Friction between solids is responsible for many phenomena such as earthquakes, wear or crack propagation 1-4 . Unlike macroscopic objects, which only touch locally owing to their surface roughness, spatially extended contacts form between atomically flat surfaces. They are described by the FrenkelKontorova model, which considers a monolayer of interacting particles on a periodic substrate potential 5-8 . In addition to the well-known stick-slip motion, such models also predict the formation of kinks and antikinks 9-12 , which greatly reduce the friction between the monolayer and the substrate. Here, we report the direct observation of kinks and antikinks in a two-dimensional colloidal crystal that is driven across different types of ordered substrate. We show that the frictional properties only depend on the number and density of such excitations, which propagate through the monolayer along the direction of the applied force. In addition, we also observe kinks on quasicrystalline surfaces, which demonstrates that they are not limited to periodic substrates but occur under more general conditions.Friction is important in our daily life and it is not surprising that systematic investigations date back more than 300 years. According to Amontons and Coulomb, friction between solids is proportional to the normal force but independent of the contact area. This intriguing result was explained by realizing that macroscopic objects touch at asperities that are deformed by the normal force 13 . A different situation occurs when atomically flat surfaces slide against each other, as for example encountered in micro-or nanoelectromechanical systems. Then, extended contacts arise and the degree of commensurability between the surfaces determines the friction. For commensurate conditions, a dissipative stick-slip motion is typically observed 14 . In contrast, at incommensurate interfaces, atomic friction studies revealed a superlubrication regime, where the friction coefficient vanishes 15,16 . This behaviour can be explained by simple mechanical models such as the FrenkelKontorova model, a generalized Prandtl-Tomlinson scheme or the double-chain model [17][18][19][20] . In the Frenkel-Kontorova approach the interface between two solids is described by a monolayer of elastically interacting beads on a periodic substrate potential [5][6][7][8] . In addition to stick-slip motion, the Frenkel-Kontorova model also predicts the formation of topological solitons, so-called kinks and antikinks [9][10][11][12] . These excitations are believed to dominate the frictional properties at atomic length scales because they provide an efficient mechanism for mass transport; so far, such excitations have never been observed in sliding friction experiments 21 .Here, we report the observation of kinks and antikinks in a colloidal system that is driven across commensurate and incommensurate substrate potentials. We use highly charged polystyrene spheres with radius R = 1.95 μm, which are suspended in water. In the presence of gravitational and op...
Monolayers on crystalline surfaces often form complex structures with physical and chemical properties that differ strongly from those of their bulk phases 1 . Such hetero-epitactic overlayers are currently used in nanotechnology and understanding their growth mechanism is important for the development of new materials and devices. In comparison with crystals, quasicrystalline surfaces exhibit much larger structural and chemical complexity leading, for example, to unusual frictional 2 , catalytical 3 or optical properties 4,5 . Deposition of thin films on such substrates can lead to structures that may have typical quasicrystalline properties. Recent experiments have indeed showed 5-fold symmetries in the diffraction pattern of metallic layers adsorbed on quasicrystals 6,7 . Here we report a real-space investigation of the phase behaviour of a colloidal monolayer interacting with a quasicrystalline decagonal substrate created by interfering five laser beams. We find a pseudomorphic phase that shows both crystalline and quasicrystalline structural properties. It can be described by an archimedean-like tiling 8,9 consisting of alternating rows of square and triangular tiles. The calculated diffraction pattern of this phase is in agreement with recent observations of copper adsorbed on icosahedral Al 70 Pd 21 Mn 9 surfaces 10 . In addition to establishing a link between archimedean tilings and quasicrystals, our experiments allow us to investigate in real space how single-element monolayers can form commensurate structures on quasicrystalline surfaces.Quasicrystals are unusual materials: they are aperiodic but retain true long-range order 11 . Although quasicrystalline structures have been theoretically also predicted in systems with a single type of particle 12,13 , experimentally their spontaneous formation has been observed only in binary, ternary or even more complex alloys 14 . Accordingly, their surfaces exhibit a high degree of structural and chemical complexity and show unexpected mechanical, electrical and optical properties 15 . To understand the origin of those characteristics it is useful to disentangle structural and chemical aspects; this can be achieved by growing single-element monolayers to quasicrystalline surfaces 16,17 . Apart from adding to our understanding of how quasicrystalline properties can be transferred to such monolayers 18 , this approach might permit the fabrication of materials with previously unobserved properties. Heteroepictatic growth experiments on decagonal and icosahedral surfaces did indeed show the formation of Bi and Sb monolayers with a high degree of quasicrystalline order as determined by low-energy electron diffraction and elastic heliumatom scattering experiments 6,18 . In comparison with reciprocal space studies, it was only recently that scanning tunnelling microscopy permitted an atomic resolution of the adsorbate morphology 7 . Even then, however, it was difficult to relate the structure of the adsorbate to that of the underlying substrate.Here we report an experi...
The worldwide trend in nanoparticle technology toward increasing complexity must be directly linked to more advanced characterization methods of size, shape and related properties, applicable to many different particle systems in science and technology. Available techniques for nanoparticle characterization are predominantly focused on size characterization. However, simultaneous size and shape characterization is still an unresolved major challenge. We demonstrate that analytical ultracentrifugation with a multiwavelength detector is a powerful technique to address multidimensional nanoparticle analysis. Using a high performance optical setup and data acquisition software, information on size, shape anisotropy and optical properties were accessible in one single experiment with unmatched accuracy and resolution. A dynamic rotor speed gradient allowed us to investigate broad distributions on a short time scale and differentiate between gold nanorod species including the precise evaluation of aggregate formation. We report how to distinguish between different species of single-wall carbon nanotubes in just one experiment using the wavelength-dependent sedimentation coefficient distribution without the necessity of time-consuming purification methods. Furthermore, CdTe nanoparticles of different size and optical properties were investigated in a single experiment providing important information on structure-property relations. Thus, multidimensional information on size, density, shape and optical properties of nanoparticulate systems becomes accessible by means of analytical ultracentrifugation equipped with multiwavelength detection.
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...
Abstract. Two-dimensional colloidal suspensions subjected to laser interference patterns with decagonal symmetry can form an Archimedean-like tiling phase where rows of squares and triangles order aperiodically along one direction (J. Mikhael et al., Nature 454, 501 (2008)). In experiments as well as in Monte Carlo and Brownian dynamics simulations, we identify a similar phase when the laser field possesses tetradecagonal symmetry. We characterize the structure of both Archimedean-like tilings in detail and point out how the tilings differ from each other. Furthermore, we also estimate specific particle densities where the Archimedean-like tiling phases occur. Finally, using Brownian dynamics simulations we demonstrate how phasonic distortions of the decagonal laser field influence the Archimedean-like tiling. In particular, the domain size of the tiling can be enlarged by phasonic drifts and constant gradients in the phasonic displacement. We demonstrate that the latter occurs when the interfering laser beams are not ideally adjusted.
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