Experimental Verification of Vuks Equation Using Hollow Prism Refractometer

The refractive indices of the cholesteric liquid crystal solution were measured using multiwavelength (visible range) refractometer for three different wavelengths. Measurements were made at different temperatures for various concentrations of the solution, mixing CLC in a soluble solvent. Vuks equation describes the wavelength and temperature dependence of refractive indices of anisotropic crystalline materials. We have used a simplified version of Vuks equation relating only to macroscopic indices and verified its validity for five-different-concentration solution at various temperatures. The result is also used to obtain molecular polarizabilities and temperature dependent material constants of our sample. 1. Introduction The importance of liquid crystals lies in their thermal, electrical, and optical properties [1–3]. After understanding these properties one can hope to exploit the full range of possible device and materials applications. In many applications the knowledge of optical anisotropy [4, 5] and refractive indices of liquid crystals, and their temperature dependence is desirable [6]. Temperature-induced refractive index change is used in many liquid-crystal (LC) devices to modulate light [7]. Since LC shows optical anisotropy and is birefringent [8] in nature, its refractive index is quite different from that of an isotropic liquid. There are various methods used for the determination of refractive index of liquid crystals [9, 10]. Vuks [11] proposed a semiempirical model which is analogous to the classical Clausius-Mossotti equation for correlating the microscopic molecular polarizabilities to the macroscopic refractive indices of some crystalline materials. The Vuks paper is cited and used by many researchers to study properties of liquid crystals [12, 13]. Vuks made a bold assumption that the internal field in a liquid crystal is the same in all directions and gave a semi-empirical equation correlating the refractive indices with the molecular polarizabilities for anisotropic materials [9]: where and are the refractive indices for the extraordinary and ordinary ray, respectively, are the corresponding molecular polarizabilities, is the number of molecules per unit volume, and is given by Li and Wu [14] modified this equation and showed that the validity of Vuks equations can be easily examined by measuring the temperature and wavelength-dependent refractive indices of liquid crystals. The modified equation (detailed derivation in [14]) given by them is where average refractive index is The importance of modified Vuks equations (3) is