Entropy, Free Energy, and a Generalized Order Parameter for Liquid Crystal Phases of Chiral and Achiral Rods

Liquid crystal (LC) phases formed by anisotropic particles have long attracted interest due to their unique combination of fluidity and directional order, as well as their prevalence in natural systems. Among them, chiral entities such as helices exhibit exotic LC phases, like the cholesteric and screw nematic, in addition to isotropic, smectic, and crystal phases that are observed in systems of achiral particles. Chiral particles are ubiquitous in nature across length scales. Helices, being the simplest examples of chiral particles, are important components in a variety of biological systems in the form of DNA, protein fragments, and others. In this work, we employ molecular dynamics to investigate the thermodynamics and structural characteristics of LC phases formed by a system of chiral particles compared to those formed by a system of achiral particles of the same aspect ratio. We consider a system of soft chiral rods modeled as made of fused beads and a system of soft repulsive spherocylinders (SRS) for this comparison. We evaluate the role of chirality in phase behavior with special emphasis on cholesteric and screw nematic phases. Extending the two-phase thermodynamic (2PT) model, we compute entropy, free energy, and fluidicity parameters to understand the thermodynamic stability of the similar phases exhibited by both systems. Our results reveal significant differences in phase stability and structure between the two systems, with crystals of achiral particles having a higher packing fraction than crystals of chiral particles. The study also demonstrates that translational and rotational fluidicity parameters can serve as effective phase identifiers, offering a simplified approach to characterizing complex LC phases. These findings deepen our understanding of chirality-induced phase behavior and also pave the way for applying fluidicity-based analysis to other anisotropic systems.