Liquid Crystal Lattice Models II. Confined Systems

Hybrid Nematic Films: A Detailed Monte Carlo Investigation

“…The different boundary conditions are mimicked assuming a layer of outside particles with a fixed orientation consistent with the desired type of alignment at the top and at the bottom surfaces [3]. As we have mentioned before, in this work we need to consider hybrid boundary conditions which are homeotropic at the top surface while at the 120 C. Chiccoli et al bottom the alignment is considered to be always planar and homogeneous (along the x direction).…”

“…The spins represent a cluster of neighboring molecules whose short range order is assumed to be maintained through the temperature range examined [3]. The bulk Nematic-Isotropic (NI) transition for this model occurs at a reduced temperature…”

“…To generate the lattice configurations we have used the standard Metropolis Monte Carlo procedure [16] where one spin at a time is updated as described in [3] or a non-Boltzmann sampling using the Wang-Landau algorithm [17,18].…”

“…The confining surfaces, for instance curved and=or possibly with antagonistic boundary conditions, can result in competing multiple minima in free energy space, leading to frustration as well as to observable transitions between a variety of non-trivial equilibrium structures which would be otherwise difficult to realize [2]. The overall effect on the director field is difficult to predict, as in confined systems there is in general a competition between effects due to the boundary conditions, the ordering interactions inside the LC system, and the disordering effects due to the temperature [3]. Different organizations can be obtained as a function of some suitable external driving parameters changing the easy axis at the boundaries (e.g., by irradiation of azobenzene covered surfaces [4] or, more frequently, just by applying an external field or changing the temperature.…”

“…The system can be conveniently studied by computer simulations of a Lebwohl-Lasher type lattice model [3,12], that represent a powerful tool for studying ordering and structural transitions in uniaxial [13] and biaxial [14] nematics and their defects [3,5,10,15], particularly when the effect of complex boundaries and temperature has to be investigated. For instance, multiple organizations were also predicted and confirmed by Monte Carlo simulations [3,5] on a closely related system with degenerate, rather than uniform boundary condition, at the planar anchoring surface.…”