On the temperature dependence of the order parameter of liquid crystals over a wide nematic range

Abstract

Based on the ideas of Landau-de Gennes theory applied to nematic liquid crystals, several forms for the variation of the order parameter as a function of temperature are investigated over a wide nematic range. These functional forms are used to fit the experimental order parameters, determined through the use of C-13 NMR, for 4-methoxybenzylidene-4'-butylaniline (MBBA) and 4-n-pentyl-4'-cyanobiphenyl (5CB), and the physical significance of the parameters is discussed. A comparison of the results shows that the functional form which fits the experimental data best is similar to the Haller equation, a useful relation which is usually regarded as empirical. In this case, the coefficients resulting from a semi-empirical approach based on the Landau-de Gennes treatment may be thought of as quantifying the importance of the structure and rigidity of the liquid crystal in determining the temperature dependence of the order parameter for that liquid crystal. In the process, we have also examined the pretransitional behaviour in the C-13 NMR chemical shifts of liquid crystals observed within a few tenths of a degree above the nematic to isotropic transition temperature. IntroductionMany interesting properties and important applications of nematic liquid crystals result from their anisotropic orientational ordering, which can be quantified through the use of the order parameter. The variation of the order parameter as a function of temperature has been the subject of much interest, and several approaches have been used to describe the temperature dependence of the order parameter. For example, the Maier-Saupe mean-field theory [ 1,2] predicts that the order parameter of nematic liquid crystals is a universal function of temperature, which is not observed experimentally. Other variations of mean-field theory do allow for differences between liquid crystals, but do not always predict experimentally observed results [3]. The Landau-de Gennes theory has also been used to derive the temperature dependence of the order parameter from a low-order polynomial which approximates the free energy density of the nematic liquid

NMR of molecular endofullerenes dissolved in a nematic liquid crystal

“…13 and 14 are the product of an order parameter for the partial orientation of the endohedral molecule with respect to the distorted C 60 cage, and an order parameter for the partial orientation of the distorted cage with respect to the liquid crystal director. The observed temperature-dependence of the dipolar splitting, as shown in Figure 3, has a similar form to the order parameter for the liquid crystal molecules themselves 20,21 , and is likely to derive predominantly from the temperature dependence of the order parameter S 2 CD , which describes the partial orientation of the distorted cages with respect to the liquid crystal director. The order parameter S 2 MC , which describes the orientation of the endohedral molecules with respect to the distorted cage, is expected to have a relatively mild temperaturedependence.…”

“…The nematic-to-isotropic phase transition of pure MBBA occurs at 320 K 20,21 . The endofullerene solutions in MBBA display somewhat depressed phase transition temperatures, as shown below.…”

Topological Formations in Chiral Nematic Droplets

“…Possible values of the order parameter S fall in the range [−0.5, 1]. In small molecule rod-like nematics they are typically between 0.3 and 0.7 [13][14][15]. In the disordered, isotropic phase the order parameter is equal to 0 and the director has no physical meaning.…”

Universal phase behaviors of intracellular lipid droplets

“…In other words, the relative contribution of the surface alignment increases as T → T c . Also, R * remained constant below T ∼ 30°C; this would be attributed to the near-saturation of the Q value when T T c [25]. There is a mounting evidence that phase transitions play important roles in living cells, particularly associating with membrane-less organelles or condensates [3,14,[26][27][28]; nevertheless, there has been little work on the phase transition in lipid droplets [29].…”