Off-lattice models both based on purely repulsive or attractive-repulsive Gay–Berne models allow us to simulate liquid crystal phases with some positional as well as orientational order. This chapter summarizes simulation results for anisotropic particles of elongated or discotic shape of the two types either pristine or decorated with charges, dipoles and quadrupoles. Beyond showing the effect of key molecular features (e.g. aspect ratios) on morphologies and phase diagrams, applications specific to liquid crystals, like the calculation of elastic constants and the simulation of a TN LCD, are reported. Tapered, bowlic and biaxial GB type single particle systems as well as more complex ones based of multi-particle mesogens (banana phases, polymers, elastomers) are discussed.

An introduction to the most important liquid crystal types and their physical properties and applications, that could also serve as a self-contained undergraduate course. Examples of the chemical structures of mesogens, i.e. molecules yielding the various liquid crystals phases, are given, providing a preliminary information needed for modelling and simulation.