A simple method to determine high-accuracy refractive indices of liquid crystals and the temperature behavior of the related optical parameters via high-resolution birefringence data

We report new high-resolution experimental data for the optical birefringence over the temperature range spanning the nematic (N) and smectic A (Sm A) phases of various liquid crystals (LCs) by means of a rotating-analyzer method. In this work we proposed a simple procedure to determine high-accuracy extraordinary (n_e) and ordinary (n_o) refractive indices of LCs both in the N and Sm A phases based on the birefringence measurements. We then show that, apart from the birefringence data, the procedure needs only a single value for the refractive index which is the value of that in the isotropic (I) phase just above the N-I transition temperature. The consistency of our approximation has been checked under the framework of the Vuks model using the criteria found in the literature. We then conclude that our proposal is self-consistent for obtaining the extraordinary and ordinary refractive indices of LCs with high accuracy and seems to be readily applied as compared to the other methods reported to date and also that temperature variation of n_eand n_orefractive indices is well portrayed by the fit expression presented here for the first time contrary to the Haller extrapolation method. Furthermore, we then show that, without addressing density measurements, the proposed method allows one to obtain the temperature dependence of normalized molecular polarizabilities for extraordinary and ordinary rays, and the effective geometry parameter α_eg. It has been observed that α_egchanges linearly with the order parameter and the same slope value has been obtained for all investigated samples, which can be ascribed to the global behavior of the nematic phase, which has been reported most recently.