Direct AFM observation of individual micelles, tile decorations and tiling rules of a dodecagonal liquid quasicrystal

We performed an atomic force microscopy study of the dendron-based dodecagonal quasicrystal, the material that had been reported in 2004 as the first soft quasicrystal. We succeeded in orienting the 12-fold axis perpendicular to the substrate, which allowed the imaging of the quasiperiodic xy plane. Thus for the first time we have been able to obtain direct real-space information not only on the arrangement of the tiles, but also on their 'decorations' by the individual spherical micelles or 'nanoatoms'. The high-resolution patterns recorded confirm the square-triangle tiling, but the abundance of different nodes corresponds closely to random tiling rather than to any inflation rule. The previously proposed model of three types of decorated tiles, two triangular and one square, has been confirmed; the basic Frank-Kasper mode of alternating dense-sparse-dense-sparse layer stacking along z is confirmed too, each of the four sublayers being 2 nm thick. The consecutive dense layers are seen to be rotated by 90°, as expected. The 2 nm steps on the surface correspond to one layer of spheres, nonetheless with a dense layer always remaining on top, which implies a layer slip underneath and possibly the existence of screw dislocations.