Chiral Surfaces Self-Assembling in One-Component Systems with Isotropic Interactions

We show that chiral symmetry can be broken spontaneously in one-component systems with isotropic interactions, i.e., many-particle systems having maximal a priori symmetry. This is achieved by designing isotropic potentials that lead to self-assembly of chiral surfaces. We demonstrate the principle on a simple chiral lattice and on a more complex lattice with chiral supercells. In addition, we show that the complex lattice has interesting melting behavior with multiple morphologically distinct phases that we argue can be qualitatively predicted from the design of the interaction.

Figure 1

The simplest form of chiral lattice, composed of scalene (acute) triangles with well separated side lengths $l_i$. (a) A low energy state obtained from a MC simulation. (b) The emerging chirality can be either left or right oriented. (c) By selecting for the reciprocal lattice (the red peaks) of the target structure, a potential (d) which causes self-assembly into one of the two possible chiralities is obtained.

Figure 2

Snub hexagonal tiling, a chiral Archimedean tiling. Note that the chirality does not originate from the positions of the hexagons (they are organized in rhombs and not parallelograms as they must when the tiles are regular polygons) but from the orientations of the triangles in between. (a)–(d) As in Fig. 1. In (a) two regions of opposite chirality are highlighted. (c) illustrates the perturbation of magnitude $ϵ$ at the maximum of $\widehat{\rho }$.

Figure 3

Time evolution of a self-assembling snub hexagonal lattice, after (from the left) 250, 2500, $1.2\times {10}^4$, and ${10}^5$ sweeps of the MC algorithm (each sweep attempting to move each particle on average once).

Figure 4

A phase diagram for the snub hexagonal model shows the equilibrium configuration as a function of inverse temperature $\beta$ and the magnitude $ϵ$ of the perturbation. Without the perturbation, striped and stripelike morphologies are observed (a), and a strong perturbation leads to vacancy unbinding (b) before complete disorder (c) as the temperature increases. A too strong perturbation results in aggregation of the vacancies (d). In the central region (e), the chiral snub hexagonal lattice is formed.