Nematic number system

In simple single-site liquid crystal models, such as hard-ellipsoids or the Gay-Berne potential, a number of elegant techniques have been devised to calculate key bulk properties which are useful for display applications. These include elastic constants for nematic systems [87, 88]. However, these techniques are dependent on large systems and long runs, and (at the present time) limitations in computer time prevent the extension of these methods to fully atomistic models. 

The rapid rise in computer speed over recent years has led to atom-based simulations of liquid crystals becoming an important new area of research. Molecular mechanics and Monte Carlo studies of isolated liquid crystal molecules are now routine. However, care must be taken to model properly the influence of a nematic mean field if information about molecular structure in a mesophase is required. The current state-of-the-art consists of studies of (in the order of) 100 molecules in the bulk, in contact with a surface, or in a bilayer in contact with a solvent. Current simulation times can extend to around 10 ns and are sufficient to observe the growth of mesophases from an isotropic liquid. The results from a number of studies look very promising, and a wealth of structural and dynamic data now exists for bulk phases, monolayers and bilayers. Continued development of force fields for liquid crystals will be particularly important in the next few years, and particular emphasis must be placed on the development of all-atom force fields that are able to reproduce liquid phase densities for small molecules. Without these it will be difficult to obtain accurate phase transition temperatures. It will also be necessary to extend atomistic models to several thousand molecules to remove major system size effects which are present in all current work. This will be greatly facilitated by modern parallel simulation methods that allow molecular dynamics simulations to be carried out in parallel on multi-processor systems [115]. 

It was first reported in the early 1970s that these melt processible polymers could best be described as thermotropic systems which usually display an nematic texture in the melt phase [5]. Subsequently, a number of additional phases have been reported ranging from discotic structures to highly ordered smectic E G systems with three dimensional order. In the last several years an IUPAC sponsored study on nomenclature on thermotropic LPCs has been underway. A more complete set of definitions will be available shortly as a result of Recommendation No. 199 IUPAC [6]. 

Such order can be described in terms of the preferential alignment of the director, a unit vector that describes the orientation of molecules in a nematic phase. Because the molecules are still subject to random fluctuations, only an average orientation can be described, usually by an ordering matrix S, which can be expressed in terms of any Cartesian coordinate system fixed in the molecule. S is symmetric and traceless and hence has five independent elements, but a suitable choice of the molecular axes may reduce the number. In principle, it is always possible to diagonalize S, and in such a principal axis coordinate system there are only two nonzero elements (as there would be, for example, in a quadrupole coupling tensor). In the absence of symmetry in the molecule, there is no way of specifying the orientation of the principal axes of S, but considerable simplification is obtained for symmetric molecules. If a molecule has a threefold or higher axis of symmetry, its selection as one of the axes of the Cartesian coordinate system leaves only one independent order parameter, with the now familiar form ... 

The most simple molecular topology of such systems reported so far is a tetrahedral supermolecule obtained by reacting tetrakis(dimethylsiloxy)-silane with alkenyloxy-cyanobiphenyls (Fig. 22), as discussed previously. Such tetramers exhibit smectic A liquid crystal phases [179]. For such end-on materials, microsegregation at the molecular level favors the formation of the smectic A phases in preference to the nematic phase exhibited by the mesogenic monomers themselves. The use of different polyhedral silox-ane systems (Fig. 24) or the Ceo polyhedron as the template for multi- and polypedal hexakis(methano)fullerenes (Fig. 70) substituted with a large number of terminally attached mesogenic groups confirm the same tendency to the formation of smectic A phases (vide supra). 

Sarman and Evans [24, 32] performed a comprehensive study of the flow properties of a variant of the Gay-Beme fluid. In order to make the calculations faster the Lennard-Jones core of the Gay-Beme potential was replaced by a 1/r core. This makes the potential more short ranged thereby decreasing the number of interactions and making the simulation faster. The viscosity coefficients were evaluated by EMD Green-Kubo methods both in the conventional canonical ensemble and in the fixed director ensemble. The results were cross checked by shear flow simulations. The studies covered nematic phases of both prolate ellipsoids with a length to width ratio of 3 1 and oblate ellipsoids with a length to width ratio of 1 3. The complete set of potential parameters for these model systems are given in Appendix II. 

The number of transitions in an NMR spectrum increases dramatically as the number of interacting nuclei in the spin system increases. The number of transitions appearing in a 1-quantum spectrum of a spin system (without any simplifying symmetry) partially oriented in a nematic phase is expressed by Eq. (2), with some examples shown in Table 1. 

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