Study of the biaxiality in the nematic phase of liquid crystals in terms of orientational order parameters by infrared spectroscopy

The observation and quantification of the biaxiality in the nematic phase of thermotropic liquid crystals is one of the topical problems in the science of liquid crystals. The biaxiality in the refractive index and/or relative permittivity, both constituting tensors of the second rank, are expressed in terms of the four scalar order parameters S, D, P and C and the relevant molecular quantities. In this paper we review the theory of determining these order parameters using polarised infrared spectroscopy and present the method that we have developed in obtaining results for the order parameters of tetrapodes (with symmetrical and asymmetrical mesogens) and tripodes with symmetrical mesogens. In the tetrapodes, four mesogens are linked through the siloxane chains to the central Si atom. In the tripode, three mesogens are linked to a benzene ring via the oxygen atom through the siloxane spacers. In the first case a platelet-like structure is formed where the major director corresponds to the highest refractive index. A disc-like structure is formed for a tetrapode with symmetrical mesogens and for a tripode. The order parameters are calculated in the framework of the quasi-flat platelets. For the discotic-like structure, the major director corresponds to the lowest of the three refractive indices. For the three cases, the compounds are shown to exhibit a biaxial nematic phase. Biaxiality in the refractive indices is expressed in terms of the biaxial order parameters. A comparison of the results on the I-NU and NU-NB transitions for tetrapodes compare favourably with the predictions from the mean field models of de Gennes, Virga and his co-workers.