Proliferation of anomalous symmetries in colloidal monolayers subjected to quasiperiodic light fields

Abstract

Quasicrystals provide a fascinating class of materials with intriguing properties. Despite a strong potential for numerous technical applications, the conditions under which quasicrystals form are still poorly understood. Currently, it is not clear why most quasicrystals hold 5-or 10-fold symmetry but no single example with 7-or 9-fold symmetry has ever been observed. Here we report on geometrical constraints which impede the formation of quasicrystals with certain symmetries in a colloidal model system. Experimentally, colloidal quasicrystals are created by subjecting micron-sized particles to two-dimensional quasiperiodic potential landscapes created by n ¼ 5 or seven laser beams. Our results clearly demonstrate that quasicrystalline order is much easier established for n ¼ 5 compared to n ¼ 7. With increasing laser intensity we observe that the colloids first adopt quasiperiodic order at local areas which then laterally grow until an extended quasicrystalline layer forms. As nucleation sites where quasiperiodicity originates, we identify highly symmetric motifs in the laser pattern. We find that their density strongly varies with n and surprisingly is smallest exactly for those quasicrystalline symmetries which have never been observed in atomic systems. Since such high-symmetry motifs also exist in atomic quasicrystals where they act as preferential adsorption sites, this suggests that it is indeed the deficiency of such motifs which accounts for the absence of materials with e.g., 7-fold symmetry.7-fold symmetry | growth mechanism | light patterns T he presence or lack of order is of primary importance in a broad range of fundamental phenomena in science. Until the early 1980s, it was unanimously established that ordered matter is always periodic (1). Accordingly, the rotational symmetry in real space was thought to be limited to N ¼ 2, 3, 4 and 6. However some metal alloys (2), polymers (3), micelles (4), and even recently colloidal nanoparticles (5) and nonspherical particles (6), have defied these crystallographic rules and selforganized into so-called quasicrystals. These structures form a unique type of matter which-unlike periodic crystals or amorphous materials-exhibit long-range positional order but are not periodic. Quasicrystals show many interesting properties which are quite different compared to that of periodic crystals. Accordingly, they are considered as materials with high technological potential e.g., as surface coatings, thermal barriers, catalysts, or photonic materials (7).Since the properties of quasicrystals are strongly connected to their atomic structure, a better understanding of their growth mechanisms is of great importance (8-11). Perhaps one of the most interesting questions in this context is why all observed quasicrystals have only 5-, 8-, 10-, and 12-fold symmetry but no single quasicrystal with 7-, 9-,11-, and 13-fold symmetry was ever found (12). For a classification of different surface symmetries it is helpful to consider the rank D, i.e., the number of incommensurate wa...

Controlled Self-Assembly of Periodic and Aperiodic Cluster Crystals

“…Figure 4 demonstrates that while the cluster size distribution is narrowly peaked for periodic cluster crystals indicating a single characteristic cluster size, the cluster size distribution has a broad peak for the decagonal cluster crystal and is flat and almost featureless for the dodecagonal cluster crystal. This observation is in agreement with experimentally observed distributions of high-symmetry stars in quasiperiodic light fields [32] and with the meanfield density profiles shown alongside the MD simulation results in Fig. 2.…”

Archimedean-like colloidal tilings on substrates with decagonal and tetradecagonal symmetry

“…However, in these experiments it is very difficult to determine the exact positions of the atoms. Therefore, a model system consisting of micron-sized colloidal particles subject to a laser interference pattern has been used to investigate the dynamics and ordering of particles in a two-dimensional quasicrystalline potential [16][17][18][19][20]. Interesting structures have been observed, such as phases with 20 bond directions [19] or colloidal orderings consisting of rows of squares and rows of triangles termed Archimedeanlike tilings [18,19] (see also fig.…”

Phase ordering of zig-zag and bow-shaped hard needles in two dimensions

“…7 The formation of liquid-crystal phases on twodimensional surfaces is also key for various nanotechnological applications. [8][9][10] Control over self-assembly has already enabled the formation of two-dimensional aggregates with quasicrystal, [11][12][13][14] hexagonal, 15 crystal, 16 and liquid crystal [17][18][19] orders. Improving control on the spontaneous formation of ordered structures, however, requires a deep understanding of how molecular geometry influences supramolecular ordering.…”