Topological phase transitions in two-dimensional bent-core liquid crystal models.

Abstract

Two-dimensional liquid crystal (LC) models of interacting V-shaped bent-core molecules with two rigid rodlike identical segments connected at a fixed angle (θ=112^{∘}) are investigated. The model assigns equal biquadratic tensor coupling among constituents of the interacting neighboring molecules on a square lattice, allowing for reorientations in three dimensions (d=2,n=3). We find evidence of two temperature-driven topological transitions mediated by point disclinations associated with the three ordering directors, condensing the LC medium successively into uniaxial and biaxial phases. With Monte Carlo simulations, temperature dependencies of the system energy, specific heat, orientational order parameters, topological order parameters, and densities of unbound topological defects of the different ordering directors are computed. The high-temperature transition results in topological ordering of disclinations of the primary director, imparting uniaxial symmetry to the phase. The low-temperature transition precipitates simultaneous topological ordering of defects of the remaining directors, resulting in biaxial symmetry. The correlation functions, quantifying spatial variations of the orientational correlations of the molecular axes show exponential decays in the high-temperature (disordered) phase, and power-law decays in the low-temperature (biaxial) phase. Differing temperature dependencies of the topological parameters point to a significant degree of cross coupling among the uniaxial and biaxial tensors of interacting molecules. This simplified Hamiltonian leaves θ as the only free model parameter, and the system traces a θ-dependent trajectory in a plane of the phenomenological parameter space.