Tilted phases

Fig. 1 Organization of rod-like molecules (top) and disc-like molecules (bottom) in LC phases (for clarity the alkyl chains are not shown in the models of the phase structures). Abbreviations Iso isotropic liquid state N nematic LC phase SmA smectic A phase, SmC smectic C phase (tilted), Col columnar phase [8]...

Whereas monophilic liquid crystals can show a high diversity of smectic phases (SmA-SmQ), the amphotropic liquid crystals normally exhibit only the SmA phase. Tilted smectic phases are only observed in a few cases. The first indication of possibly tilted phases was given in 1933 for thallium stearate [ 170]. A disordered SmC phase was also clearly deseribed for mesogens containing a classical calamitic core aside to their amphiphilic structure [171]. Monophilic liquid crystals can show various ordered tilted smectic phases, for example, smectic I, F, G, J, H, and K. In the case of lipids only one mesophase, the j8 phase,... 

This structure, when it is present, appears always as the first stable tilted phase below the orthogonal SmA phase. Tilts in all layers are equal and also all phase differences a are equal. From this point of view the phase is equal to the SmC and the SmC phase. The main difference in the macroscopic properties is the magnitude of the angle a, which is neither close to zero nor close to tt (Fig. 5.4c and d). The structure is helicoidally modulated but has a very short pitch, which extends from a few tens of layers to shorter periods than four layers. Due to the short pitch, the structure optically does not differ from the orthogonal phase and does not exhibit other properties like optical rotatory power, typical for other helicoidally modulated structmes. 

Non-Tilted Phases Tilted Phases In Plane Order Molecular Rotation... 

The remaining quadratic factor may have two real (equal or unequal) roots, or a conjugate complex pair of roots, depending upon system parameters. The latter would generate damped time-domain oscillations. These are not usually observed experimentally. The real roots would generate further exponential damping factors that would further degenerate wave-form risetime, or cause phase tilt of the pulse top. 

Figure 10.21. Electroclinic effect in TGB phases tilt angle of the smectic layers versus temperature for different electric field strengths, (a) Experimental values of the compound IIF2BTFO1M7, obtained from X-ray investigations, (b) Solutions of the minimization of the free energy given in (10.21), according to Petit et al. (from [138]).

Case (a) may be interpreted as an electroclinic effect similar to the one observed in nontilted smectic phases tilt is induced because the inclination of disks with chiral polar side chains generates a dipole that counteracts the field. This effect is observed with triphenylene-2,3,6,7,10,ll-hexayl, tricycloquinazoline-2,3,7,8,12,13-hexayl, and truxene-2,3,7,8,12,13-hexayl (9-alkyllactates [19], [21],... 

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

This region has been divided into two subphases, L and S. The L phase differs from the L2 phase in the direction of tilt. Molecules tilt toward their nearest neighbors in L2 and toward next nearest neighbors in L (a smectic F phase). The S phase comprises the higher-ir and lower-T part of L2. This phase is characterized by smectic H or a tilted herringbone structure and there are two molecules (of different orientation) in the unit cell. Another phase having a different tilt direction, L, can appear between the L2 and L 2 phases. A new phase has been identified in the L 2 domain. It is probably a smectic L structure of different azimuthal tilt than L2 [185]. 

LS. In the LS phase the molecules are oriented normal to the surface in a hexagonal unit cell. It is identified with the hexatic smectic BH phase. Chains can rotate and have axial symmetry due to their lack of tilt. Cai and Rice developed a density functional model for the tilting transition between the L2 and LS phases [202]. Calculations with this model show that amphiphile-surface interactions play an important role in determining the tilt their conclusions support the lack of tilt found in fluorinated amphiphiles [203]. 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

This transition is usually second order [18,19 and 20]. The SmC phase differs from the SmA phase by a tilt of the director with respect to the layers. Thus, an appropriate order parameter contains the polar (0) and azimuthal ((]i) angles of the director ... 

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

Hydrated bilayers containing one or more lipid components are commonly employed as models for biological membranes. These model systems exhibit a multiplicity of structural phases that are not observed in biological membranes. In the state that is analogous to fluid biological membranes, the liquid crystal or La bilayer phase present above the main bilayer phase transition temperature, Ta, the lipid hydrocarbon chains are conforma-tionally disordered and fluid ( melted ), and the lipids diffuse in the plane of the bilayer. At temperatures well below Ta, hydrated bilayers exist in the gel, or Lp, state in which the mostly all-trans chains are collectively tilted and pack in a regular two-dimensional... 

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