Splay-induced order in systems of hard wedges

We studied equilibrium systems composed of wedge-shaped monodisperse molecules using hard-particle Monte Carlo simulations. Each model molecule was made up of six colinear tangent spheres with linearly decreasing diameters. Thus, the shape was unequivocally described by a single parameter $d$: the ratio of the smallest and largest diameters of the spheres. The phases of the systems were analyzed as a function of $d$ and packing density $\eta$. As interactions were purely of the excluded volume type, the emergent phases were governed solely by the configurational entropy. For $\eta < 0.5$, in addition to the isotropic liquid, we observed standard nematic and smectic A liquid crystalline phases. However, for $\eta > 0.5$, apart from the ordinary non-polar hexagonal crystal, three new frustrated polar crystalline phases with splay modulation appeared: antiferroelectric splay crystal ($\text{Cr}_\text{S}\text{P}_\text{A}$), antiferroelectric double splay crystal ($\text{Cr}_\text{DS}\text{P}_\text{A}$) and ferroelectric double splay crystal ($\text{Cr}_\text{DS}\text{P}_\text{F}$). All configurations were studied in terms of nematic, smectic, and hexatic order parameters, as well as the radial distribution function and the polarization correlation function.