Columnar hexagonal

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. 

In the mesophase, the molecules exist in a discotic hexagonal columnar ordered stmcture, schematically shown in Figure 4. 

These compounds show a nematic and smectic C phase for relatively short chain lengths (n 7-10) and a hexagonal (columnar) phase for longer chains. 

Kim, S.J., Kang, S.H., Park, K.-M., Kim, H Zin, W.-C., Choi, M.-G. and Kim, K. (1998) Trinuclear Gold(l) Pyrazolate Complexes Exhibiting Hexagonal Columnar Mesophases with Only Three Side Chains. Chemistry of Materials, 10, 1889-1893. 

Fig. 3. An idealized representation of the supramolecular cylinder self-assembled from a single chain of the dendrimer derived from monomer 9 (R=OC12H25, n=3) in the hexagonal columnar phase, assuming one single backbone per cylinder, drawn to proportion with existing experimental data a tilted side view b top view. Reproduced with permission from references 5 a...

Trzaska and co-workers showed a similar propeller mechanism for the formation of helical columns from disclike metallomesogens (29-31).34 These metallomesogens also have C3 symmetry and 30 and 31 are provided with chiral side chains. In the hexagonal columnar mesophase these chiral side chains induce a Cotton effect in the chromophore of the helically arranged core. Heating the mesophase to the isotropic liquid results in the disappearance of the Cotton effect because of the loss of helical order. This effect illustrates the need for the molecules to be positionally ordered in order for the side-chain chirality to be transferred to the supramolecular column. 

Knight, D., and Vollrath, F. (1999a). Hexagonal columnar liquid crystal in the cells secreting spider silk. Tissue Cell 31, 617-620. 

Figure 16.10 Conformational changes of polypropylene imine) dendrimers in LC materials from spherical to (a) cylindrical, in hexagonal columnar mesophase [130], and (b) ellipsoid, in smectic A mesophase [132]...

Nucleosome-nucleosome interaction potentials can be calibrated by comparison with the characteristics of liquid crystals of mononucleosomes at high concentrations. Under suitable conditions, nucleosome core particles form a hexagonal-columnar phase with a distance of 11.55 1 nm between the columns and a mean distance of 7.16 0.65 nm between the particles in one column [44,46]. These distances may be assumed to correspond to the positions of the minima of an attractive internucleosomal potential. The depth of the interaction potential (i.e., the binding energy per nucleosome) was estimated in the stretching experiments of Cui and Bustamante [66] to 2.6-3.4 kT. A slightly lower potential minimum of 1.25 kT is obtained by a comparison of the stability of the nucleosome liquid crystal phase with simulations [50]. 

For some systems, at high concentration, inverse phases are observed. That is, one may generate an inverse hexagonal columnar phase (columns of water encapsulated by amphiphiles), or an inverse micellar phase (a bulk LC sample with spherical water cavities). 

Bicontinuous cubic phase Lamellar phase Bicontinuous cubic phase Reverse hexagonal columnar phase Inverse cubic phase (inverse micellar phase)... 

Jang et al. (2004) observed that ABA triblock copolymers composed of a docosyl chain, a rigid aromatic segment, and a flexible PEO dendrimer assemble into a hexagonal columnar or body-centered cubic structure in the solid state for the first- and second-generation dendrons, respectively (Fig. 11.27). 

Figure 11.27 Schematic representation of the hexagonal columnar strucmre of an ABA trihlock copolymer with a G1 dendton and the body-centered cubic strucmre of an ABA triblock with a G2 dendron.

Figure 5.4 Self-assembly of wedge-shaped molecules (modified from Zeng et al 2004). (a) Dendrons with fewer tethered chains adopt a flat slice-like shape (X is a weakly binding group), (b) The slices stack up and form cylindrical columns, which assemble on a two-dimensional hexagonal columnar (Col ) lattice (c). (d) Dendrons with more end-chains assume a conical shape, (e) The cones assemble into spheres, which pack on three different three-dimensional lattices (f) with different symmetries.

Frenkel [412] also examined the behaviour of systems consisting of hard spheres in which the top and bottom have been cut off to form disclike structures. Here it is possible to demonstrate the existence of both discotic nematic and hexagonal columnar discotic phases. 

The X-ray diffraction patterns show that the materials obtained from the various configurational isomers of tartaric acid have different architectures. Both are hexagonal columnar mesophases, but, whereas the data for (LP2, LU2) are consistent with columns formed by three polymeric strands having a triple helix superstructure (Figure 41), those for the (MP2, MU2) mixture fit a model built on three strands in a zig-zag conformation. The LD mixture has another arrangement again. 

Dendritic molecules, forming predominately hexagonal columnar and micellar cubic phases, have been introduced and intensively investigated by Percec et al. and this field has recently been reviewed [143], The mesophases of these dendrons can also be stabilized and modified by replacing alkyl chains by fluorinated chains selected examples will be discussed in the next sections. 

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