When fluctuating fields are confined between two surfaces, long range forces arise. A famous example is the quantum electrodynamical Casimir force that results from zero point vacuwn fluctuations confuted between two conducting metal plates'. A thermodynamic analogue is the critical Casimir force: it acts between surfaces immersed in a binary liquid mixture dose to its critical point and arises from the confiuement of con centra tion fluctuations within the thin film of fluid separating the sur faces 2 • So far, all ell:peri.mental evidence for the existence of this effect has been indirece 5 • Here we report the direct measurement of critical Casimir force between a single colloidal sphere and a flat silica surface immersed in a mixture of water and 2,6 lutidi.ne near its critical point. We use total internal reflection microscopy to detemti.ue in situ the forces between the sphere and the surface, with femtonewton resolution 6 • Depending on whether the adsorp tion preferences of the sphere and the surface for water and 2,6 lutidi.ne are identical or opposite, we measure attractive and repulsive forces, respectively, that agree quantitatively with theoretical predictions and exhibit exquisite dependence on the temperature of the system. We expect that these features of critical Casimir forces may result in novel uses of colloids as model systems.The simple act of confining a fluid can give rise to new ph en om en a not observed in the bulk. An intriguing example is the critical Casi.urir force predicted to occur in binary fluid mixtures close to their critical point; like other critical phenomena, it is characterized by universal scaling functions that depend only on the internal symmetries of the system rather than on its specific material properties' . Colloidal particles suspended in binary liquids offer a particularly interesting setting for the experintental observations of such forces. At suffi ciently small particle distances, concentration fluctuations of the solvent become confined between neighbouring colloidal surfaces and modify the pair interaction 8 • If tlte Casinlir interaction strengtlt is comparable to the thermal energy, drastic changes in the phase behaviour are expected. Reversible flocculation of silica colloids in water 2,6 lutidi.ue mixtures close to the critical point has in fact been observed 9 , and critical Casinlir forces may be invoked to explain tills phenomenon. However, flocculation was observed even far away from tlte critical point where critical fluctuations are negligible, so it cannot serve as conclusive evidence for the presence of Casi.utir forces 10 " 11 • Our experiments, ainted at directly measuring critical Casi.utir forces, use a single colloidal sphere and a planar surface immersed in a binary liquid mixture of water and 2,6 lutidine. Forces are deter mined using total internal reflection microscopy (TIRM, see Methods) 6 which allows itt situ measurements with femtonewton resolution 12 (Fig. 1). The binary liquid mixture bas a lower critical demixing point at Tc = ...

If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimirlike effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy with femtonewton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.

We study the motion of an overdamped colloidal particle in a time-dependent nonharmonic potential. We demonstrate the first lawlike balance between applied work, exchanged heat, and internal energy on the level of a single trajectory. The observed distribution of applied work is distinctly non-Gaussian in good agreement with numerical calculations. Both the Jarzynski relation and a detailed fluctuation theorem are verified with good accuracy. DOI: 10.1103/PhysRevLett.96.070603 PACS numbers: 05.40.ÿa, 05.70.ÿa, 82.70.Dd Since more than a century, the first law relating the work applied to a system with both the exchanged heat and an increase in internal energy is one of the cornerstones of macroscopic physics. Its consistent formulation for a mesoscopic system like a driven colloidal particle, however, was suggested only about a decade ago [1]. Since on these scales thermal fluctuations are relevant, probability distributions for work, heat, and internal energy replace the sharp values of their macroscopic counterparts. Various theoretical relations like the fluctuation theorem [2,3], the Jarzynski relation [4], and the Hatano-Sasa relation [5] involving these distributions in different settings extend the second law to the mesoscopic realm at least as long as the notion of a constant temperature of the ambient heat bath remains meaningful [for a review, see [6]]. Such theorems have been tested experimentally using both biomolecules manipulated mechanically [7,8] as well as colloidal particles in time dependent laser traps [9][10][11]. Common to all colloidal experiments, so far, is that these laser traps generate a harmonic potential albeit with a timedependent center or ''spring constant.'' Consequently, often the interesting distributions are Gaussian even though for certain quantities non-Gaussian distributions can occur [10,12].In this Letter, we study the thermodynamics of single colloidal trajectories in a time-dependent nonharmonic potential which, generically, gives rise to non-Gaussian distributions. Only for very short or very long trajectories, one expects Gaussian distributions even in this nonharmonic case [13]. In particular, we identify applied work, exchanged heat, and change in internal energy along a single trajectory and thus test the consistency of these notions on this level, or, put differently, illustrate the validity of the first law. We measure the distribution of work in the non-Gaussian regime and compare it to theoretical prediction. Such a comparison does not involve a single fit parameter since all quantities are measured independently, which is another advantage of colloidal systems. Finally, we test the Jarzynski relation which expresses the free energy difference between two equilibrium states in terms of the nonequilibrium work spent in the transition between the two states. Such an illustration of the Jarzynski relation in the non-Gaussian regime comes timely given ongoing theoretical criticism of its validity [14,15]. In our study, particle trajectories were determined usi...

We investigate the behavior of colloidal particles immersed in a binary liquid mixture of water and 2,6-lutidine in the presence of a chemically patterned substrate. Close to the critical point of the mixture, the particles are subjected to critical Casimir interactions with force components normal and parallel to the surface. Because the strength and sign of these interactions can be tuned by variations in the surface properties and the mixtures temperature, critical Casimir forces allow the formation of highly ordered monolayers but also extend the use of colloids as model systems.PACS numbers: 82.70. Dd, 68.35.Rh, 81.16.Dn Analogous to the geometrical confinement of quantumelectrodynamical (QED) vacuum fluctuations between two parallel metallic plates [1], the constraint of concentration fluctuations in fluid mixtures close to their critical point gives rise to critical Casimir forces acting on the confining surfaces [2]. The range of this interaction is set by the bulk correlation length ξ of the mixture which diverges when approaching the critical point. Therefore, critical Casimir forces are sensitive to minute changes in temperature. Despite several quantitative measurements of such forces [3,4], it was only recently when the amplitude of measured critical Casimir forces in quantumand classical liquids has been directly compared to theoretical predictions [5,6,7,8]. Direct force measurements of a single colloidal particle above a flat surface and immersed in a critical water-lutidine mixture demonstrated, that critical Casimir interactions can easily exceed multiples of the thermal energy k B T [8]. Accordingly, they offer a versatile opportunity to control the pair interaction in colloidal suspensions by weak temperature changes [9,10]. Apart from their exquisite temperature dependence, critical Casimir forces respond sensitively to the chemical properties of the confining surfaces. Depending on whether both surfaces preferentially attract the same mixture's component or not (symmetric or asymmetric boundary conditions), attractive or repulsive critical Casimir forces arise [8,11,12].So far, experimental investigations of critical Casimir interactions were limited to homogeneous surfaces (in contrast to QED Casimir forces [13]) where the corresponding forces act perpendicular to the confining walls. However, when one or both surfaces are chemically patterned, also lateral critical Casimir forces have been predicted [14] In this Letter we experimentally study the interaction between colloidal particles and chemically patterned substrates immersed in a binary critical mixture. Close to the critical point lateral critical Casimir forces lead to the formation of highly ordered colloidal assemblies whose structure is controlled by the underlying chemical pattern. This may suggest a novel route for templated growth of colloidal crystals. At higher particle concentrations, additional critical Casimir forces between nearby particle surfaces arise and eventually lead to the formation of three-dimensional, face...

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...