General Remarks on the Role of Chirality

The nematic phase has point group symmetry Dooh- If we add some amount of chiral, e.g., right-handed molecules, the symmetry is reduced from Dooh to Dqo (symmetry of a twisted cylinder). Such a phase is called chiral nematic phase. Chiral molecules used as a dopant (solute) in nematic solvent considerably modify the nematic surrounding and the overall structure becomes twisted with a helical pitch Pc, incommensurate with a molecular size a, na (n is an integer) and usually Po a. Typically, a 10 nm, Pq = 0.1-10 pm. 

The pitch of the helix depends on concentration c of a dopant for small c Po ac and a is called helical twisting power of the dopant [15]. However, with increasing c the dependence becomes nonlinear and the heUx handedness can even change sign (the case of cholesteryl chloride dopant in p-butoxybenzyli-dene-p -butylaniline, BBBA, see Fig. 4.24). The same chiral, locally nematic phase with a short pitch in the range of 0.1-1 pm is traditionally called cholesteric phase because, at first, it has been found in cholesteryl esters. Such short-pitch phases manifest some properties of layered (smectic) phases. 

The smectic C phase formed by chiral molecules (SmC phase) has also a helical superstructure having a pitch incommensurate with the smectic layer thickness. Theoretically chiral phases can also be formed by achiral molecules due to very specific packing [16]. For instance, three achiral rod-Uke molecules of dijfer-ent length may form a chiral trimer or a tripod due to Van der Waals interactions between their fragments, see Fig. 4.25a, and such trimers, in their turn, may form a kind of helical structure. Another example is bent-core or banana like-molecules [17] 

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