Columnar phase

Hence, there are two options for molecules with unlike end-chains either the incompatible chains mix which retains the lamellar structure, or these chains segregate and layer modulation with formation of ribbon phases (columnar phases)... 

Columnar phase Columnar phase Columnar phase Molecular ji - 10 3 cmJ/Vs 10 2 cm2/Vs - 10 1 cmWs order... 

The simplest phase corresponds to a compact triangular packing (still called hexagonal) of isotropic columns (see Fig. 9.3). The equivalent phases in smectic C liquid crystals are such that molecules are tilted relative to columns. A priori molecules may tilt towards the nearest or second nearest neighbour columns, or in any other direction. These three possibilities correspond to three distinct phases. Columns may also deform themselves into ellipses without molecules tilting relative to the columnar axis this is yet another phase. Columnar symmetry may also occur with local smectic order and an example is shown in Fig. 9.19 for long thin molecules with polar heads. All these phases have common elastic, hydrodynamic and topological properties. 

Number of chains in meta position (Nm) Number of chains in para position (Np) Lamellar phase Cubic phase Columnar phase... 

Figure C2.2.7. Schematic illustrating tire classification and nomenclature of discotic liquid crystal phases. For tire columnar phases, tire subscripts are usually used in combination witli each otlier. For example, denotes a rectangular lattice of columns in which tire molecules are stacked in a disordered manner (after [33])...

As for crystals, tire elasticity of smectic and columnar phases is analysed in tenns of displacements of tire lattice witli respect to the undistorted state, described by tire field u(r). This represents tire distortion of tire layers in a smectic phase and, tluis, u(r) is a one-dimensional vector (conventionally defined along z), whereas tire columnar phase is two dimensional, so tliat u(r) is also. The symmetry of a smectic A phase leads to an elastic free energy density of tire fonn [86]... 

A simple derivation of tliis equation based on tire lowest-order derivative (curvature) of tire layer displacement field u(r) has been provided [87]. A similar expression can be obtained for a uniaxial columnar phase [20] (witli tire columns lying in tire z direction) ... 

McMillan s model [71] for transitions to and from tlie SmA phase (section C2.2.3.2) has been extended to columnar liquid crystal phases fonned by discotic molecules [36, 103]. An order parameter tliat couples translational order to orientational order is again added into a modified Maier-Saupe tlieory, tliat provides tlie orientational order parameter. The coupling order parameter allows for tlie two-dimensional symmetry of tlie columnar phase. This tlieory is able to account for stable isotropic, discotic nematic and hexagonal columnar phases. 

Monte Carlo computer simulations of spheres sectioned into a disc [104, 105] show tliat steric interactions alone can produce a nematic phase of discotic molecules. Columnar phases are also observed [104, 105]. 

Fig. 11. Orientational order in discotic Hquid crystal phases (a) nematic phase (b) columnar phase.

The other type of porous glass that has cylindrical pores is mesoporous silicate (MPS) (14,15). The advantage of MPS is in its feasibility to make a small pore diameter, typically below 10 nm. A columnar-phase liquid crystal, formed from surfactant molecules with a long alkyl chain tail and silicate molecules, is calcined to remove hydrocarbons. At the end, a hexagonal array of straight and uniform cylindrical holes is created in a crystalline order. MPS is not available commercially either. 

Columnar ferrite formed from austenite 4. /3-phase layer apparently the coating in... 

Thermotropic liquid-crystalline properties of different metal alkanesulfonates are studied by microscopy and X-ray diffraction [59]. Sodium soaps show smectic polymorphism of smectic A and smectic B phases. Ammonium soaps only show smectic A phases but polymorphism in the crystalline state. Calcium soaps show columnar mesophases. In Figs. 32 and 33 some textures and x-ray diffraction patterns are depicted. 

It is clear that systems of hard ellipsoids exhibit an intriguingly simple phase behaviour with some resemblance to that of real nematogens. However, such systems cannot form smectic or columnar phases and in addition the phase transitions are not thermally driven as they are for real mesogens. As we shall see in the following sections the Gay-Berne potential with its anisotropic repulsive and attractive forces is able to overcome both of these limitations. 

The prime requirement for the formation of a thermotropic liquid crystal is an anisotropy in the molecular shape. It is to be expected, therefore, that disc-like molecules as well as rod-like molecules should exhibit liquid crystal behaviour. Indeed this possibility was appreciated many years ago by Vorlander [56] although it was not until relatively recently that the first examples of discotic liquid crystals were reported by Chandrasekhar et al. [57]. It is now recognised that discotic molecules can form a variety of columnar mesophases as well as nematic and chiral nematic phases [58]. 

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