Liquid crystals bond-orientational

Given that the supercooling of a liquid can lead to structurally distinct possibilities (the stable crystal or a glass), structural order parameters are especially valuable in understanding low-temperature metastabiUty. In particular, it has been demonstrated (van Duijneveldt and Frenkel, 1992) that the bond-orientational order parameters introduced by Steinhardt et al (1983) are well suited for detecting crystalline order in computer simulations of simple supercooled liquids. The bond-orientational order parameters are so named because they focus on the spatial orientation of imaginary bonds" that connect molecules to their nearest neighbors defined as above with... 

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

In contrast to the case of the 8CB liquid crystal, no contact potential differences between first and second layers were observed with these lubricants. This indicates that there is no special orientation of the dipole active end groups, or perhaps that the end groups form hydrogen-bonded pairs with neighboring molecules so as to give no net dipole moment. 

Liquid crystal behavior is a genuine supramolecular phenomenon based on the existence of extended weak interactions (dipole-dipole, dispersion forces, hydrogen bonding) between molecules. For the former two to be important enough, it is usually necessary for the molecules to have anisotropic shapes, able to pack efficiently so that these weak interactions can accumulate and co-operate, so as to keep the molecules associated in a preferred orientation, but free enough to move and slide, as they are not connected by rigid bonds. 

To discuss the models in this section, we should mention two issues. First, the models assume the membrane is sufficiently soft that the tilt direction can vary with an energy cost that scales as (Vc(j)2. This is appropriate if the membrane is in a fluid phase like a smectic-C liquid crystal, with order in the tilt direction but not in the positions of the molecules. It is also appropriate if the membrane is in a tilted hexatic phase, with order in the orientations of the intermolecular bonds as well as the tilt. However, this assumption is not appropriate if the membrane is in a crystalline phase, because the tilt direction would be locked to the crystalline axes, and varying it would cost more energy than (V(f>)2. 

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The molecular structure of arsabenzene,49) 4-methylarsabenzene 50) and 4-methyl-stibabenzene 50) have been determined from an NMR study of liquids oriented in a liquid crystal phase. Unfortunately, no structural data are yet available for bisma-benzene. Selected bond lengths and angles of the complete family of group 5 heterobenzenes are illustrated in Fig. 1. 

Figure 3. (a) Two-dimensional, bond orientational order parameter average values in the molecular fluid layers of LI ecu confined in a multi-walled carbon nanotube of diameter D=9norder parameter values for the contact, second, third and fourth layers, respectively. The dotted line represents the bulk solid-fluid transition temperature, (b) Positional and orientational pair correlation functions in the unwraiqred contact layer of U CCU confined in a multi-walled carbon nanotube of diameter D=9.1< (5 nm) showing liquid phase at 7=262 K and crystal phase at 7=252 K. 

They then explained (in a descriptive fashion only) the dielectric constant as the result of the reorientation of indefinite liquid crystals in the applied field. Within the crystals the H bonds are more or less regularly oriented in such a manner that the bond dipoles do not cancel. A large dielectric constant results. The temperature variation of is attributed to changes in the relative amount of the three lattice types present. 

The order parameter used is the bond orientational order parameter, Qe, originally introduced by Steinhardt, Nelson and Ronchetti [89] and later used by van Duijneveldt and Frenkel [96] to simulate crystallization. It is sensitive to the overall degree of crystallinity in the system, irrespective of the crystal structure, i.e., it distinguishes the liquid from the crystal. The values of Qe for pure fee, body-centered-cubic (bcc), and for the liquid are 0.57452, 0.51069, and 0.0, respectively. Previous work [96] has shown that a defective fee crystal, which crystallizes from the liquid in simulations, has an order parameter below 0.5 and that finite-size effects lead to small positive values for the order parameter in the liquid phase. 

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