The einstein tile rocked mathematics. Meet its molecular cousin

Amazing stuff!

"... Now, a team of chemists has described a molecule that naturally assembles into these irregular patterns, laying the groundwork for engineering materials that behave differently from regular solids. ..."

From the abstract:

"Studying the self-assembly of chiral molecules in two dimensions offers insights into the fundamentals of crystallization. Using scanning tunneling microscopy, we examine an uncommon aggregation of polyaromatic chiral molecules on a silver surface. Dense packing is achieved through a chiral triangular tiling of triads, with N and N ± 1 molecules at the edges.

The triangles feature a random distribution of mirror-isomers, with a significant excess of one isomer. Chirality at the domain boundaries causes a lateral shift, producing three distinct topological defects where six triangles converge. These defects partially contribute to the formation of supramolecular spirals.

The observation of different equal-density arrangements suggests that entropy maximization must play a crucial role. Despite the potential for regular patterns, all observed tiling is aperiodic. Differences from previously reported aperiodic molecular assemblies, such as Penrose tiling, are discussed. Our findings demonstrate that two-dimensional molecular self-assembly can be governed by topological constraints, leading to aperiodic tiling induced by intermolecular forces."

The einstein tile rocked mathematics. Meet its molecular cousin

One molecule, endless patterns / The molecular einstein (original news release) "Is it possible to tile a surface with a single shape in such a way that the pattern never repeats itself? In 2022, a mathematical solution to this “einstein problem” was discovered for the first time. Empa researchers have now also found a chemical solution: a molecule that arranges itself into complex, non-repeating patterns on a surface. The resulting aperiodic layer could even exhibit novel physical properties."

An aperiodic chiral tiling by topological molecular self-assembly (open access)

A close-up simulation shows the two mirror versions of the molecule tris(tetrahelicenebenzene), which is made of carbon (blue) and hydrogen (white) atoms.

Fig. 1: Self-assembly in two-dimensions containing topological defects.