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
This talk reviews our recent work on how charge-stabilized colloidal
particles order on a substrate with decagonal symmetry using Monte-Carlo
simulations . 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 .
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.
 J. Mikhael et al., Nature (London) 454, 501 (2008).
 M. Schmiedeberg and H. Stark, Phys. Rev. Lett. 101, 218302 (2008).
 M. Schmiedeberg et al., to be published in Eur. Phys. J. E.