Determination of orientational order parameter in various liquid-cryst alline phases

Many methods for the determination of the order parameter in nematic liquid crystals are known. However, most of them are not applicable to cholesteric and smectic phases. Therefore, experimental data on the order parameter in cholesteric and smectic phases are hardly available. To determine the orientational order parameter S we exploited the de Gennes observation, that any anisotropic physical quantity may be a measure of orientational ordering in nematic mesophase. The order parameter can be calculated directly from a macroscopic quantity measured in the experiment. From this idea we developed a simple method for the determination of the order parameter based on birefringence measurements, which can be applied for nematic, cholesteric, and smectic phases. A precise and simple method for measurement of the optical birefringence is described. An approximate empirical formula is applied for normalization of the optical birefringence similar to that used by Haller for polarizabilities. The results are in excellent agreement with the literature data. We proved that in the case of optical anisotropy the order parameter is equal within +/-1% to the one evaluated from polarizability anisotropy. Thus, the discussion concerning the local field can be omitted. Using the described method we determined the orientational order parameter in various mesophases.