S. Dietrich

Direct measurement of critical Casimir forces.

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 vacuum fluctuations confined between two conducting metal plates. A thermodynamic analogue is the critical Casimir force: it acts between surfaces immersed in a binary liquid mixture close to its critical point and arises from the confinement of concentration fluctuations within the thin film of fluid separating the surfaces. So far, all experimental evidence for the existence of this effect has been indirect. 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-lutidine near its critical point. We use total internal reflection microscopy to determine in situ the forces between the sphere and the surface, with femtonewton resolution. Depending on whether the adsorption preferences of the sphere and the surface for water and 2,6-lutidine 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.

Depletion Potential in Hard-Sphere Mixtures: Theory and Applications

We present a versatile density functional approach (DFT) for calculating the depletion potential in general fluid mixtures. For the standard situation of a single big particle immersed in a sea of small particles near a fixed object, the system is regarded as an inhomogeneous binary mixture of big and small particles in the external field of the fixed object, and the limit of vanishing density of the big species, rho(b)-->0, is taken explicitly. In this limit our approach requires only the equilibrium density profile of a one-component fluid of small particles in the field of the fixed object, and a knowledge of the density independent weight functions which characterize the mixture functional. Thus, for a big particle near a planar wall or a cylinder or another fixed big particle, the relevant density profiles are functions of a single variable, which avoids the numerical complications inherent in brute force DFT. We implement our approach for additive hard-sphere mixtures, comparing our results with computer simulations for the depletion potential of a big sphere of radius R(b) in a sea of small spheres of radius R(s) near (i) a planar hard wall, and (ii) another big sphere. In both cases our results are accurate for size ratios s=R(s)/R(b) as small as 0.1, and for packing fractions of the small spheres eta(s) as large as 0.3; these are the most extreme situations for which reliable simulation data are currently available. Our approach satisfies several consistency requirements, and the resulting depletion potentials incorporate the correct damped oscillatory decay at large separations of the big particles or of the big particle and the wall. By investigating the depletion potential for high size asymmetries we assess the regime of validity of the well-known Derjaguin approximation for hard-sphere mixtures and argue that this fails, even for very small size ratios s, for all but the smallest values of eta(s) where the depletion potential reduces to the Asakura-Oosawa potential. We provide an accurate parametrization of the depletion potential in hard-sphere fluids, which should be useful for effective Hamiltonian studies of phase behavior and colloid structure. Our results for the depletion potential in a hard-sphere system, with a size ratio s=0.0755 chosen to mimic a recent experiment on a colloid-colloid mixture, are compared with the experimental data. Although there is good overall agreement, in particular for the dependence of the oscillations on eta(s), there are some significant differences at high values of eta(s).

Transport of cargo by catalytic Janus micro-motors

Catalytically active Janus micro-spheres are capable of autonomous motion and can potentially act as carriers for transportation of cargo at the micron-scale. Focusing on the cases in which a single or a pair of Janus micro-motors is used as carrier, we investigate the complex dynamics exhibited by various active carrier–cargo composites.

Precursor films in wetting phenomena

The spontaneous spreading of non-volatile liquid droplets on solid substrates poses a classic problem in the context of wetting phenomena. It is well known that the spreading of a macroscopic droplet is in many cases accompanied by a thin film of macroscopic lateral extent, the so-called precursor film, which emanates from the three-phase contact line region and spreads ahead of the latter with a much higher speed. Such films have been usually associated with liquid-on-solid systems, but in the last decade similar films have been reported to occur in solid-on-solid systems. While the situations in which the thickness of such films is of mesoscopic size are fairly well understood, an intriguing and yet to be fully understood aspect is the spreading of microscopic, i.e. molecularly thin, films. Here we review the available experimental observations of such films in various liquid-on-solid and solid-on-solid systems, as well as the corresponding theoretical models and studies aimed at understanding their formation and spreading dynamics. Recent developments and perspectives for future research are discussed.

Conceptual aspects of line tensions

We analyze two representative systems containing a three-phase-contact line: a liquid lens at a fluid-fluid interface and a liquid drop in contact with a gas phase residing on a solid substrate. In addition we study a system containing a planar liquid-gas interface in contact with a solid substrate. We discuss to which extent the decomposition of the grand canonical free energy of such systems into volume, surface, and line contributions is unique in spite of the freedom one has in positioning the Gibbs dividing interfaces. Curvatures of interfaces are taken into account. In the case of a lens it is found that the line tension is independent of arbitrary choices of the Gibbs dividing interfaces. In the case of a drop, however, one arrives at two different possible definitions of the line tension. One of them corresponds seamlessly to that applicable to the lens. The line tension defined this way turns out to be independent of choices of the Gibbs dividing interfaces. In the case of the second definition, however, the line tension does depend on the choice of the Gibbs dividing interfaces. We also provide form invariant equations for the equilibrium contact angles which properly transform under notional shifts of dividing interfaces which change the description of the system but leave the density configurations unchanged. It is shown that in order to accomplish this form invariance, additional stiffness coefficients attributed to the contact line must be introduced. The choice of the dividing interfaces influences the actual values of the stiffness coefficients. We show how these coefficients transform as a function of the relative displacements of the dividing interfaces. Our formulation provides a clearly defined scheme to determine line properties from measured dependences of the contact angles on lens or drop volumes. This scheme implies relations different from the modified Neumann or Young equations, which currently are the basis for extracting line tensions from experimental data. These relations show that the experiments do not render the line tension alone but a combination of the line tension, the Tolman length, and the stiffness coefficients of the line. In contrast to previous approaches our scheme works consistently for any choice of the dividing interfaces. It further allows us to compare results obtained by different experimental or theoretical methods, based on different conventions of choosing the dividing interfaces.

Polymer depletion effects near mesoscopic particles.

The behavior of mesoscopic particles dissolved in a dilute solution of long, flexible, and nonadsorbing polymer chains is studied by field-theoretic methods. For spherical and cylindrical particles the solvation free energy for immersing a single particle in the solution is calculated explicitly. Important features are qualitatively different for self-avoiding polymer chains as compared with ideal chains. The results corroborate the validity of the Helfrich-type curvature expansion for general particle shapes and allow for quantitative experimental tests. For the effective interactions between a small sphere and a wall, between a thin rod and a wall, and between two small spheres, quantitative results are presented. A systematic approach for studying effective many-body interactions is provided. The common Asakura-Oosawa approximation modeling the polymer coils as hard spheres turns out to fail completely for small particles and still fails by about 10% for large particles.

Critical Casimir effect in classical binary liquid mixtures

If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like 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.

Understanding Depletion Forces beyond Entropy

The effective interaction energy of a colloidal sphere in a suspension containing small amounts of non-ionic polymers and a flat glass surface has been measured and calculated using total internal reflection microscopy (TIRM) and a novel approach within density functional theory (DFT), respectively. Quantitative agreement between experiment and theory demonstrates that the resulting repulsive part of the depletion forces cannot be interpreted entirely in terms of entropic arguments but that particularly at small distances (

Phoretic motion of spheroidal particles due to self-generated solute gradients.

\lesssim

Depletion potential in hard-sphere fluids

100 nm) attractive dispersion forces have to be taken into account.