Order, hexatic long-range

Fig. 9.12. Wide angle X-ray scattering patterns produced by correlations between molecules in the plane of the layers, (a) The diffuse ring of a smectic A phase, characteristic of short range correlations, (b) Appearance of six diffuse traces in the case of a hexatic smectic phase. Intensity modulation is characteristic of long range bond order (i.e. a subtle orientational order), whereas the diffuse nature of the traces indicates liquid-type long range order...

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. 

Hexatic smectic mesophase in which the director is perpendicular to the layers with the long-range hexagonal bond-orientational order. 

Within a smectic layer, a state of order called hexatic can exist that is intermediate between the liquid order of the smectic A, and the crystalline order of crystalhne smectic B. This state of order characterizes the hexatic smectic-B phase. Flexatic order consists of long-range bond orientational order, but no long-range positional order. This is illustrated... 

The quasi-long-range bond orientational order present in the hexatic phase is destroyed at a second, disclination-unbinding, transition, which occurs at a temperature T >T. In this transition the tightly bound... 

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 hexatics, there is no chemical bond between neighboring molecules. The hexatic bond order can be viewed as resulting from the loss of the long-range positional but not orientational order of a hexagonal crystal. 

B) phase resembles the SmA phase, but with long-range hexatic bond-orientational order. The SmI and SmF phases are tilted versions of SmB. In the SmI phase, the molecules are tilted towards a vertex (nearest neighboiu) whereas in the SmF phase they are tilted towards an edge of the hexagonal net. 

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