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

Abstract

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.

A simple mechanism for emergent chirality in achiral hard particle assembly

“…7,8 Simulations have also shown that particles with complex but isotropic interaction potentials can be designed to self-assembly into chiral surface structures. 9 It now appears that chiral symmetry breaking is possible even with the simplest interparticle interaction-excluded volume due to particle shape-without specific attractions. In particular, Mason and co-workers 10 recently observed the spontaneous, thermally driven formation of locally chiral domains in simple equilateral triangles.…”

Chiral symmetry breaking in a reaction-diffusion system

“…The occurrence of single chirality, a process termed chiral symmetry breaking, is ubiquitously observed and remains a fundamental question still not fully explained. To date, several mechanisms responsible for the selection of chirality have been put forward [2][3][4][5][6][7]. One particularly interesting mechanism enabling nonequilibrium systems to select spatially asymmetric solutions with preferred chirality was proposed by Nicolis and Prigogine about 30 years ago [8].…”

A strict epistemic approach to physics

“…The explicit form of epistemic minimalism (Assumption 1. 19) says that the introduction in a physical model of elements that cannot be verified or refuted should give rise to wrong predictions. If we introduce elementary objects as the basic building blocks in a physical model of the world, then the world functions as if there were a fixed number of such elements present.…”

“…However, the seed for the development of left-right asymmetry is poorly understood. It might be the result of spontaneous symmetry breaking from a random fluctuation, like the direction of magnetization in the absence of external fields [19]. But since almost all bodies of a given species are oriented in the same way [37], there must be a preferred direction.…”

“…To motivate Statement 2.6, recall that u 1 is assumed to be noiseless (Assumption 1.14); it depends on independent objects, and independent attributes of these (Definitions 1.18 and 1. 19), but on nothing else. If the evolution is not deterministic for an exact state Z, there must be a stochastic term in u 1 , contrary to Assumption 1.14.…”