Gay-Beme model

A5 The Gay-Beme model for liquid crystal systems and some typical arrangements. 

Lii J-H and N L Allinger 1989. Molecular Mechanics. The MM3 Force Field for Hydrocarbons 2 Vibrational Frequencies and Thermod5mamics Journal of the American Chemical Society 111-8566-8582 London F 1930 Zur Theori und Systematik der Molekularkrafte Zeiischrift fur Physik 63 245-279 Luckhurst G R, R A Stephens and R W Phippen 1990 Computer Simulation Studies of Anisotropic Systems XIX Mesophases Formed by the Gay-Beme Model Mesogen Liquid Crystals 8-451-464 Luque F J, F lias and M Orozco 1990 Comparabve Study of the Molecular Electrostatic Potential Obtained from Different Wavefunctions - Reliability of the Semi-Empirical MNDO Wavefunction Journal of Computational Chemistry 11-416-430. 

The original form of the GB potential applies to systems consisting of identical uniaxial particles. Some extensions of the Gay-Beme model have been proposed to overcome this Hmitaticai by generalizing the potential to dissimilar biaxial molecules [69, 70]. Moreover, the GB model can easily be combined with other potentials to add a few chemical details and establish a closer link with the structure of real molecules [71]. TTie effects of adding electric multipoles to the GB potential have been studied and important modifications have been observed in the overall molecular organization [68, 72]. 

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]... 

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

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. 

We have presented EMD and NEMD simulation algorithms for the study of transport properties of liquid crystals. Their transport properties are richer than those of isotropic fluids. For example, in a uniaxially symmetric nematic liquid crystal the thermal conductivity has two independent components and the viscosity has seven. So far the different algorithms have been applied to various variants of the Gay-Beme fluid. This is a very simple model but the qualitative features resembles those of real liquid crystals and it is useful for the development of molecular dynamics algorithms for transport coefficients. These algorithms are completely general and can be applied to more realistic model systems. If the speed of electronic computers continues to increase at the present rate it will become possible to study such systems and to obtain agreement with experimental measurements in the near future. 

A commonly used model system in liquid crystal simulation is the Gay-Beme fluid. It can be regarded as a Lennard-Jones fluid generalised to ellipsoidal molecular cores. 

The range parameter is denoted by a and the strength parameter denoted by e they are pair-wise functions of the relative orientation of corresponding Gay-Berne particles. The Gay-Beme potential is associated with a set of parameters describing the shape of Gay-Berne particles as well as the orientation of its principal axis defined according to its corresponding all-atom model in the inertial frame. The term dw is introduced in order to control the "softness" of the Gay-Berne potential. 

Golubkov, P. A., and Ren, P. [2006). Generalized coarse-grained model based on point multipole and Gay-Beme potentials,/. Chem. Phys., 125, pp. 064103... 

Fig. 1.11 (a) A typical coarse-graining method replaces groups of atoms by ellipsoidal rigid bodies, (b) The Gay-Beme potential models the anisotropic interaction between nonspherical coarse-grained molecules potentials are described by the orientation of the molecules with respect to a fixed frame and the separation between their centers of mass... 

A simple hybrid model for a siloxane side-chain liquid crystalline polymer is shown in figure 4. Here, the methylsiloxane backbone and the flexible alkyl spacer of the real polymer have been replaced by a series of united atom potentials, and the mesogenic groups have been replaced by Gay-Beme [16] potentials. 

LAMMPS [225] is a classical MD program implementing potentials for soft materials (biomolecules, polymers), solid-state materials (metals, semiconductors), and coarse-grained or mesoscopic systems. The code is designed to be easy to modify or extend with new functionalities. The comprehensive manual compensates for the somewhat clumsy input script syntax. Most of its model potentials have been parallelized and run on systems with multiple CPUs and GPUs, granting very good speedups, especially for the most compUcated pair potential styles, like the Gay-Beme and other CG potentials. 

Finally we note that there exist some special model potentials that combine an attraction at large separation and repulsion at short distances. The most popular potential of this kind is the Gay-Beme potential [22] which is a generalization of the Lennard-Jones potential for anisotropic particles. The Gay-Berne potential is very often used in computer simulations but not in the molecular theory because it is rather complex. 

Gaussian model, phase transitions 282,303 Gay-Beme interaction... 

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]. 

The cases discussed here have concerned simple one-site models. More complex molecular structures can be simulated by suitable combinations of various ellipsoidal Gay-Beme and spherical Lennard-Jones particles, for example to attempt modelling asymmetric molecules [62,63] or to include flexible chains [67,68]. 

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