Characteristic lengths smectic

Theoretical work on dislocations in smectic liquid crystals was first done by de Gennes Q) followed by Pershan (2). For an incompressible smectic A liquid crystal in the hnear hydrodynamic approximation, the elastic strain can be described in terms of a single variable w(x,y,z) Aat specifies local displacements of the smectic layers. The stress-strain field was derived for an isolated dislocation in an unbounded liquid crystal media and extended their results to bounded media using the concept of an "image dislocation." The solution is valid for a thick wedge (relative to a characteristic length of the dislocation) of small angle. However, the... 

For the smectic A phase the permeation effect is even more important [16]. In fact, with the layers fixed at the walls of a capillary, a smectic may flow only as a whole, like a plug, without velocity gradients. Fig. 9.10b. The velocity is again given by equation Vp = kpV, where kp is the permeation coefficient depending on the smectic characteristic length given by Eq. (8.46), cmiventional nematic viscosity q and temperature ... 

Fig. 9.12. The wavevector of the distortion is proportional to inverse geometrical average of cell thickness and smectic characteristic length, = njy/Xsd. Therefore, a typical undulation period is about 0.3 pm (d 10 pm, pa 0.01 pm) and may be observed optically. A similar instability arises in cholesterics under the influence of the magnetic or electric field, see Section 12.2.3.

Figure 2 shows a polarizing optical micrograph of a 35% solution of the DP 76 variant in a 97 3 mixture of chloroform and trifluoroacetic acid. The solution exhibits the fan-like texture characteristic of smectic order [18]. When films of monodisperse PBLGs were probed by small-angle X-ray scattering, well-defined maxima were observed at spacings of 11.4 and 14.0 nm, in excellent agreement with the calculated chain lengths of the helices of DP 76 and 94, respectively (Fig. 3). In striking contrast, the conventional polydisperse sample showed no evidence of a maximum in the scattering pattern.

Modulated smectic phases are just one of a number of classes of frustrated smectic phases, all of which arise from the competition between different characteristic length scales but differ in the manner by which this frustration is relieved. In the incommensurate SmA phases the competing periodicities coexist along the layer normal and the first example of such a phase was observed for a nonsymmetric dimer, KI5 (see Fig. 1 g). In this phase the larger periodicity appears to correspond to the molec-... 

We conclude that the existence of side chain smectic LC-polymers is basically dependent on the length of the spacer. This length must be sufficiently large to allow rotation of segments in the mesogenic units as well as to allow a perfect separation of these units from the incompatible spacer-chain-complex. This hypothesis is qualitatively justified by finding analogous characteristics of WAXS-patterns as shown in this paper. 

In the X-ray experiments on nematic 8CB, the smectic ordering was observed at the free surface (air-nematic interface). The same phenomenon has also been observed at the solid-nematic interface by the X-ray, an electrooptical technique and molecular force measurements. The principle of the latter is shown in Fig. 10.7. For two mica cylinders submerged in nematic liquid crystal, their interaction force measured with a balance oscillates with a distance between the cylinders and the period of oscillations was found to be equal to molecular length 1. This clearly shows the periodicity in density characteristic of a smectic phase [8]. 

Another experimental characteristic of polar mesogens is the intrinsic incommensurability of their structures. Nematic phases of polar compounds often exhibit diffuse X-ray scattering corresponding to a short range smectic order. Two sets of diffuse spots centered around incommensurate wavevectors i and 2 withqiassociated with the classical monolayer order is clearly of order 2 ydl where I is the length of a molecule in its most extended configuration. The wavevector q associated with the head to tail association of the polar molecules reveals the existence of another natu-... 

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