Lattice columnar phases

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]... 

The discotic mesophases are classified in two types columnar, and nematic discotic. The structure of the nematic discotic mesophase (Np, Figure 8.3, left) is similar to that of rod-like molecules, but constituted by disk-like units. In columnar mesophases, the molecules are stacked in a columnar disposition and, depending on the type of columnar arrangement, several columnar mesophases are known. The most common lattices of the columnar phases are nematic discotic (No), columnar nematic (Ncoi), columnar hexagonal (Coin), and columnar rectangular (Col,) mesophases. 

For polycatenar hydrogen bonded complexes with fluorinated chains at both ends (e.g., 138,139, see Fig. 36) formation of columnar phases was observed [246]. However, compound 137, having a branched Rp-chain at one end and three RH-chains at the other has a sequence of three distinct phases in the unusual sequence Cub-Col-SmA-Iso. For the SmA phase of compound 137 a structure with intercalated aromatic cores and RF-chains and separated layers of the hydrocarbon chains was proposed. At lower temperature, when incompatibility rises and the aromatics and Rp-chains disintegrate, all three components form their own layers. However, this produces interface curvature and a columnar phase with square lattice is formed. On further cooling a transition to a cubic phase with Im3m lattice takes place which is most likely of the bicontinuous type [262]. This leads to the unusual phase sequence Cubv-Col-SmA where the positions of the Cubv and Col phases are exchanged with respect to the usually observed phase sequences. The Col-Cub transition at lower temperature could be the result of the decreased conformational disorder of the terminal chains which reduces the steric frustration and hence reduces the interface curvature. 

Fig. 9 (a) Sketch of the structure of the hexagonal columnar phase of DNA, showing parallel molecules hexagonally packed in the plane perpendicular to their axis, a and 4 are the lattice parameters, (b) COL developable domains observed in polarized microscopy, w indicates defect walls between differently oriented domains, while 7t stands for point defect around which DNA molecules continuously bend (size bar is 10 pm). Adapted with permission from [27]... 

Ewert KK, Evans HM, Zidovska A, Bouxsein NF, Ahmad A, Safinya CR (2006) A columnar phase of dendritic lipid-based cationic liposome-DNA complexes for gene delivery hexago-nally ordered cylindrical micelles embedded in a DNA honeycomb lattice. J Am Chem Soc 128 3998-4006... 

Molecules of a disc-like shape form either nematic or columnar phases. Structurally the most simple mesophase is the discotic nematic phase (Nd). Just as in the case of the nematic phase formed by calamitic molecules, the molecules possess orientational order, but no positional order (Figure 2.8). The columnar nematic phase (Nc) consists of short columns of a few molecules that act like the rod-like molecules in the nematic calamitic phase (Figure 2.9). There is no organisation of the columns in a two-dimensional lattice. 

Figure 12 Representations of the lattices of the (a) hexagonal, (b) oblique, and (c) and (d) rectangular columnar phases.

Such molecules exhibit columnar mesophases and smectic C phases. In contrast to the corresponding tetracatenar compounds described above, the columnar phase is, in most of these swallow-tailed compounds, the low temperature phase with respect to the smectic C phase [58]. This inversion of thermotropic sequence with respect to the biforked compounds described just above has not found any explanation in relation with molecular parameters. The symmetry of the columnar two-dimensional lattice is found to be hexagonal, oblique and even rectangular [59] in some cases. For the latter case, the model proposed involves several molecules packed side by side to form the lattice unit, the different moieties being packed alternately in order to form a two-dimensional centred cell as shown in Fig. 11. 

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