Computer simulation of liquid crystals

Abstract

Computer simulations, using the molecular dynamics and Monte Carlo techniques, and employing simple molecular models, yield insight into general features of phase equilibria, structure, and dynamics of liquid crystals. Here, results are reported from extensive simulations of the Gay-Berne family of molecular models, in which potential parameters are adjusted to vary the molecular length-to-width ratio in a systematic way. Attention is paid to the characterization of nematic, smectic-A and smectic-B phases as functions of these parameters.A simulation study of the approach to the isotropic-nematic phase transition, using a large system size and lengthy runs on the T3D parallel supercomputer, is described. Spatially longranged collective orientational correlations develop in the isotropic phase, close to the transition. The direct correlation function has been calculated for these systems, and remains short-ranged, as expected, as the transition is approached. The simulation results are compared with the density functional analysis of isotropic instability relative to the nematic phase.

The global phase diagram of the Gay–Berne model

“…Although identified as SmB, whether it was smecticlike or crystalline was recognized as a subtle problem. As noted by Allen et al, 16 on cooling the SmB phase to very low temperatures no transition to a crystal could be identified and the SmB exhibited well-defined correlations characteristic of crystalline packing. Further evidence of the crystalline nature of the SmB phase was obtained after the calculation of the shear elastic modulus by Brown et al 17 On the basis of all this evidence, it was suggested that the reported SmB phase for the GB model was in fact crystalline and that it might be more appropriate to refer to this phase as a solid.…”

“…6,9,12 Simulations using different combinations of parameters have shown that the GB model exhibits an additional phase identified as smectic A ͑SmA͒. [15][16][17][18] All these simulation studies suggest that the occurrence of the SmB is not very sensitive to the particular parameterization, whereas the formation of the SmA phase requires the molecular elongation be large enough.…”

Molecular dynamics study on evaporation and reflection of monatomic molecules to construct kinetic boundary condition in vapor–liquid equilibria

“…The cutoff radius was set to 15Åin accordance with the previous studies [6,12], although it may be too short not to consider specific longrange interactions taking the extreme inhomogeneity of the two-phase system into account [22]. The initial condition was obtained from the temperaturecontrol simulation [23] of the system. After the system reached the vapor-liquid equilibrium state, we performed the equilibrium simulation without temperature control.…”

Spatial Order in Liquid Crystals: Computer Simulations of Systems of Ellipsoids

“…We were the first to determine the direct correlation function from computer simulations of a nematic fluid without any approximations. Direct correlation functions in isotropic fluids have been calculated earlier by Allen et al [85,86], and approximate data for nematic fluids have been derived from simulations by Stelzer et al [87,88]. Figure 6 shows the orientational average of the total correlation function and the direct correlation function.…”

“…Perhaps the most obvious anisotropic generalization of hard spheres are hard ellipsoids of revolution with one symmetry axis of length L and transverse thickness D. The phase diagram in three dimensions has been established from computer simulations by Frenkel, Allen and coworkers [9,10,11,12,13,14]. It is shown for a range of elongations κ = L/D in Figure 2.…”