A two-dimensional, non-periodical network with rotational order but lacking translational symmetry is formed via hydrogen bonding
Aperiodic arrangements, in which ions, atoms or molecules are arranged in a spatial order but with no translational symmetry, can be obtained by organizing rhombus-shaped tiles in particular ways. Such tilings can lead to antiferromagnetic properties, and have also been investigated as models for quasi-crystals — materials between crystalline structures (having ordered, repeating patterns) and glasses (amorphous solids).
Neil Champness, Peter Beton and co-workers at the University of Nottingham have created1 a molecular network with the characteristics of an aperiodical rhombus tiling. Molecules with an aromatic linear backbone and four carboxylic acid groups, which connect via hydrogen bonding, were chosen as building blocks. The molecules tile like rhombuses because the position of the carboxylic acids enables adjacent ones to adopt two possible orientations — either parallel or at an angle. When groups of three to six molecules connect like this on a graphite surface, it creates a nearly regular hexagonal space or pore, because the length of the backbone is close to that of a hydrogen-bonded junction. The resulting pores are regularly arranged into a hexagonal network, even though the molecules themselves are orientated at random.
Triangular voids, observed where the molecular tiling is not perfect, can propagate through the structure by tile rearrangement. Calculations show that the propagation of these defects occurs via transitions between a variety of aperiodic tilings of similar energy, which could be used to study dynamically arrested materials such as glasses.
Blunt, M. O. et al. Random tiling and topological defects in a two-dimensional molecular network. Science 10.1126/science.1163338 (2008).
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Pichon, A. Random order. Nature Chem (2008). https://doi.org/10.1038/nchem.96