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

Abstract

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

Predictions of molecular chirality and helical twisting powers: A theoretical study

“…33,34 However, we can use the model to determine what conformations give rise to particularly high chirality order parameters ͑and hence HTPs͒ and also examine how a change in temperature influences the selection of these conformations. Figure 5͑a͒ shows how the chirality order parameter varies with the dihedral angle 8 for structure B at 350 K. ͑Noting that the behavior of 8 is identical to that of 4 .) For 8 ͑and 4 ) the chirality order parameter varies as a cosine wave with a period of .…”

“…An actual quantitative measure of the magnitude of chirality for a given molecular conformation and a link to pseudoscalar properties such as the HTP or circular dichroism, has been more difficult to obtain. However, recent success has been found through calculations of the difference in chemical potential for enantiomers in a twisted nematic host, 4,5 in calculations of a scaled chiral index, 6,7 using a mean field approximation that takes into account chiral dispersive interactions 8 and with the chirality order parameter approach of Nordio, Ferrarini, and co-workers. [9][10][11][12][13][14][15][16] In order to determine a relationship between the molecular shape and a pseudoscalar property such as the HTP, these studies have, by necessity, been limited to relatively rigid chiral dopants where the molecular conformation is unlikely to vary significantly from the minimum energy structure that can be found from x-ray diffraction experiment and by theoretical techniques such as molecular mechanics and density functional theory.…”

Some Calculations of Molecular Chirality

“…These vary from experimental such as [1] to theoretical such as [2][3][4][5][6][7][8][9][10] to studies of single molecules such as [8,11] to simulation studies of mixtures such as [12]. The single molecule studies either of the optimized geometry of a molecule such as [8,14] or of conformational averages of a property [11,12] allow calculation of the helical twisting power (HTP) values for a range of chiral dopant molecules consistent with experimentally determined values.…”

Progress in computer simulations of liquid crystals

“…In addition to the chirality order parameter, there are other methods of studying HTPs. Recent success has been achieved with a scaled chiral index [120,121] and a mean field approximation that takes into account chiral dispersive interactions [122]. In the case of the former, no account is taken of the surrounding fluid.…”