Entropic chiral symmetry breaking in self-organized two-dimensional colloidal crystals

Abstract

Long-range chiral symmetry breaking (CSB) has been recently observed in 2D self-organized rhombic crystals of hard, achiral, 72 degree rhombic microparticles. However, purely entropic selection of a CSB crystal in an idealized system of hard achiral shapes, in which attractions are entirely absent and the shape does not dictate a chiral tiling, has not yet been quantitatively predicted. Overcoming limitations of a purely rotational cage model, we investigate a translational-rotational cage model (TRCM) of dense systems of hard achiral rhombs and quantitatively demonstrate that entropy can spontaneously drive the preferential self-organization of a chiral crystal composed of achiral shapes that also tile into an achiral crystal. At different particle area fractions, ϕA, we calculate the number of accessible translational-rotational microstates, Ω, of a mobile central rhomb in a static cage of neighboring rhombs, which can have different orientation angles, γ, relative to the bisector of the crystalline axes. As we raise ϕA, two maxima emerge in Ω(γ) at non-zero cage orientation angles, ±γmax. These maxima correspond to additional translational microstates that become accessible in the CSB crystalline polymorph through reduced translational tip-tip interference. Thus, entropy, often associated with structural disorder, can drive CSB in condensed phase systems of non-attractive achiral objects that do not tile into chiral structures. The success of the TRCM in explaining the entropic origin of CSB in systems of hard rhombs indicates that the TRCM will have significant utility in predicting the self-organized behavior of dense systems of other hard shapes in 2D.

Lock-and-key dimerization in dense Brownian systems of hard annular sector particles

“…By contrast, a cage model containing only a single mobile ASP surrounded by a fixed cage does not accurately predict the experimental results. This is an important finding, considering that singleparticle translational-rotational cage models have proven to be useful for predicting structures that match experimental measurements reasonably well for other shapes, such as squares, tri-stars, and rhombs [14,19,21]. Therefore, when treating Brownian systems of shapes that can interpenetrate to a significant degree, such as hard ASPs, in order to obtain reasonable results using a cage model, a collective form of entropy that goes beyond a single-particle entropy serves as a reasonable starting point.…”

“…Here, we investigate the degree of dimerization of colloidal ASPs in dense 2D Brownian systems using a translational-rotational cage model simulation that is similar to prior cage model simulations of dense Brownian systems of hard rhombs [19,20] and hard tri-stars [21]. Using a collision detection routine that detects when two ASPs overlap, this simulation enumerates accessible translational and rotational microstates associated with either one or two mobile ASPs surrounded by a static cage of ASPs.…”

Dynamics in two-dimensional glassy systems of crowded Penrose kites

“…1(c) (point 1 ). Non-local chiral symmetry, whose breaking has been found to originate from entropy in Penrose rhombs [32], is clear in the crystal phase of the kites. This investigation of the equation of state is instrumental because it provides a value of the area fraction at which the system enters the metastable supercooled regime.…”

A novel chiral phase of achiral hard triangles and an entropy-driven demixing of enantiomers

“…The mismatch with the experimental 9 isotropic-liquid-crystal phase transition point is likely due to the fact that the particle interactions in the experimental system cannot be described by excluded-volume interactions, which may be caused by the presence of depletants, charges, and polydispersity. 9,22…”