Nematic confined

Elastic deformation of the director, induced by a magnetic induction or electric field, in a uniformly aligned, thin sample of a nematic confined between two surfaces. 

Fig. 8.6 Splay, bend and twist distortions in nematics confined between two glasses that align liquid crystal at the surfaces either homogeneously (for splay and twist) or homeotropically (for bend)...

Feldman DE (2000) Quasi-Long-Range Order in Nematics Confined in Random Porous Media Phys Rev Lett 84 4886-4889... 

However, there is no physical reason why the coefficient 24 itself should be exactly zero, and therefore in special geometries the saddle-splay contribution must be taken into consideration. The 24 term is nonzero for director configurations containing stable point defects [52]. For example, it influences the director fields in cylindrical [43, 44, 178, 194, 201-203] and spherical [47,204,205] cavities, in nematics confined between concentric cylinders in bend geom-... 

Experimentally, access may be gained to 24 by studying director configurations in stripe textures (e.g. [ 196]), or in the non-pla-nar geometries cited above (e.g. [43, 47]). As an example, we discuss the saddle-splay term in nematics confined to cylindrical cavities. A means of measuring 24> on the basis of an analysis of the nematic director field, has been proposed and performed by Allender et al. [43]. The director configuration in the cylinders is monitored by deuterium NMR lineshape analysis [44, 191] or polarizing microscopy [194]. The submicrometer cylindrical pores of a nuclepore filter are treated such that the director is anchored perpendicular to the pore walls everywhere. The nematic liquid crystal 4 -pentyl-4 -cyanobiphenyl (5-CB) is adsorbed to the filter pores. 

FIG. 7 Same as Fig. 5, but for a nematic Gay-Berne film confined between homeotropically anchoring substrates (from Ref. 48). 

T. Gruhn, M. Schoen. Substrate-induced order in confined nematic liquid-crystal films. J Chem Phys 705 9124-9136, 1998. 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Many other interesting examples of spontaneous reflection symmetry breaking in macroscopic domains, driven by boundary conditions, have been described in LC systems. For example, it is well known that in polymer disperse LCs, where the LC sample is confined in small spherical droplets, chiral director structures are often observed, driven by minimization of surface and bulk elastic free energies.24 We have reported chiral domain structures, and indeed chiral electro-optic behavior, in cylindrical nematic domains surrounded by isotropic liquid (the molecules were achiral).25... 

Note 4 The director precession in a chiral nematic mesophase is spontaneous and should be distinguished from an induced twisted structure produced by a mechanical twist of a nematic mesophase between confining surfaces. 

Nano-Confinement. There are limited, but interesting studies, regarding the confinement in ordered mesoporous materials. First observations were made on nematic liquids within mesoporous SBA-15 host materials which showed a change in the phase transition, when confined within the mesoporous cavities. To evidence also that there are many studies of confinement in mesoporous materials in the polymer diffusion and membrane literature, but they refer essentially to entropic effects due to restricted motion of these materials inside the ordered mesoporous materials which in enhanced by more hydrophobic and less polar surfaces. This is especially true as the molecules become larger, because the number of conformations the molecule can adopt in a confined space is limited. We refer here, on the contrary, to aspects relevant for catalysis and in which thus the dimensions of the molecules (of the order of 0.1 nm) is far below the dimensions of the cavities (around 5 nm for SBA-15, for example). 

Various other instances of hydrodynamic and electrohydrodynamic instabilities in nematic and, to a lesser extent, smectic liquid crystals have been investigated. No attempt is made here to review this work. For the present discussion, it is sufficient to note that (a) most of the work has dealt with oriented layers having anisotropic properties, and (b) some interesting instabilities arise in oriented layers which do not occur for isotropic materials. An example of the latter is cellular convection in a fluid layer confined between horizontal plates maintained at different temperatures. With an isotropic fluid, convection can arise only if the lower plate is hotter than the upper plate. Then, fluid near the lower plate is less dense and tends to rise while fluid near the upper plate is denser and tends to sink. With an oriented layer, however, convection can arise even when the upper plate is hotter if the anisotropy of thermal conduction properties is of a particular type (8). 

The procedure appears to much more efficient in the isotropic phase than in the nematic phase. In the nematic phase polymerization may be confined largely to the surface for thicker films in the isotropic phase, polymerization is much more uniform. 

Nakaya, K., Imai, M., Komura, S., Kawakatsu, T. andUrakami, N. (2005) Polymer-confinement-induced nematic transition of microemulsion droplets. Europhys. Lett., 71, 494-500. 

In the Ni phase, Sa > 0, but SB < 0. The conformation of the backbone chain is discus-like, i.e., is oblate shape, in which the mean square end-to-end distance along the director, (R%) is less than the perpendicular component (R%). In the smectic phase the anisotropy of two components is greater than that in the nematic phase. At the extreme case the backbone is surpassed in a plane, which was predicted by Renz Warner (1986) to exist in smectic polymers where backbones become confined between smectic layers formed by side chains, and has been seen by Moussa et al. (1987). In the extreme case, the backbone becomes a two-dimensional random walk when SB = — and Sa = 1. 

If the side chain liquid crystalline polymers goes into the smectic A phase from the nematic phase, the backbone chain is confined between two successive smectic layers, occasionally jumping into the neighboring layer gap. See Figure 2.30 where the cylinders denote side groups and thick lines represent backbones. The mean square end-to-end distances parallel and perpendicular to the director differs more than that in the nematic phase. 

Lyotropic liquid crystals occur abundantly in nature, being ubiquitous in living systems.Their structures are quite complex and are only just beginning to be elucidated. However, in this monograph we shall be confining our attention mainly to the physics of low molecular weight thermotropic liquid crystals and do not propose to discuss polymer and lyotropic systems in any further detail. In chapters 2-5, we deal with the nematic, cholesteric and smectic mesophases of rod-like molecules and in chapter 6 discotic systems. 

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