Splay-induced order in systems of hard wedges

TL;DR

This study uses Monte Carlo simulations to explore how wedge-shaped molecules self-organize into various liquid crystalline and crystalline phases, revealing new polar splay crystal structures driven by shape-induced entropy effects.

Contribution

It introduces a model of wedge-shaped molecules with a single shape parameter and uncovers novel polar crystalline phases induced by particle shape and packing density.

Findings

Identification of new polar splay crystal phases at high packing densities.

Demonstration of shape parameter $d$ influencing phase behavior.

Observation of entropy-driven phase transitions in hard-particle systems.

Abstract

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.