Spontaneous breaking of chiral symmetry in achiral bent-core liquid crystals: Excluded volume effect.

Bent-Core banana-shaped molecules exhibit tilted polar smectic phases with macroscopically chiral layer order even though the constituent molecules are achiral in nature. Here, we show that the excluded volume interactions between the bent-core molecules account for this spontaneous breaking of chiral symmetry in the layer. We have numerically computed excluded volume between two rigid bent-core molecules in a layer using two types of model structures of them and explored the different possible symmetries of the layer that are favored by the excluded volume effect. For both model structures of the molecule, the C_{2} symmetric layer structure is favored for most values of tilt and bending angle. However, the C_{s} and C_{1} point symmetries of the layer are also possible for one of the model structures of the molecules. We have also developed a coupled XY-Ising model and performed Monte Carlo simulation to explain the statistical origin of spontaneous chiral symmetry breaking in this system. The coupled XY-Ising model accounts for the experimentally observed phase transitions as a function of temperature and electric field.