Local chiral symmetry breaking in triatic liquid crystals

Abstract

understanding the behaviour of thermally excited many-particle systems, composed of a single particle type having a well-defined shape and size, is important in condensed matter, notably protein crystallization. Here we observe and explain the origin of local chiral symmetry breaking in a surprisingly simple system of hard Brownian particles: achiral regular triangles confined to two dimensions. using enhanced optical video particle-tracking microscopy, we show that microscale lithographic triangular platelets form two different triatic liquid crystal phases. Above a particle area fraction φ A ≈0.55, the simple triatic phase is spatially disordered, yet has molecular orientational characteristics that distinguish it from a hexatic liquid crystal. At higher φ A ≥0.61, we find a second triatic phase exhibiting local chiral symmetry breaking; rotational entropy favours laterally offsetting the positions of nearest-neighbouring triangles. By contributing to spatial disordering, local chiral symmetry breaking can limit the range of shapes that can be entropically crystallized.

Shape-designed frustration by local polymorphism in a near-equilibrium colloidal glass

“…Thus, the dense system forms a glassy disordered structure, even when the kites could potentially tile into a large crystal of ASX. By contrast, experimental 2D Brownian systems of other similarly sized platelets, such as squares (30), 72°rhombs (32), and equilateral triangles (29), when compressed in the same manner, all form phases having at least some form of long-range translational or orientational order (i.e., crystals or liquid crystals). Although we have increased the equilibration period to 7 months for kites, much longer than for other shapes, the interacting kites still do not produce any domains exhibiting long-range order.…”

“…or a crystal phase possessing at least quasi-long-range order (29)(30)(31)(32). Thus far, no empirical observations of 2D Brownian systems exist that show a disordered liquid phase being slowly compressed into a disordered glassy solid-like state.…”

Perspective: Geometrically frustrated assemblies

“…While the many models of assembly consider of locally isotropic elements spheres or cylinders, many assembly units possess a valence z of cohesive binding to neighbors. Examples include "patchy" particles possessing z symmetrically distributed attractive zones, 147,148 z-fold polygonal [149][150][151] or polyhedral particles, 152 or z-fold protein complexes like capsomer assemblies, 6 clathrin triskeletal units, or mechano-sensitive membrane channels. 153,154 Consider first an assembly of z-valent elements confined to the 2D plane that forms cohesive bonds with symmetrically distributed neighbors.…”

Biological Water Dynamics and Entropy: A Biophysical Origin of Cancer and Other Diseases

“…Thus, at least some of the closed-chain hydrogen-bonded supramolecular water structures proposed by Pang [83,84,86,87] for magnetized water (see discussion in Section 4C above) could be chiral. As suggested by the results of two-dimensional studies of non-chiral, equilateral triangle-shaped polymer particles in aqueous solution, formation of such local chiral "supraparticle" clusters appears to be driven by the increased entropy afforded by increased motion of the monomers within the chiral arrangement relative to that attainable with the more-ordered tight packing of individual particles [181]. Based on these considerations, we propose that formation of chiral supramolecular water clusters, facilitated by magnetic fields, can help to solve the intracellular crowding problem.…”