Martin Oettel

Nanoparticles at fluid interfaces

Nanoparticles at fluid interfaces are becoming a central topic in colloid science studies. Unlike in the case of colloids in suspensions, the description of the forces determining the physical behavior of colloids at interfaces still represents an outstanding problem in the modern theory of colloidal interactions. These forces regulate the formation of complex two-dimensional structures, which can be exploited in a number of applications of technological interest; optical devices, catalysis, molecular electronics or emulsions stabilization. From a fundamental viewpoint and typical for colloidal systems, nanoparticles and microparticles at interfaces are ideal experimental and theoretical models for investigating questions of relevance in condensed matter physics, such as the phase behavior of two-dimensional fluids. This review is a topical survey of the stability, self-assembly behavior and mutual interactions of nanoparticles at fluid interfaces. Thermodynamic models offer an intuitive approach to explaining the interfacial stability of nanoparticles in terms of a few material properties, such as the surface and line tensions. A critical discussion of the theoretical basis, accuracy, limitations, and recent predictions of the thermodynamic models is provided. We also review recent work concerned with nanoparticle self-assembly at fluid interfaces. Complex two-dimensional structures varying considerably with the particle nature have been observed in a number of experiments. We discuss the self-assembly behavior in terms of nanoparticle composition, focusing on sterically stabilized, charged and magnetic nanoparticles. The structure of the two-dimensional assemblies is a reflection of complex intercolloidal forces. Unlike the case for bulk colloidal suspensions, which often can be described reasonably well using DLVO (Derjaguin-Landau-Verwey-Overbeek) theory, the description of particles at interfaces requires the consideration of interfacial deformations as well as interfacial thermal fluctuations. We analyze the importance of both deformation and fluctuations, as well as the modification of electrostatic and van der Waals interactions. Finally, we discuss possible future directions in the field of nanoparticles at interfaces.

Direct Measurements of the Effects of Salt and Surfactant on Interaction Forces between Colloidal Particles at Water−Oil Interfaces

The forces between colloidal particles at a decane-water interface, in the presence of low concentrations of a monovalent salt (NaCl) and the surfactant sodium dodecyl sulfate (SDS) in the aqueous subphase, have been studied using laser tweezers. In the absence of electrolyte and surfactant, particle interactions exhibit a long-range repulsion, yet the variation of the interaction for different particle pairs is found to be considerable. Averaging over several particle pairs was hence found to be necessary to obtain a reliable assessment of the effects of salt and surfactant. It has previously been suggested that the repulsion is consistent with electrostatic interactions between a small number of dissociated charges in the oil phase, leading to a decay with distance to the power -4 and an absence of any effect of electrolyte concentration. However, the present work demonstrates that increasing the electrolyte concentration does yield, on average, a reduction of the magnitude of the interaction force with electrolyte concentration. This implies that charges on the water side also contribute significantly to the electrostatic interactions. An increase in the concentration of SDS leads to a similar decrease of the interaction force. Moreover, the repulsion at fixed SDS concentrations decreases over longer times. Finally, measurements of three-body interactions provide insight into the anisotropic nature of the interactions. The unique time-dependent and anisotropic interactions between particles at the oil-water interface allow tailoring of the aggregation kinetics and structure of the suspension structure.

Precursor-mediated crystallization process in suspensions of hard spheres.

We report on a large scale computer simulation study of crystal nucleation in hard spheres. Through a combined analysis of real- and reciprocal-space data, a picture of a two-step crystallization process is supported: First, dense, amorphous clusters form which then act as precursors for the nucleation of well-ordered crystallites. This kind of crystallization process has been previously observed in systems that interact via potentials that have an attractive as well as a repulsive part, most prominently in protein solutions. In this context the effect has been attributed to the presence of metastable fluid-fluid demixing. Our simulations, however, show that a purely repulsive system (that has no metastable fluid-fluid coexistence) crystallizes via the same mechanism.

Ellipsoidal particles at fluid interfaces

Abstract.For partially wetting, ellipsoidal colloids trapped at a fluid interface, their effective, interface-mediated interactions of capillary and fluctuation-induced type are analyzed. For contact angles different from 90° , static interface deformations arise which lead to anisotropic capillary forces that are substantial already for micrometer-sized particles. The capillary problem is solved using an efficient perturbative treatment which allows a fast determination of the capillary interaction for all distances between and orientations of two particles. Besides static capillary forces, fluctuation-induced forces caused by thermally excited capillary waves arise at fluid interfaces. For the specific choice of a spatially fixed three-phase contact line, the asymptotic behavior of the fluctuation-induced force is determined analytically for both the close-distance and the long-distance regime and compared to numerical solutions.

Curvature dependence of surface free energy of liquid drops and bubbles: A simulation study

We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite L×L×L boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density ρ in the simple fluid or the relative concentration x(A) of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the miscibility gap) to a slablike configuration of two parallel flat interfaces. Extending the analysis of Schrader et al., [Phys. Rev. E 79, 061104 (2009)], we extract the surface free energy γ(R) of both spherical and cylindrical droplets and bubbles in the vapor-liquid case and present evidence that for R→∞ the leading order (Tolman) correction for droplets has sign opposite to the case of bubbles, consistent with the Tolman length being independent on the sign of curvature. For the symmetric binary mixture, the expected nonexistence of the Tolman length is confirmed. In all cases and for a range of radii R relevant for nucleation theory, γ(R) deviates strongly from γ(∞) which can be accounted for by a term of order γ(∞)/γ(R)-1∝R(-2). Our results for the simple Lennard-Jones fluid are also compared to results from density functional theory, and we find qualitative agreement in the behavior of γ(R) as well as in the sign and magnitude of the Tolman length.

Effective capillary interaction of spherical particles at fluid interfaces

We present a detailed analysis of the effective force between two smooth spherical colloids floating at a fluid interface due to deformations of the interface in an inhomogeneous pressure field. The results hold in general and are applicable independently of the source of the deformation provided the capillary deformations are small so that a superposition approximation for the deformations is valid. We conclude that an effective long-ranged attraction is possible if the net force on the system does not vanish. Otherwise, the interaction is short ranged and cannot be computed reliably based on the superposition approximation. As an application, we consider the case of like-charged, smooth nanoparticles and electrostatically induced capillary deformation. The resulting long-ranged capillary attraction can be easily tuned by a relatively small external electrostatic field, but it cannot explain recent experimental observations of attraction if these experimental systems were indeed isolated.

Octet and decuplet baryons in a covariant and confining diquark - quark model

In a covariant model where constituent quarks and diquarks interact through quark exchange, the Bethe-Salpeter equation in ladder approximation for octet and decuplet baryons is solved. Quark and diquark confinement is thereby effectively parametrised by choosing appropriately modified propagators. Numerical results for the baryon masses are presented. In a second step electromagnetic, weak and pionic currents are coupled to the bound state according to Mandelstam’s technique. The arising matrix elements are evaluated in a generalised impulse approximation and observable form factors are extracted.

Tension and Stiffness of the Hard Sphere Crystal-Fluid Interface

A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66k(B)T/σ(2) with a small anisotropy of about 0.025k(B)T and stiffnesses with, e.g., 0.53k(B)T/σ(2) for the (001) orientation and 1.03k(B)T/σ(2) for the (111) orientation. Here k(B)T is denoting the thermal energy and σ the hard-sphere diameter. We compare our results with existing experimental findings.

Numerical approaches to determine the interface tension of curved interfaces from free energy calculations

A recently proposed method to obtain the surface free energy σ(R) of spherical droplets and bubbles of fluids, using a thermodynamic analysis of two-phase coexistence in finite boxes at fixed total density, is reconsidered and extended. Building on a comprehensive review of the basic thermodynamic theory, it is shown that from this analysis one can extract both the equimolar radius R(e) as well as the radius R(s) of the surface of tension. Hence the free energy barrier that needs to be overcome in nucleation events where critical droplets and bubbles are formed can be reliably estimated for the range of radii that is of physical interest. It is found that the conventional theory of nucleation, where the interface tension of planar liquid-vapor interfaces is used to predict nucleation barriers, leads to a significant overestimation, and this failure is particularly large for bubbles. Furthermore, different routes to estimate the effective radius-dependent Tolman length δ(R(s)) from simulations in the canonical ensemble are discussed. Thus we obtain an instructive exemplification of the basic quantities and relations of the thermodynamic theory of metastable droplets/bubbles using simulations. However, the simulation results for δ(R(s)) employing a truncated Lennard-Jones system suffer to some extent from unexplained finite size effects, while no such finite size effects are found in corresponding density functional calculations. The numerical results are compatible with the expectation that δ(R(s) → ∞) is slightly negative and of the order of one tenth of a Lennard-Jones diameter, but much larger systems need to be simulated to allow more precise estimates of δ(R(s) → ∞).

Charge renormalization for effective interactions of colloids at water interfaces

We analyze theoretically the electrostatic interaction of surface-charged colloids at water interfaces with special attention to the experimentally relevant case of large charge densities on the colloid-water interface. Whereas linear theory predicts an effective dipole potential, the strength of which is proportional to the square of the product of charge density and screening length, nonlinear charge renormalization effects change this dependence to a weakly logarithmic one. These results appear to be particularly relevant for structure formation at fluid interfaces with arbitrarily shaped colloids.