Helicoidal chirality helicates

In coordination chemistry helicoidal chirality is frequently encountered. It is the chirality of OC-6 complexes possessing two cis geometry) or three bis(chelate) substituents, and also of helicates in supramolecular chemistry. 

Fig. 33. a Concentric cylindrical twist walls separating different chiral smectic regions. Inside each region the layer surface adopts a helicoidal shape, b Each cylindrical twist wall is comparable to that found in a conventional TGB phase, a helical shape being given to the screw dislocations constituting them (after Gilli and Kamaye [43])... 

Cellulose and some derivatives form liquid crystals (LC) and represent excellent materials for basic studies of this subject. A variety of different structures are formed, thermotropic and lyotropic LC phases, which exhibit some unusual behavior. Since chirality expresses itself on the configuration level of molecules as well as on the conformation level of helical structures of chain molecules, both elements will influence the twisting of the self-assembled supermolecular helicoidal structure formed in a mesophase. These supermolecular structures of chiral materials exhibit special optical properties as iridescent colors, and... 

The above gels of compound 25a and b do not form helical fibers that can be observed by SEM. However, several chiral gelators do selectively self-assemble into helicoidal fibers. For example, Escuder et al. have reported that (S,S)-26 gelated several organic solvents. SEM of the gel formed in benzene showed the presence of isolated right-handed twisted ribbons of several micrometers of... 

We should note that (8.15) is only an approximation. Because of the helical structure in the chiral smectic-C phase, the divergence of /g is in principle incomplete since a real divergence would be obtained only as a response to a helicoidal electric field [68], [69]. Including the helical structure into the Landau model leads to a modification of (8.15) and a truncation of the divergence with a finite value of /g at 7), similar to the case of a first-order transition. However, whereas the truneation at a first-order smectic-yl-smectic-C transition can be observed experimentally, measurements of Xe around a tricritical point, where the transition changes from first-order to second-order, have shown that the influence of the helix on the divergence of Xg is probably beyond experimental resolution [70]. 

As we have repeatedly stressed, flexoelec-tricity is a phenomenon that is a priori independent of chirality. But we have also seen that some flexoelectric deformations do have a tendency to occur spontaneously in a chiral medium. All except the helical C state are, however, suppressed, because they are not space-filling. A flexoelectric deformation may of course also occur spontaneously in the nonchiral case, namely, under exactly the same conditions where the deformation is space-filling and does not give rise to defect structures. In other words, in creating the twist-bend structure which is characteristic of a helielectric. Imagine, for instance, that we have mesogens which have a pronounced bow shape and, in addition, some lateral dipole. Sterically they would prefer a helicoidal structure, as depicted in Fig. 52, which would minimize the elastic... 

Planar chirality with loss of a symmetry plane (paracyclophanes). Helical chirality molecules develop a helicoidal structure (trans-cyclooctene and helicenes). 

---