Phase behavior of the confined Lebwohl-Lasher model

Phase behavior of the generalized chiral Lebwohl-Lasher model in bulk and confinement

One of the simplest models that is used to study the isotropic-nematic tranition in liquid crystalline systems is the Lebwohl-Lasher model. Several extensions of this model further enhanced its applicability. We combine two of these extensions (a generalization and the inclusion of a chiral term) and study the phase behavior and the nature of phase transitions of the resulting generalized chiral Lebwohl-Lasher model using Monte Carlo simulations. We find that the type (and even the existence) of the transition depends on the combination of the width of the interaction potential, the strength of the chiral part of the interaction, and the geometry of the system. As well, the pitch of the cholesteric bulk phase changes on approaching the phase transition if the interaction width differs from the one of the original Lebwohl-Lasher model. Thus, we identify parameter combinations that allow one to tune the properties of the ordered phase and the nature of the order-disorder transition.

Lattice Monte Carlo study of orientational order in a confined system of biaxial particles: Effect of an external electric field

In this work we have used lattice Monte Carlo to determine the orientational order of a system of biaxial particles confined between two walls inducing perfect order and subjected to an electric field perpendicular to the walls. The particles are set to interact with their nearest neighbors through a biaxial version of the Lebwohl-Lasher potential. A particular set of values for the molecular reduced polarizabilities defining the potential used was considered; the Metropolis sampling algorithm was used in the Monte Carlo simulations. The relevant order parameters were determined in the middle plane of the sample and for some cases across the whole thickness of the sample. We have determined the temperature-electric field phase diagram for this system and found, as expected, five different system configurations corresponding to three different mesophases. At low temperatures and low fields the system finds itself in an undistorted biaxial phase. On increasing the field at low temperatures, a Freedericksz transition takes place and the secondary directors reorient towards the field while the primary director stays undistorted and parallel to the walls. On increasing the field further, a second Freedericksz transition occurs and the primary director orients also towards the field direction. The orientational order measured at the field strengths tested is not affected by the field. On increasing the temperature, a transition to a uniaxial phase occurs and within the range of this phase a field increase leads also to a Freedericksz transition where the main director reorients towards the field. At higher temperature a transition to a disordered phase is found. We have performed finite size scaling analysis for the Freedericksz critical fields and found that they scale with the distance L between the walls as L^{-1} as expected from continuum theory. From these fields we have also determined the temperature dependence of two elastic constant ratios. Critical exponents and critical temperatures for the order parameter and the correlation length for the biaxial-uniaxial phase transition and the uniaxial to disordered phase transition were also determined by finite size scaling and are discussed.

Theory and simulation of the confined Lebwohl-Lasher model

We discuss the Lebwohl-Lasher model of nematic liquid crystals in a confined geometry, using Monte Carlo simulation and mean-field theory. A film of material is sandwiched between two planar, parallel plates that couple to the adjacent spins via a surface strength ε(s). We consider the cases where the favored alignments at the two walls are the same (symmetric cell) or different (asymmetric cell). In the latter case, we demonstrate the existence of a single phase transition in the slab for all values of the cell thickness. This transition has been observed before in the regime of narrow cells, where the two structures involved correspond to different arrangements of the nematic director. By studying wider cells, we show that the transition is in fact the usual isotropic-to-nematic (capillary) transition under confinement in the case of antagonistic surface forces. We show results for a wide range of values of film thickness and discuss the phenomenology using a mean-field model.