Complexity of two-dimensional self-assembled arrays at surfaces

The self-assembly of supramolecular arrays at solid surfaces is discussed with an emphasis on the degree of complexity that can be generated in such structures. The preparation of multi-component arrays is reviewed illustrating the approaches to generating many-component networks and the challenges that are encountered. The complexity of quasicrystalline and fractal molecular structures is also demonstrated along with recent developments in the synthesis of complexity perpendicular to the solid substrate through the formation of bilayer structures. Overall the importance of characterisation by scanning probe microscopy is evident in determining the complexity of structures at the molecular level.