Nature Commun. 3, 801 (2012)

Sometimes a little Brownian motion is all you need: by looking at lithographic triangular platelets small enough to show substantial spatial and orientational fluctuations at room temperature, Kun Zhao and colleagues have uncovered local chiral symmetry breaking in a system of achiral polygons.

Packing problems are by no means immune to the unexpected. Spheres exhibit a spatial disorder–order transition at densities lower than those prohibiting translation, and disks betray a six-fold symmetry, with quasi-long-range orientational order — but only short-range spatial order. Shapes bearing significant anisotropies can even give rise to spatially disordered liquid crystal phases. But the idea that packing achiral shapes might induce chirality distinguishes the triangular system of Zhao et al. from previous studies, including the group's own survey of pentagonal and square packings.

The revelation that the symmetry breaking arises from a simple combination of entropy and geometry makes it all the more intriguing. The rotational entropy of the thermally excited particles favours a spatial ordering in which neighbours are laterally offset from one another. The ensuing chirality persists locally, and effects a spatial disordering on longer scales. This reduces the range of shapes that can be entropically crystallized, which in turn sets a limit on the set of structures that can be probed crystallographically.