Quasicrystals are structures with long-range positional and orientational order. However, they cannot be periodic since they possess rotational symmetries such as 5- or 10-fold axis that are forbidden for conventional crystals. These structures lead to new and unique features of matter. Therefore, a lot of effort has recently been initiated to grow atomic quasicrystals on quasicrystalline surfaces. To mimic this situation, 2D light-interference patterns have been used to study the phase behavior of micron-sized colloidal particles in a 2D quasicrystalline potential and new ordered phases have been identified [1,2].
This talk reviews our recent work on how charge-stabilized colloidal particles order on a substrate with decagonal symmetry using Monte-Carlo simulations [2]. We report phasediagrams as a function of particle density and strength of substrate potential and identify quasicrystalline phases with 10- and also pure 20-fold bond-orientational order but also a modified version of an Archimedean tiling. We demonstrate that so-called phasonic displacements help to grow domains of these Archimedean-like tilings [3].
Finally, we present first results on how hard needles realized by nanorods, such as organic molecules, or needle-shaped colloidal rods order in a decagonal potential. For small substrate strength $V_0$, we still observe a well established nematic order that decreases with increasing $V_0$ when the hard needles cluster together in domains oriented along the five equivalent directions of the substrate potential.

[1] J. Mikhael et al., Nature (London) 454, 501 (2008).
[2] M. Schmiedeberg and H. Stark, Phys. Rev. Lett. 101, 218302 (2008).
[3] M. Schmiedeberg et al., to be published in Eur. Phys. J. E.