Liquid crystals Lennard-Jones potential

One important point we should stress, in conjunction with our current interest, is that similar slow relaxation as liquid water is observed in much simpler model systems The binary mixture of Lennard-Jones liquids, which consist of two species of particles, is now studied extensively as a toy model of glass-forming liquids. It is simulated after careful preparation of simulation conditions to avoid crystallization. Also, the modified Lennard-Jones model glass, in which a many-body interaction potential is added to the standard pairwise Lennard-Jones potential, is also studied as a model system satisfying desired features. 

In the area of liquid crystals, a popular coarse-graining approach involves the use of the Gay-Berne potential [16-20] (figure 2). Here, a liquid crystal molecule can be represented by a single anisotropic site with both anisotropic attraction and repulsion acting between molecules. Prom figure 2, the Gay-Berne can be seen to take a similar form to the well-known 12 6 Lennard-Jones potential. However, the energy at which the attractive and repulsive energies cancel, a, and the depth of the attractive well, e, depend on the relative orientations, e<, of the two particles, i.e. UoB = Four parameters, , fi and i/, control... 

In the early 1970s, molecular simulation of liquid crystals started by Monte Carlo simulations of simple shaped models (rigid body ellipses, etc.) to estimate the excluded volume effect [77]. At the same time, there were already attempts to use the so-called Lennard-Jones potential to calculate the anisotropic potential in model liquid crystals [78]. This has developed into the nowadays well-known Gay-Beme potential [79]. 

Lennard-Jones mixture 53, 81 Lennard-Jones parameters 67, 74, 78 Lennard-Jones particle 95 Lennard-Jones potential 22-24, 34, 67, 69 Line tension 196 LiouvUle equation 142 Liquid crystal 243... 

For a structure-property relation, structural features have to be tak into account which cannot be covered with EQNS (9) and (10). Taking all structinal features into catom-atom Lennard-Jones potential in Monte Carlo or molecular dynamic calculations would allow the calculation of the chirality transfer [3]. Unfortunately at present these techniques allow onty calculations to a sufficiently good approximation for larger ensembles by the use of the Gay-Beme model potential with the simplest possible chiral term [3]. Thus, it is of interest to find a description which introduces molecular parameters as a bridge between the structure and the measurable reciprocal pitch or the HTP. Experimentally the HTP for a chiral molecule in achiral or chiral liquid crystal phase, in which a helical structure is induced, can be given by [18]... 

An important addition compared to previous models was the parameterization of the internucleosomal interaction potential in the form of an anisotropic attractive potential of the Lennard-Jones form, the so-called Gay-Berne potential [90]. Here, the depth and location of the potential minimum can be set independently for radial and axial interactions, effectively allowing the use of an ellipsoid as a good first-order approximation of the shape of the nucleosome. The potential had to be calibrated from independent experimental data, which exists, e.g., from the studies of mononucleosome liquid crystals by the Livolant group [44,46] (see above). The position of the potential minima in axial and radial direction were obtained from the periodicity of the liquid crystal in these directions, and the depth of the potential minimum was estimated from a simulation of liquid crystals using the same potential. 

An example drawn from Deitrick s work (Fig. 2) shows the chemical potential and the pressure of a Lennard-Jones fluid computed from molecular dynamics. The variance about the computed mean values is indicated in the figure by the small dots in the circles, which serve only to locate the dots. A test of the thermodynamic goodness of the molecular dynamics result is to compute the chemical potential from the simulated pressure by integrating the Gibbs-Duhem equation. The results of the test are also shown in Fig. 2. The point of the example is that accurate and affordable molecular simulations of thermodynamic, dynamic, and transport behavior of dense fluids can now be done. Currently, one can simulate realistic water, electrolytic solutions, and small polyatomic molecular fluids. Even some of the properties of micellar solutions and liquid crystals can be captured by idealized models [4, 5]. 

Tanemura et al. examined crystallization in a liquid of soft spheres and found both fee and bcc structures. They used the method of Voronoi polyhedra to characterize the evolving solid clusters. Hsu and Rahman extended the use of Voronoi polyhedra in a systematic study of the effect of potential on the structure observed. They found that a model rubidium potential always crystallized to a bcc structure, while a truncated rubidium, Lennard-Jones,... 

Hansen and Verlet [156] observed an invariance of the intermediate-range (at and beyond two molecular diameters) form of the radial distribution function at freezing, and from this postulated that the first peak in the structure factor of the liquid is a constant on the freezing curve, and approximately equal to the hard-sphere value of 2.85. They demonstrated the rule by application to the Lennard-Jones system. Hansen and Schiff [157] subsequently examined g r) of soft spheres in some detail. They found that, although the location and magnitude of first peak of g r) at crystallization is quite sensitive to the intermolecular potential, beyond the first peak the form of g(r) is nearly invariant with softness. This observation is consistent with the Hansen-Verlet rule, and indeed Hansen and Schiff find that the first peak in the structure factor S k) at melting varies only between 2.85 n = 8) to 2.57 (at n= ), with a maximum of 3.05 at n = 12. 

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