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Liquid crystals are a state of matter with the properties of both liquids and solids. They have a long research history dating back to the 19th century and have found countless applications, with LCDs being arguably the most important one of them. As demonstrated by Onsager, the phase transition between isotropic liquid and nematic liquid crystal can be induced by excluded volume effects within the hard spherocylinder model. It turns out that other hard-core particle systems exhibit a variety of different liquid crystal phases. We have performed molecular dynamic Monte Carlo simulations of achiral banana-shaped particles built from hard spheres in the NpT ensemble with varying bend angle and particles density. We have identified four distinct liquid crystal phases. The most notable one is twist-bend nematic, where the preferred direction varies in space with a periodic, heliconical pattern, displaying a broken chiral symmetry.
