Monte Carlo simulation of twisted nematic and supertwisted nematic liquid crystal cells

Abstract

The orientational properties of liquid crystals in twisted nematic (TN) and supertwisted nematic (STN) cells were studied by Monte Carlo (MC) simulation depending on the strength of an external field. The liquid crystals sandwiched between planar surfaces were described by three-dimensional lattice systems of dimensions 10 × 10 × 13 up to 10 × 10 × 33 with pairwise interactions given by the chiral Lebwohl–Lasher potential between objects taken as directors representing a cluster of neighbouring molecules in a cubic unit cell. The electro-distortional curves showing the midlayer tilt angle as function of the applied voltage have been investigated depending on a set of cell and material parameters including e.g. the cell twist angle, the surface pretilt angle, and the thickness to pitch ratio. At very low temperature, in spite of the small system sizes studied a very good agreement has been obtained for MC simulation results and continuum theoretical predictions, both with respect to the dependency of the obtained threshold voltages necessary for the field-induced unwinding transition on cell twist angle and thickness to pitch ratio even for non-zero surface pretilt angles. This enabled the calculation of the elastic constants of the chiral Lebwohl–Lasher model. The applied method, the analysis of director arrangements in liquid crystal cells by means of Monte Carlo simulations starting from pairwise interactions, will be helpful as an alternative route to a continuum theoretical approach in designing advanced liquid crystal displays.