Determination of Orientational Order Parameter in Various Liquid-Crystalline Phases

Abstract

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 AE 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.

Refractive Indices, Order Parameter and Optical Transmittance Studies of a Nematic Liquid Crystal Mixture

“…4, the microscopic order parameter (S) as calculated from refractive indices data using the Vuks approach (relation) matches very well with macroscopic order parameter (Q) for nematic mixture E-24. Kuczyński [33] has suggested that one can expect that within a given local field they may be found to be nearly the same as is seen in the present study. The value of both order parameters decreases as temperature increases and shows a sharp change at nematic-isotropic transition temperature.…”

Biaxial order parameter in the homologous series of orthogonal bent-core smectic liquid crystals

“…Kuczynski et al [23] suggested an approximate empirical formula for normalization of the optical birefringence similar to that used by Haller [24] for polarizabilities. It has been shown that the nematic order parameter obtained from the optical anisotropy is equal to the one evaluated from magnetic polarizability anisotropy with the accuracy of ±5%.…”

“…In this extrapolation one assumes that for temperatures far enough from the clearing point, the expression log χ (T ) [23] is a linear function of the logarithm of the reduced temperature. On the other hand, one postulates that the order parameter is equal to 1 at the absolute zero of temperature which means that all molecules are parallel to each other, i.e., lim T →0 [log( n)] = log n 0 .…”

Order parameter studies from effective order geometry in a number of liquid crystals of different homologous series

“…Journal of Molecular Liquids 174 (2012) [1][2][3][4] where Δn is the birefringence at perfect order (T = 0 K) and this can be obtained by following Kuczynski et al [3,4] and by using the following equation.…”

“…Different physical properties of the liquid crystals (LCs) can be understood from the important parameter viz., the order parameter [1][2][3][4]. For the display technology, the knowledge of optical anisotropy, refractive indices and their temperature dependence is necessary [1].…”