Orientational order parameter from birefringence

The strain-indueed orientation is analyzed with the help of birefringence measurements [107, 115, 120, 123] (realized in the isotropic state, close to the transition), measurements of the IR dichroism [124, 126], and X-ray experiments [93, 108,120, 122, 125]. It was observed that the orientational order parameter, labeled P2 on Fig. 32, obtained from X-ray experiments [122], quiekly inereases with strain at the beginning, then saturates at a P2 value of about 0.4-0.6 for a sample synthesized in an isotropic state [99, 107, 121, 122]. On condition that they were realized above the gel point [122], the networks display reproducible and reversible behavior independent of the sample history. 

Figure 10.17 (a) The birefringence of an oriented one-comb PLC (polyacrylate obtained by photopolymerization of a surface aligned MLC) as a function of temperature. The various phases (K, crystalline S, smectic N, nematic and I, isotropic) are shown in the graph, (b) The order parameter of the same polymer (open symbol) in its nematic state as a function of reduced temperature, T/T., where Tj is the isotropization temperature. Data for the monomer (filled symbol) are shown in the same graph, ((a) and (b) from data of Broer et al [111].)... 

Thermo-optic effects in liquid crystals were investigated extensively from the point of view of device applications. Nematics are particularly suitable for such purposes because in this phase the refractive indices have an unusually large temperature dependence, especially near the nematic-isotropic phase transition. This strong temperature dependence is connected to the corresponding variation of the order parameter, 5. The order parameter is a measure of the degree to which the molecules are oriented along the director. The birefringence, is... 

The picture predicted by Fig. 3.2 has been confirmed by birefiringence measurements on the isotropic phase [3, 7-10]. Such measurements are much more precise than attempts to measure the influence of an interface on the order parameter of the nematic phase, because there is no contribution to birefringence from the bulk of an isotropic liquid. For nematic layers with the director homogeneously oriented along the surface of a solid substrate rubbed unidirectionally, the birefiringence is observed at temperatures exceeding the N-I transition point. Moreover, it depends on the surface potential. Fig. 3.3, as predicted by theory [5]. The thickness of the quasi-nematic layers adjacent to the substrate can be calculated from the observed birefringence... 

The second rank-order parameter S can be derived from measurements of the macroscopic tensor properties such as birefringence and diamagnetic susceptibility. It varies typically between 0.4 at the clearing temperature to 0.7 at T ni- r= 20K in nematic phase. The fourth rank-order parameter (P ) may play an important role for a subtle analysis of the orientational distribution function and can be determined using polarized Raman spectroscopy. ... 

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