Hexatic liquid crystal

There are the smectic B, F and I phases belonging to this kind of liquid crystal, the so-called hexatic phase. The newly discovered smectic M phase is also catalogued to the hexatic liquid crystal phase. These hexatic phases have a six-fold symmetry which can be observed from the X-ray scattering intensity at q = 2n/a. 

Pindak R, Moncton D E, Davey S C and Goodby J W X-ray observation of a stacked hexatic liquid-crystal B phase Phys.Rev.Lett 46 1135-8... 

As noted in the introductory section, disordered crystals have long-range positional order whereas liquid crystals have short-range periodic order. The extent of the bond orientational order differentiates the hexatic and non-hexatic liquid crystal phases [41-43], The positional order can be described in terms of an ideal average lattice structure... 

To discuss the models in this section, we should mention two issues. First, the models assume the membrane is sufficiently soft that the tilt direction can vary with an energy cost that scales as (Vc(j)2. This is appropriate if the membrane is in a fluid phase like a smectic-C liquid crystal, with order in the tilt direction but not in the positions of the molecules. It is also appropriate if the membrane is in a tilted hexatic phase, with order in the orientations of the intermolecular bonds as well as the tilt. However, this assumption is not appropriate if the membrane is in a crystalline phase, because the tilt direction would be locked to the crystalline axes, and varying it would cost more energy than (V(f>)2. 

It is possible for chiral mesogens to produce essentially achiral mesophases. For instance, in certain ranges of concentration and molecular weight, DNA will form an achiral line hexatic phase. A curious recent observation is of the formation of chiral mesophases from achiral mesogens. Specifically, bent-core molecules (sometimes called banana LCs) have been shown to form liquid crystal phases that are chiral. In any particular sample, various domains will have opposite handedness, but within any given domain, strong chiral ordering will be present. 

In fact, with increasing temperature, these materials may not completely lose their translational order while retaining their orientational order. All liquid crystals are characterized by their orientational order, but liquid crystal phases show varying amounts of translational order with the only exception of nematics. Apart from the above basic symmetries, there is another important symmetry — bond orientation symmetry. This symmetry is important when dealing with hexatic phases. Liquid crystals are classified in terms of following criterion ... 

In addition to the one-dimensional order which forms the layer structure, there is a two-dimensional translational order within the layers. The molecules of this class of liquid crystals are arranged into a hexatic lattice with a correlation length of tens of nm that is one order of magnitude higher than that in the Sa and Sc phases within layers. In addition, there is two dimensional, long range bond symmetry. In the literature, the SB, SF, S phases are sometimes called stack hexatic phases. 

In the smectic B phase, the molecules within the layers are aligned perpendicularly to the layers, but the molecules of the Sp and Si phases within layers are tilted with respect to the layer normal by a tilt angle. The azimuthal of the tilt direction or the projections onto the smectic layers of the Sp and Si phases are different. In the former, the projections of molecules onto the layer point to the edge of the hexatic, while in the latter, to the apex. The difference seems not so significant, but Sp and Si liquid crystals are not miscible, and there is a phase transition between them when the temperature varies. 

In the Sl phase, the molecules are perpendicular to layers and are arranged in a hexatic lattice within layers. This symmetry is the same as that of the Sb phase. Both of the Sl and Sb phases are optically uniaxial, their molecules within smectic layers rotate more freely around their long axes or rotate in groups simultaneously. In some of the literature, the Sb phase is called the hexatic B phase while the Sl phase is named the Sb phase or crystal B phase. The molecules within the Sq and Si phases are tilted with respect to the layers while the molecules of the Sl phase are aligned more or less perpendicularly to the layers. The stacking of molecules within the layer of the Sl, Sq and Sj phases is similar to those shown in Figure 1.7 as well. The crystallography classifications of these three liquid crystal phases are the same as those of the Sb, Sp and Si phases. 

Nd phase. A phase similar to the rod-like smectic liquid crystal phase is the column phase in which molecules are packed as columns parallel to each other. The columns are arranged in a hexatic or rectangular array. Inside the columns, the spacings of the molecules are either constant or random. The axes of the columns may be tilted with respect to the normal of discotic molecules. Figure 1.12 sketches the chemical formulae of one example of a discotic liquid crystal molecule. 

As the concentration increases, the amphiphilic molecules form micelles and then form columns. The columns are arranged into a hexatic array. As the concentration further increases, the system forms a laminar structure, i.e., a smectic liquid crystal phase. Sometimes, a cubic phase may appear between the micelle and hexatic phases. In fact, the micelles are packed to form a cubic phase. The three phases are all liquid crystal phases hexatic phase, laminar phase and cubic phase. As seen in the figure, the phase diagram of amphiphilic molecules actually depends on the temperature as well. Tk in Figure 1.15 is the Kraft temperature, below which the system is phase separated into crystal and water. 

Oscillating forces are not a prerogative of smectics, but have been reported as well for nematics [45,50,51] and even for simple liquids of nearly spherical molecules [52]. In fact, as it was mentioned in the Introduction, the presence of a molecularly flat surface always produces some layering (i.e. positional ordering) of the nearby liquid molecules, because it breaks the translational invariance of the liquid. In liquid crystals this tendency is often enhanced by the presence of a fully layered bulk phase at low temperature (smectic, hexatic, columnar phases, etc.). 

Between crossed polars these defects appear as dark lines or brushes with curved or irregular shapes that correspond to extinction positions of the director and molecular long axes. Thus, the director can be either parallel or perpendicular to the polarizer and analyzer. The brushes tend to cover the specimen in rather a continuous way, indicating the liquid-like nature of the mesophase. The points where the brushes meet are called singularities in the texture (see Figure 3A). For nematic phases two forms of schlieren defect are found, one where two brushes meet at a point and one where four brushes meet. All tilted smectic phases (C, I, F, and ferrielectric C), except for the antiferroelectric phase, exhibit four brush singularities. Therefore, this provides a simple way of distinguishing between smectic and nematic phases. It should be noted that phases such as smectics A and B(hexatic) and crystal phases B(crystal), E, G, H, J, and K do not exhibit schlieren textures and so this narrows down the possibilities for phase identification. 

OrderAayer t3q>e Liquid layer Hexatic layer Crystal layer... 

Since the first discovery of the liquid crystalline phase over one hundred years ago, the classification of the distinct liquid crystalline phases in small-molecule liquid crystals has been well established (7,2). As shown in Figure 1, the least ordered liquid crystalline phase is the nematic phase that only possesses molecular orientational order due to the anisotropy of the molecular geometric shape. The next ordering level introduced is the layer structure in addition to the molecular orientation to lorm a smectic A (S/J or a smectic C (Sc) phase. Following the phase the hexatic B (Ho), smectic crystm B (So) and smectic crystal E (S ) phases are observed. In this series the long axis of the molecules is oriented perpendicular to the layer surface while order is increasingly developed from positional order normal to the layer in bond... 

Brock, J.D., Birgeneau, R.J., Litster, J.D., and Aharony, A. (1989) Hexatic Ordering in Liquid Crystal Films. Contemporary Physics, 30,321-335,... 

Thus, smectics A, C, Cait, hexatic B, 1, and F are essentially smectic liquid crystals, whereas Bcryst, E, G, H, J, and K are soft crystal phases. The latter phases, however. 

Free suspended films of smectic liquid crystals can show a change in the crystalline order from the quasi-two-dimensional to the three-dimensional one [11]. Very thin smectic B films (number of monolayers n < 10) are two dimensional with the hexatic in-plane order, and with (low temperatures) or without (higher temperatures) a tilt of molecules. With increasing n (n > 20) the transition to various three-dimensional crystalline structures is observed. 

Although liquid crystals have been known for more than 100 years, discovering the structures of their many thermodynamic phases is an activity that persists to this day [1]. The sheer variety has been impressive, including such novelties as uniaxial, biaxial, and ferroelectric fluids phases with hexatic order and chiral phases such as the blue phase (BP) and twist grain boundary (TGB) phase, which are stabilized by a lattice of defects. Many of these phases are unique in condensed matter physics their presence never fails to challenge our notions of how matter can arrange itself in the aggregate. 

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