Smectic phase structure

A smectic liquid crystalline phase is characterized primarily by its layered structure. In addition to the overall alignment of the molecules with a particular c director, as in the nematic phase, smectics have an additional degree of order, the layer structure. Smectic phases are typically much more viscous than the nematic phase and occur at lower temperatures. A large number of different smectic-like phases have been observed and studied, each with their own structural features. In this section, we describe some of these. 

FIG. 33 X-Ray Diffraction Patterns of Ammonium Dodecane 1-Sulfonate. 2-D (a) and 3-D plots (b) of oriented samples. Both pictures show the presence of a nonordered smectic phase, since the diffuse, weak, wide-angle diffraction indicates only an average distance between the molecules and the sharp, intense small angle reflections a very well defined layer distance. The reflections are perpendicular to each other, so the structure should correspond to an orthogonal smectic A type. The pictures were obtained using an x-1000 area detector from Siemens. 

For smectic phases the defining characteristic is their layer structure with its one dimensional translational order parallel to the layer normal. At the single molecule level this order is completely defined by the singlet translational distribution function, p(z), which gives the probability of finding a molecule with its centre of mass at a distance, z, from the centre of one of the layers irrespective of its orientation [19]. Just as we have seen for the orientational order it is more convenient to characterise the translational order in terms of translational order parameters t which are the averages of the Chebychev polynomials, T (cos 2nzld)-, for example... 

Complementary information about the structure of the smectic phases is contained in the X-ray scattering patterns, as in studies of real mesogens. The intermolecular scattering patterns calculated (see Sect. 3) for GB(4,4, 20,0, 1,1)... 

Fig. 14. A snapshot of a configuration showing the stripe-like structure of the smectic phase formed hy the polar mesogen GB(3.0, 5.0, 1, 3) and the antiferroelectric compensation in adjacent layers. The different orientations of the dipoles are indicated hy the different shading of the ellipsoids...

We conclude that the dipolar models may exhibit many interesting features, such as the influence of the strength of the dipole moment on the nematic-isotropic and smectic-nematic transitions. Determining the structure of the various smectic phases is clearly an area which needs more investigation. However, an appropriate simulation scheme must be used to avoid misunderstanding the behaviour caused by the method rather than the model. This may be as simple as checking for system size dependence, or running... 

In 1978, Bryan [11] reported on crystal structure precursors of liquid crystalline phases and their implications for the molecular arrangement in the mesophase. In this work he presented classical nematogenic precursors, where the molecules in the crystalline state form imbricated packing, and non-classical ones with cross-sheet structures. The crystalline-nematic phase transition was called displacive. The displacive type of transition involves comparatively limited displacements of the molecules from the positions which they occupy with respect to their nearest neighbours in the crystal. In most cases, smectic precursors form layered structures. The crystalline-smectic phase transition was called reconstitutive because the molecular arrangement in the crystalline state must alter in a more pronounced fashion in order to achieve the mesophase arrangement [12]. 

Mandal et al. [89-91] investigated the crystal structures of three members of the homologous series of 5-(4 -n-alkylcyclohexyl)-2-(4"-cyanophenyl)-pyrimi-dines. The crystal structures of the ethyl (ECCPP), pentyl (PCCPP), and heptyl (HCCPP) compounds were determined. The chemical structure of the compounds is presented in Fig. 15. The two lower homologues possess only a nematic phase, while the heptyl compound has a smectic phase in addition to a nematic phase. 

In 1995, Mandal et al. [151] described the crystal structure of N,AT-bis-(p-butoxybenzylidene)-a,a -bi-p-toluidine. They found that the two symmetrical fractions of the molecule are almost planar, but the angle between these planes is 63.5°. The molecules are arranged in tilted layers. This tilted layer-like structure is referred as a precursor to the tilted smectic phase. 

In this section, we will present the crystal structures of chiral mesogenic compounds exhibiting ferroelectric liquid crystalline phases which are listed in Table 18 [152-166]. Moreover, four compounds of the list show antiferroelectric properties and two compounds form only orthogonal smectic phases. The general chemical structures of the investigated chiral compounds are shown in Fig. 27. 

The compounds crystallise in noncentrosymmetric space groups namely PI, P2i, C2, and P2i2i2i (but with priority of P2i) due to the chirality of the molecules. Most of the compounds have a tilted layer structure in the crystalline state. The tilt angle of the long molecular axes with respect to the layer normal in the crystal phase of the compounds is also presented in Table 18. Some compounds show larger tilt angles in the crystalline state than in the smectic phase. In the following only the crystal structures of some selected chiral liquid crystals will be discussed. 

X-ray measurements have shown that the positional and orientational ordering in highly ordered crystalline smectic phases is more comparable with the ordering in the solid state than the structures of the fluid smectic phases and the nematic phase. Therefore, a comparison of the structures of crystals and highly ordered smectic phases is possible because of their closer similarities. Up to now, only the crystal structures of few mesogenic compounds exhibiting highly ordered smectic phases have been reported in... 

An orthogonal layered structure in the solid state of rod-like molecules is the exception rather than the rule. Therefore, there is no conclusive evidence that a tilted layer structure in the solid state melts to a tilted smectic phase. In other words, if we consider the solid state as precursor for the type of the liquid crystalline state, no real precursor for an orthogonal fluid smectic phase would exist. As demonstrated in Fig. 19, the compound B-A for example exhibiting a smectic A phase has a tilted layer structure in the solid state. 

We start with some elementary information about anisotropic intermolec-ular interactions in liquid crystals and molecular factors that influence the smectic behaviour. The various types of molecular models and commonly accepted concepts reproducing the smectic behaviour are evaluated. Then we discuss in more detail the breaking of head-to-tail inversion symmetry in smectic layers formed by polar and (or) sterically asymmetric molecules and formation of particular phases with one and two dimensional periodicity. We then proceed with the description of the structure and phase behaviour of terminally fluorinated and polyphilic mesogens and specific polar properties of the achiral chevron structures. Finally, different possibilities for bridging the gap between smectic and columnar phases are considered. 

In this section we will discuss in some detail the application of X-ray diffraction and IR dichroism for the structure determination and identification of diverse LC phases. The general feature, revealed by X-ray diffraction (XRD), of all smectic phases is the set of sharp (OOn) Bragg peaks due to the periodicity of the layers [43]. The in-plane order is determined from the half-width of the inplane (hkO) peaks and varies from 2 to 3 intermolecular distances in smectics A and C to 6-30 intermolecular distances in the hexatic phase, which is characterized by six-fold symmetry in location of the in-plane diffuse maxima. The lamellar crystalline phases (smectics B, E, G, I) possess sharp in-plane diffraction peaks, indicating long-range periodicity within the layers. 

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