Liquid crystal media order parameters

We note that earlier research focused on the similarities of defect interaction and their motion in block copolymers and thermotropic nematics or smectics [181, 182], Thermotropic liquid crystals, however, are one-component homogeneous systems and are characterized by a non-conserved orientational order parameter. In contrast, in block copolymers the local concentration difference between two components is essentially conserved. In this respect, the microphase-separated structures in block copolymers are anticipated to have close similarities to lyotropic systems, which are composed of a polar medium (water) and a non-polar medium (surfactant structure). The phases of the lyotropic systems (such as lamella, cylinder, or micellar phases) are determined by the surfactant concentration. Similarly to lyotropic phases, the morphology in block copolymers is ascertained by the volume fraction of the components and their interaction. Therefore, in lyotropic systems and in block copolymers, the dynamics and annihilation of structural defects require a change in the local concentration difference between components as well as a change in the orientational order. Consequently, if single defect transformations could be monitored in real time and space, block copolymers could be considered as suitable model systems for studying transport mechanisms and phase transitions in 2D fluid materials such as membranes [183], lyotropic liquid crystals [184], and microemulsions [185],... 

Examples of the order parameter are the density of the liquid, p(r), polarization vector of a dielectric medium, P(r), magnetic moment, p(r), spin of the atom in the crystal lattice of a solid, S, and charge density in the electrolyte solution, q(r). 

A molecular dynamics simulation has been performed on 4-n-pentyl-4(-cyanobiphenyl (5CB) in the nematic phase. Order parameters and dipolar couplings have been calculated and used to test theoretical models. Theoretical models have also been developed to explain the shielding of a noble-gas atom in an anisotropic environment and applied to explain the medium-induced shielding of the noble gases Xe and Ne in the nematic liquid crystal 4(-ethoxybenzylidene-4-n-butylaniline (EBBA). ... 

In experiments with the field-induced SHG we always tried to obtain the phase-matched generation, having in mind to study the zero-field SHG in the same synchronism directions when the external field is switched off. The search for zero-field SHG in the phase-matched conditions increases markedly the sensitivity of an experimental set-up and allows the pump beam intensity to be lowered. The study of the field-induced SHG was also used for the calculation of the number of parameters of the liquid crystalline medium (a cubic non-linear susceptibility a quadratic hyperpolarizability " and the discussion of their connection with molecular structure. In contrast to isotropic liquids, the value of Fy / depends not only on molecular parameters but on the orientational order parameters P- and (P4) of liquid crystal as well. The latter opens the possibility to measure (P2) and (P4). 

Sect. 5.7.5). A collinear pump geometry allows optimum overlap between the pump beam and the waist of the fundamental resonator mode in the crystal. The mode-matching parameter (i.e., the ratio of pump-beam waist to resonator-mode waist) can be chosen by appropriate mirror curvatures. The optical density of the active medium, which depends on the preparation of the Fa centers [5.146], has to be carefully adjusted to achieve optimum absorption of the pump wavelength. The crystal is mounted on a cold finger cooled with liquid nitrogen in order to achieve a high quantum efficiency t]. 

For isotropic media < 2> and < 4> are zero. Hence X333 reduces to the first term of the Langevin function. If the first-order parameters approach unity, the value of is five times larger than for an isotropic medium. This large difference has created interest in the use of liquid crystals, both low-molar-mass and polymeric, for nonlinear optics [24]. The nonlinear optical properties of poled polymers and poled pre-oriented polymers have been analysed thoroughly by the group at AT T Bell Laboratories [25, 26]. 

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