STRUCTURAL AND OPTICAL ANISOTROPY OF BIAXIAL NEMATICS

Abstract

It is shown that biaxial thermotropic nematics have anomalously small parameters of biaxial orientational order of molecules, which are one or two orders of magnitude lower than the limit of their detection by NMR. This accounts for the dramatic discrepancy between the optical and NMR data on biaxiality of these compounds. 1. The dramatic discrepancy between the optical data and the results of NMR and molecular statistic studies and computer simulations of biaxial thermotropic nematics N b have recently been an intriguing problem in liquid crystal physics [1]. The optical biaxiality of some nematics N b [2-4] is reliably determined from the presence of force disclinations |s| = 1/2 in textures of disoriented samples and also by conoscopic observations on oriented samples corresponding to an angle α = 5-10° between the optical axes [5]. However, the NMR technique has failed to detect biaxiality of the orientational ordering of the substance or impurity molecules for the same compounds [6, 7]. This also conflicts with the predictions obtained by using molecular statistic theory and computer simulations [8]. The reasons for this disagreement are being the subject of lively debates in the literature [1], but are not clear as yet, undermining the very fact of existence of biaxial thermotropic nematics [1, 6, 7]. Here we establish a relationship between the optical biaxiality of nematics N b and the properties of molecules and their orientational ordering. It is shown that the parameters of the biaxial orientational order of molecules in these compound s are anomalously small, being one or two orders of magnitude lower than the limit of their NMR detection. This may be caused by variation of conformation and anisotropy of the form of biaxial molecules in the nematic phase. 2. Consider a nematic N b with point symmetry group D2h consisting of molecules with the same symmetry. The orientational ordering of the i(xyz) axes of the molecular coordinate system relative to the α(XYZ) axes of the laboratory system is defined by the matrix elements S αβ,ij = 〈3cos θ iα cos θ jβ - δ αβ δ ij 〉 / 2 [9] or by the following order parameters: