Liquid crystals modeling

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. 

Figure 3.4 Plausible mechanism of the formation of MCM-41 by a liquid-crystal model (1) formation of cylindrical surfactant micelles, (2) hexagonal assembly, (3) formation of the silica around the micelles, and (4) surfactant elimination.

The topic of this article is the study of transport properties of liquid crystal model systems by various molecular dynamics simulations techniques. It will be shown how GK relations and NEMD algorithms for isotropic liquids can be generalised to liquid crystals. It is intended as a complement to the texts on transport theory such as the monograph "Statistical Mechanics of Nonequilibrium liquids [8] by Evans and Morriss and "Recent Developments in Non-Newtonian Molecular Dynamics [9] by Sarman, Evans and Cummings and textbooks on liquid crystals such as "The physics of liquid crystals" [2] by de-Gennes and Frost and "Liquid Crystals" [3] by Chandrasehkar. 

We finally note that these methods for the evaluation of the thermal conductivity have been generalised to flexible molecules as well [21]. They have been found to give fairly accurate results for the thermal conductivity of alkanes. This implies that it is possible to obtain reasonable values for the thermal conductivity of more realistic liquid crystal models too even though considerably longer calculations are required. 

The first attempt to evaluate the viscosities of a liquid crystal model system by computer simulation was made by Baalss and Hess [31]. They mapped a perfectly ordered liquid crystal onto a soft sphere fluid in order to simplify the interaction potential and thereby make the simulations faster. The three Mies-owicz were evaluated by using the SLLOD equations of motion. Even though the model system was very idealised, the relative magnitudes of the various viscosities were fairly similar to experimental measurements of real systems. 

Interpretation of the results is straightforward. If addition of the diacid to a lamellar liquid crystal model dirt system does not increase the interlayer spacing, the conformation on the right in Figure 2.13 is correct if an increase does take place, the situation on the left in Figure 2.13 would describe the structural organization of the diacid molecule. 

Penzien K. and Schmidt G.M. (1969) Reactions in chiral crystals an absolute asymmetric synthesis, Angew. Chem. Int. Ed. Engl. 8, 608-609. Saeva F.D., Sharpe P.E. and Olin G.R. (1975) Asymmetric synthesis in a cholesteric liquid crystal solvent, J. Amer. Chem. Soc. 97, 204-205. Thiemann W. and Teutsch H. (1990) Possible amplification of enantiomeric excess through structural properties of liquid crystals-model for origin of optical activity in the biosphere. Origin ofLife Evolution of Biosphere 20, 121-126 1986,16,420. 

Alben, R., Pretransition effects in nematic liquid crystals model calculations. Mol. Cryst. Uq. Cryst., 13,193-231 (1971). 

Figure 2. Lamellar liquid crystal model of the carbonaceous mesophase 977) 38,19 ...

Many membrane functions can be directly related to the physical properties of the liquid-crystalline lipid bilayer. Variations in curvature and area per unit mass and diffusion properties can thus be explained by the liquid-crystal model. Membrane proteins contain hydrophobic segments in an alpha-helical conformation which constitute the anchor in the hydrophobic core of the bilayer. The proteins contain short chains of sugar groups on the outer surface of the plasma membrane and this surface zone is involved in recognition phenomena. A covalent link between the peptide and the oligo-... 

The surprising result is that our liquid crystal model system with just these three broken symmetries of life knows time, another feature of living systems. It does not learn about time after it has been pushed far from equilibrium and is close to turbulence. It knows time as soon as the nonequilibrium driving force is strong enough to enforce a pattern. Even its first pattern is characterized by a frequency, co. When i 0, the interface reverts back to its featureless dead state = 0 and co = 0. 

Structure may affect the phase situation. Smectic phases have been identified in computer simulations of liquid crystal models with semiflex-ible molecules. The well-known odd-even effects for the nematic properties could be recovered. Paolinl et al. employed a soft-core site-site potential and could reveal both nematic and smectic phases. 

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