Structure of the Smectic A Phase

In the smectic A phase the molecules are arranged in layers so that their long axes are 

Alternatively, it is also possible to have polar molecular systems where the mole-eules do not overlap with eaeh other to form a bilayer structure, but instead the molecules form lamellae where they are arranged in a disordered head-to-tail way so that a mono-layer structure results (see Fig. 6). This phase has been given the symbol SmA i, and transitions ean be found from monolayer SmA, to bilayer SmA2 and SmAj phases. 

It is also possible to have other variants of the smectic A phase, for instance it is feasible to have a structure composed of SmA2 layers where the layers have a periodic in- 

it can be seen, that the smectic A phase is rather more complicated than the simple picture often presented of molecules arranged in orthogonal layers. It is very important to remember that the layer structure is only weak and that dimeric interactions can play an important part in the structuring of the phase. 

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Fig. 41 Schematic drawing of the bilayer structure of the smectic A phase of multipede 39. The 16 mesogenic units (cylinders and spheres which represent the cyano groups) per molecule are accommodated in the layers without the introduction of curvature in the packing of the mesogenic units together...

The structure of the smectic A phase when it is composed of optically active material (i.e., smectic A ) remains the same as that for the achiral phase. The molecules are arranged in diffuse disordered layers, and there is no long-range periodic order. However, because of the molecular chirality, the environmental symmetry is reduced to [10]. As a consequence, when an electric field is applied to a chiral smectic A= phase there will be a coupling of the electroclinic susceptibility to the field and the long axes of the molecules will tilt with respect to the layer planes. The tilt angle, for relatively low applied fields, varies linearly with the field. This linear electrooptic phenomenon is called the electroclinic effect. 

Fig. 30. The normal layered structure of the smectic A phase of a side chain liquid crystal polymer, and the proposed twisted structure of the layered smectic phase of a chiral side...

The structure of the smectic A phase, therefore, is governed by the relative lengths of the spacer and terminal chains. For short spacers, n = 3-7, the CBOnO.lO series exhibits the SmAa phase while for long spacers, n= 10-12, the SmAc phase is observed. The disappearance of smectic behaviour for intermediate chain lengths (see Fig. 11) implies that neither smectic modification is favourable and hence nematic behaviour results. There is a strong similarity here to re-entrant nematic behaviour which is also driven by two different length scales. 

There are many types of defects originated from the layered structure of the smectic A phase. Here, we shall only present a brief survey of the most important cases. 

Estimate the ratio pi/Pi at these three temperatures. What does this typical data tell you about the structure of the smectic A phase and its temperature dependence Why is the above equation an approximation, and does it over- or underestimate the true ratio p//pi ... 

At a normal chiral nematic to smectic A transition, the helical ordering of the chiral nematic phase collapses to give the layered structure of the smectic A phase. However, for a transition mediated by a TGB phase, there is a competition between the need for the molecules to form a helical structure due to their chiral packing requirements and the need for the phase to form a layered structure. Consequently, the molecules relieve this frustration by trying to form a helical structure, where the axis of the helix is perpendicular to the long axes of the molecules (as in the chiral nematic phase), yet at the same time they also try to form a lamellar structure, as shown in Fig. 21. These two... 

Figure 6. Bilayer and monolayer structures of the smectic A phase.

Fig. 1—Schematic representation of the structure of the smectic-A phase of iiquid crystais.

In the nematic phase, one can induce macroscopic orientation by controlling the surface boundary conditions. However, because nematic ordering is the result of a spontaneously broken symmetry, fluctuations of the director n are a soft mode. Indeed a macroscopically oriented nematic phase is much more turbid than a macro-scopically oriented smectic-A phase because of light scattering from orientational fluctuation domains. The layered structure of the smectic-A phase suppresses these orientational fluctuations, and it is this coupling that affects the character of the transition (see [5] for a broad survey of such phase transitions). However, smectic phases exhibit one-dimensional orientational order, characterized by the Landau-Peierls fluctuation of the layer spacing [6, 7]. As a result, the essential features needed to capture the NA transition are ... 

Smectic liquid crystalline polymers have more ordered structures than nematic liquid crystalline polymers, as their molecular arrangements have not only long-range orientational order, but also positional order. The positional order refers to the layer packing structures of the polymers. The less ordered smectic liquid crystals, such as smectic A, are true one-dimensional crystals. The packing structure of the smectic A is illustrated in Figure 5.6. The smectic A phase can be considered as convolution of a layer of two-dimensional liquid, i.e., a layer of randomly packed hard rods that are uniaxially oriented in the direction of the layer normal, and a one-dimensional lattice as shown in Figure 5.7. 

In Section 5.7.2 we discussed a general problem of stability of one, two- and three-dimensional phases. Here, we shall analyze stability of the smectic A liquid crystal, which is three-dimensional structure with one-dimensional periodicity. The question of stability is tightly related to the elastic properties of the smectic A phase. Consider a stack of smectic layers (each of thickness Z) with their normal along the z-direction. The size of the sample along z is L, along x and y it is L, the volume is V = Lj L. Fluctuations of layer displacement u(r) = u(z, r i) along z and in bofli directions perpendicular to z can be expanded in the Fourier series with wavevec-tors q and q (normal modes) ... 

Fig. 8. 27 Steps at the edge of a drop of the smectic A phase (left)-, the structure of each step containing a single 7c-disciination is seen in the blown part right)...

As mentioned earlier, the helical structure of the smectic C phase should be untwisted by an electric or magnetic field, or suppressed by a surface effect, to observe ferroelectric properties of the phase. In the first publication on ferroelectric liquid crystals [5] an approach to nontwisted ferroelectric LC materials was suggested. By mixing two individual ferroelectric liquid crystals having opposite signs of P but different absolute values, one can compensate the helical twisting without zeroing the polarization. That has been done for low-molar-mass liquid crystals... 

In general, the structural organizational of the smectic A phase is determined by a subtle balance between different contributions into free energy, among which the most important are the dispersion, steric, and dipole-dipole interactions. 

The structure [3,4,23,39,40] of the hexatic B phase is relatively close to that of the smectic A phase, in that the molecules are arranged in layers so that their long axes are orthogonal to the layered planes. Loeally, the molecules are essentially hexagonally close packed and are undergoing rapid reor-ientational motion about their long axes on a similar time scale to the smectic A phase. 

The symmetry and structure of the smectic-A liquid crystals are reviewed the natural order parameters are identified. The relationship of the smectic-A phase to the nematic (or cholesteric) and isotropic phases in homologous series is also examined. The McMillan form of the single molecule potential function is then deduced starting from the Kabayashi form of the potentiaP and using the formal development presented earlier. The derivation of the statistical thermodynamics then follows, along with a presentation of McMillan s numerical results and a comparison with experiment. Improvements in the theory introduced by Lee et al are also considered. In the last section, the important question of whether the smectic-A to nematic (cholesteric) phase transition can ever be second order is examined. 

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