Making ends meet

It's impossible to tile a floor using only regular pentagons without leaving voids — a manifestation of five-fold rotational symmetry being incompatible with total spatial periodicity. Yet it is possible to tile a surface in a regular way, with five-fold overall symmetry, if you allow at least two different tile shapes — Roger Penrose came up with a few variants in the 1970s.

Synthesizing structures that display the symmetries of Penrose tilings, which belong to the broader class of quasicrystals, presents a challenge for material scientists. Now Natalie Wasio and colleagues report in Nature that they have succeeded in making 2D quasicrystallites — through the self-assembly of ferrocenecarboxylic acid (FcCOOH) molecules on a gold substrate — that resemble the structure of a particular Penrose tiling (Nature 507, 86–89; 2014).

Credit: © NPG 2014

The FcCOOH molecule consists of an iron atom sandwiched between a C₅H₅ ring and a C₅H₄COOH unit; the latter can be thought of as another C₅H₅ ring with one of the hydrogen atoms replaced by a carboxyl (COOH) group, acting as a 'hook'.

Scanning tunnelling microscopy images of the FcCOOH molecules reveal flower-like patterns (pictured), and Wasio et al. have mapped patches of such images to a so-called P1 Penrose tiling, consisting of four different tiles: pentagon, star, boat and rhombus. They found that the origin of the molecules' self-assembly into five-fold symmetric motifs lies in the COOH groups — molecular endings that are known to engage easily in hydrogen bonds. Five FcCOOH molecules hook together into a pentamer structure with two hydrogen bonds between two neighbouring molecules. Calculations from first principles confirm that the pentamer arrangement corresponds to an energy minimum.

Analogous experiments with ferroceneacetic acid (having a CH₂COOH group instead of a COOH group) result in dimers that pack into 'ordinary' 2D crystalline structures. It seems that the self-assembly into pentamers and quasicrystalline patterns requires the chemistry of specific side-groups; the extra CH₂ unit in the case of ferroceneacetic acid prevents the realization of the two hydrogen bonds that stabilize a five-fold symmetric pentamer.