Helical twisting power and circular dichroism in nematic liquid crystals doped with chiral molecules

Explicit expressions for the helical twisting power of a chiral dopant in the nematic phase have been obtained in the mean field approximation taking into account chiral dispersion intermolecular interactions. The results of the theory enable one to explain a correlation between the signs of helical twisting power and circular dichroism of selected electronic transitions which have recently been established experimentally for some mono- and bis-aminoantroquinones. Helical twisting power is proportional to the pseudoscalar parameter that specifies the chirality of the dopant molecule in terms of its dipole and quadrupole matrix elements. This expression is simplified for a special class of molecules in which chirality is induced by a perturbing achiral group into an achiral skeleton. In this case both helical twisting power and circular dichroism are approximately proportional to some simple pseudoscalar functions that specify the location of the achiral perturbing group with respect to the symmetry planes of the unperturbed achiral skeleton. Simple sector rules have been proposed to determine the sign change of the helical twisting power associated with the change of location of the perturbing group.