Chiral symmetry breaking in crystals of achiral polymers

Chirality hierarchical transfer in homochiral polymer crystallization under high-pressure CO2

Ordered phase transitions are commonly correlated to symmetry breaking, while disordered phase transitions are characterized by symmetry restoration. Nevertheless, this study demonstrates that these correlation relations are not always applicable in chiral polymers under high-pressure Carbon Dioxide. Without racemization, homochiral Poly (lactide acid) can generate two vortex-shaped dendritic crystals with opposite spiral chirality, and snowflake-shaped dendritic crystals without spiral chirality. The transition from homochiral molecules to achiral crystals signifies the chiral symmetry restoration during the ordering process. The primary elements responsible for the various hierarchical transfers of homochiral Poly (lactide acid) are related to chain tilt, surface stress, and frustrated structures of Poly (lactide acid) crystals. Here, we show the entropy impact of Carbon Dioxide can be utilized to programmatically regulate the morphological chirality of crystal superstructure and crystal form of homochiral Poly (lactide acid).

Simulation study of twisted crystal growth in organic thin films

Many polymer and organic small-molecule thin films crystallize with microstructures that twist or curve in a regular manner as crystal growth proceeds. Here we present a phase-field model that energetically favors twisting of the three-dimensional crystalline orientation about and along particular axes, allowing morphologies such as banded spherulites, curved dendrites, and "s"- or "c"-shaped needle crystals to be simulated. When twisting about the fast-growing crystalline axis is energetically favored and spherulitic growth conditions are imposed, crystallization occurs in the form of banded spherulites composed of radially oriented twisted crystalline fibers. Due to the lack of symmetry, twisting along the normal growth direction leads to heterochiral banded spherulites with opposite twist handedness in each half of the spherulite. When twisting is instead favored about the axis perpendicular to the plane of the substrate and along the normal growth direction under diffusion-limited single-crystalline growth conditions, crystallization occurs in the form of curved dendrites with uniformly rotating branches. We show that the rate at which the branches curve affects not only the morphology but also the overall kinetics of crystallization, as the total crystallized area at a given time is maximized for a finite turning rate.

Chiral structures from achiral liquid crystals in cylindrical capillaries

We study chiral symmetry-broken configurations of nematic liquid crystals (LCs) confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls (i.e., perpendicular surface alignment). Interestingly, achiral nematic LCs with comparatively small twist elastic moduli relieve bend and splay deformations by introducing twist deformations. In the resulting twisted and escaped radial (TER) configuration, LC directors are parallel to the cylindrical axis near the center, but to attain radial orientation near the capillary wall, they escape along the radius through bend and twist distortions. Chiral symmetry-breaking experiments in polymer-coated capillaries are carried out using Sunset Yellow FCF, a lyotropic chromonic LC with a small twist elastic constant. Its director configurations are investigated by polarized optical microscopy and explained theoretically with numerical calculations. A rich phenomenology of defects also arises from the degenerate bend/twist deformations of the TER configuration, including a nonsingular domain wall separating domains of opposite twist handedness but the same escape direction and singular point defects (hedgehogs) separating domains of opposite escape direction. We show the energetic preference for singular defects separating domains of opposite twist handedness compared with those of the same handedness, and we report remarkable chiral configurations with a double helix of disclination lines along the cylindrical axis. These findings show archetypally how simple boundary conditions and elastic anisotropy of confined materials lead to multiple symmetry breaking and how these broken symmetries combine to create a variety of defects.

Saddle-splay screening and chiral symmetry breaking in toroidal nematics

We present a theoretical study of director fields in toroidal geometries with degenerate planar boundary conditions. We find spontaneous chirality: despite the achiral nature of nematics the director configuration shows a handedness if the toroid is thick enough. In the chiral state the director field displays a double twist, whereas in the achiral state there is only bend deformation. The critical thickness increases as the difference between the twist and saddle-splay moduli grows. A positive saddle-splay modulus prefers alignment along the meridian of the bounding torus, and hence promotes a chiral configuration. The chiral-achiral transition mimics the order-disorder transition of the mean-field Ising model. The role of the magnetisation in the Ising model is played by the degree of twist. The role of the temperature is played by the aspect ratio of the torus. Remarkably, an external field does not break the chiral symmetry explicitly, but shifts the transition. In the case of toroidal cholesterics, we do find a preference for one chirality over the other - the molecular chirality acts as a field in the Ising analogy.

Stable nematic droplets with handles

We stabilize nematic droplets with handles against surface tension-driven instabilities, using a yield-stress material as outer fluid, and study the complex nematic textures and defect structures that result from the competition between topological constraints and the elasticity of the nematic liquid crystal. We uncover a surprisingly persistent twisted configuration of the nematic director inside the droplets when tangential anchoring is established at their boundaries, which we explain after considering the influence of saddle splay on the elastic free energy. For toroidal droplets, we find that the saddle-splay energy screens the twisting energy, resulting in a spontaneous breaking of mirror symmetry; the chiral twisted state persists for aspect ratios as large as ∼20. For droplets with additional handles, we observe in experiments and computer simulations that there are two additional -1 surface defects per handle; these are located in regions with local saddle geometry to minimize the nematic distortions and hence the corresponding elastic free energy.

Chiral symmetry breaking by spatial confinement in tactoidal droplets of lyotropic chromonic liquid crystals

In many colloidal systems, an orientationally ordered nematic (N) phase emerges from the isotropic (I) melt in the form of spindle-like birefringent tactoids. In cases studied so far, the tactoids always reveal a mirror-symmetric nonchiral structure, sometimes even when the building units are chiral. We report on chiral symmetry breaking in the nematic tactoids formed in molecularly nonchiral polymer-crowded aqueous solutions of low-molecular weight disodium cromoglycate. The parity is broken by twisted packing of self-assembled molecular aggregates within the tactoids as manifested by the observed optical activity. Fluorescent confocal microscopy reveals that the chiral N tactoids are located at the boundaries of cells. We explain the chirality induction as a replacement of energetically costly splay packing of the aggregates within the curved bipolar tactoidal shape with twisted packing. The effect represents a simple pathway of macroscopic chirality induction in an organic system with no molecular chirality, as the only requirements are orientational order and curved shape of confinement.