ray scattering studies of 7O.7 demonstrated that the smectic-F phase set in for a narrow temperature range in films as thick as 180 layers, and that the temperature range increases with decreasing layer number. For films of the order of 25 layers thick, the smectic-I phase is observed at approximately 334 K, and with decreasing thickness the temperature range for this phase also increases. Below approximately 10 to 15 layers, the smectic-I phase extends up to ∼342 K where bulk samples undergo a first-order transition from the crystalline-B to the smectic-C phase. Synchrotron X-ray scattering experiments show that, in thin films (five layers for example), the homogeneous smectic-I film undergoes a first-order transition to one in which the two surface layers are smectic-I and the three interior layers are smectic-C (Sirota et al., 1985[link]; Sirota, Pershan, Sorensen & Collett, 1987[link]). The fact that two phases with the same symmetry can coexist in this manner tells us that in this material there is some important microscopic difference between them. This is reaffirmed by the fact that the phase transition from the surface smectic-I to the homogeneous smectic-C phase has been observed to be first order (Sorensen et al., 1987[link]).

In contrast to 7O.7, Birgeneau and co-workers found that in racemic 4-(2-methylbutyl)phenyl 4′-octyloxylbiphenyl-4-carboxylate (8OSI) (Brock et al., 1986[link]), the X-ray structure of the smectic-I phase evolves continuously into that of the smectic-C. By applying a magnetic field to a thick freely suspended sample, Brock et al. were able to obtain a large monodomain sample. They measured the X-ray scattering intensity around the circle in the reciprocal-space plane shown in Fig. 4.4.4.4(b)[link] that passes through the peaks. For higher temperatures, when the sample is in the smectic-C phase, the intensity is essentially constant around the circle; however, on cooling, it gradually condenses into six peaks, separated by 60°. The data were analysed by expressing the intensity as a Fourier series of the form [S(\chi) = I_{0} \left[{\textstyle{1\over 2}} + {\textstyle\sum\limits_{n=1}^{\infty}} C_{6n} \cos 6n (90^{\circ} - \chi)\right] + I_{B},] where [I_{0}] fixes the absolute intensity and [I_{B}] fixes the background. The temperature variation of the coefficients scaled according to the relation [C_{6n} = C_{6}^{\sigma n}] where the empirical relation [{\sigma_{n}} = 2.6 (n - 1)] is in good agreement with a theoretical form predicted by Aharony et al. (1986[link]). The only other system in which this type of measurement has been made was the smectic-C phase of 7O.7 (Collett, 1983[link]). In that case, the intensity around the circle was constant, indicating the absence of any tilt-induced bond orientational order (Aharony et al., 1986[link]).

It would appear that the near-neighbour molecular packing of the smectic-I and the crystalline-J phases is the same, in just the same way as for the packing of the smectic-F and the crystalline-G phases. The four smectic-I widths analogous to those illustrated in Fig. 4.4.4.4(a)[link] are, like that of the smectic-F, both anisotropic and temperature dependent (Sirota et al., 1985[link]; Sirota, Pershan, Sorensen & Collett, 1987[link]; Brock et al., 1986[link]; Benattar et al., 1979[link]).

References

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