Order parameter columnar phase

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. 

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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. 

In other, more ordered LC phases, the reduced symmetry yields additional degrees of freedom of the order parameter, such as a density modulation in smectic and columnar phases. 

The classification of polymer mesophases have been considered in many reports (P-70). On analyzing the published data there arises much controversy in the identification. In order to avoid confusion in terminology it is necessary to define the basic terms relating to polymer columnar mesophases before further discussion. Columnar polymer systems have both a correlation of the centers of gravity and molecular orientation, but have mesomorphic properties due to the conformational disorder both of the polymer back-bone and side chains. The structural unit of the polymeric columnar mesophase is a macromolecule. In columnar phases macromolecules form regular 2D-periodic arrays. The two-dimensional symmetry of the column packing and the parameters of two-dimensional lattice are strongly dependent on the form and dimensions of the cross-section of a polymer molecule. 

Columnar phases have two degrees of translational order, and the corresponding order parameters now require averages over periodic functions in two spatial dimensions for completeness we include the distribution function for a uniaxial columnar phase consisting of uniaxial disc-like molecules ... 

Deuterium NMR spectroscopy of the columnar phase of hexa-n-hexyloxytripheny-lene has revealed the marked difference between the order parameters of the cores and the tails [13]. Spectra of two selectively deuteriated isotopic species, one in which all aromatic positions are substituted and the other in which only the a-carbon side chains... 

The diffusion anisotropy depends on the shape on the molecules and on the structure of the phase for example, for columnar liquid crystals tire ratio can be as large as 10 In nematic phase of rod-shape molecules, the anisotropy is positive and typically increases at lower temperatures in proportion to the increase of the order parameter. However, the presence of a smectic phase below the nematic may modify this picture, because the conductivity anisotropy is usually negative in the smectics due to the reduced diffusion constant normal to the smectic layers in connection with the density modulation in this direction. 

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