Chiral segregation of hockey-stick shaped particles in two dimensions

Abstract

Chiral segregation and liquid crystalline aggregates in two dimensions are studied for a heterochiral mixture of oversimplified versions of so called hockey stick-shaped particles, made with two line segments that interact via an infinitely repulsive potential. The goal of this study is to explore the possibility of producing chiral segregation and finding liquid crystalline mesophases using this model which has an extreme level of idealization. In particular, by considering infinitely thin particles and infinite repulsions interacting exclusively side to side, the substrate does not act on the molecules. Since only infinite repulsions are considered, the phase behavior is ruled by entropic effects, where self-assembly takes place. Onsager theory and Monte Carlo simulations in the Gibbs and canonical ensembles were used to study several molecular conformations in order to delineate the mesophase diagram which includes the chiral segregation region and several liquid crystalline mesophases, most of them heterochiral. The enantiomerically pure phase is of the smectic kind and corresponds to the highest density regime. The heterochiral mesophases are nematic, smectic with antiferroelectric order and tetratic. The appearance of the different assemblies strongly depends on the molecular conformation defined by the angle between the segments and their lengths. To study the phase transitions, the molar concentration, the nematic and tetratic order parameters, as well as the distribution functions were calculated.