Depletion potentials near geometrically structured substrates

Using the recently developed so-called White Bear version of Rosenfeld's Fundamental Measure Theory we calculate the depletion potentials between a hard-sphere colloidal particle in a solvent of small hard spheres and simple models of geometrically structured substrates: a right-angled wedge or edge. In the wedge geometry, there is a strong attraction beyond the corresponding one near a planar wall that significantly influences the structure of colloidal suspensions in wedges. In accordance with an experimental study, for the edge geometry we find a free energy barrier of the order of several $k_B T$ which repels a big colloidal particle from the edge.Comment: 7 pages, 7 figure

Discrete solvent effects on the effective interaction between charged colloids

Using computer simulations of two charged colloidal spheres with their counterions in a hard sphere solvent, we show that the granular nature of the solvent significantly influences the effective colloidal interaction. For divalent counterions, the total effective force can become attractive generated by counterion hydration, while for monovalent counterions the forces are repulsive and well-described by a solvent-induced colloidal charge renormalization. Both effects are not contained in the traditional "primitive" approaches but can be accounted for in a solvent-averaged primitive model.Comment: 4 pages, 3 figure

Depletion forces near curved surfaces

Based on density functional theory the influence of curvature on the depletion potential of a single big hard sphere immersed in a fluid of small hard spheres with packing fraction \eta_s either inside or outside of a hard spherical cavity of radius R_c is calculated. The relevant features of this potential are analyzed as function of \eta_s and R_c. There is a very slow convergence towards the flat wall limit R_c \to \infty. Our results allow us to discuss the strength of depletion forces acting near membranes both in normal and lateral directions and to make contact with recent experimental results

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 ($\lesssim$ 100 nm) attractive dispersion forces have to be taken into account

Entropic torque

Quantitative predictions are presented of a depletion-induced torque and force acting on a single colloidal hard rod immersed in a solvent of hard spheres close to a planar hard wall. This torque and force, which are entirely of entropic origin, may play an important role for the key-lock principle, where a biological macromolecule (the key) is only functional in a particular orientation with respect to a cavity (the lock)

Theory of asymmetric non-additive binary hard-sphere mixtures

We show that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard-sphere mixture works equally well for non-additive as it does for additive mixtures. For highly asymmetric mixtures (small size ratios) the resulting effective Hamiltonian of the one-component fluid of big spheres, which consists of an infinite number of many-body interactions, should be accurately approximated by truncating after the term describing the effective pair interaction. Using a density functional treatment developed originally for additive hard-sphere mixtures we determine the zero, one, and two-body contribution to the effective Hamiltonian. We demonstrate that even small degrees of positive or negative non-additivity have significant effect on the shape of the depletion potential. The second virial coefficient $B_2$, corresponding to the effective pair interaction between two big spheres, is found to be a sensitive measure of the effects of non-additivity. The variation of $B_2$ with the density of the small spheres shows significantly different behavior for additive, slightly positive and slightly negative non-additive mixtures. We discuss the possible repercussions of these results for the phase behavior of binary hard-sphere mixtures and suggest that measurements of $B_2$ might provide a means of determining the degree of non-additivity in real colloidal mixtures

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. In contrast to brute force DFT, our approach requires only the equilibrium density profile of the small particles {\em before} the big (test) particle is inserted. 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. 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. 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

Negative length orbits in normal-superconductor billiard systems

The Path-Length Spectra of mesoscopic systems including diffractive scatterers and connected to superconductor is studied theoretically. We show that the spectra differs fundamentally from that of normal systems due to the presence of Andreev reflection. It is shown that negative path-lengths should arise in the spectra as opposed to normal system. To highlight this effect we carried out both quantum mechanical and semiclassical calculations for the simplest possible diffractive scatterer. The most pronounced peaks in the Path-Length Spectra of the reflection amplitude are identified by the routes that the electron and/or hole travels.Comment: 4 pages, 4 figures include

Can Polymer Coils be modeled as "Soft Colloids"?

We map dilute or semi-dilute solutions of non-intersecting polymer chains onto a fluid of ``soft'' particles interacting via a concentration dependent effective pair potential, by inverting the pair distribution function of the centers of mass of the initial polymer chains. A similar inversion is used to derive an effective wall-polymer potential; these potentials are combined to successfully reproduce the calculated exact depletion interaction induced by non-intersecting polymers between two walls. The mapping opens up the possibility of large-scale simulations of polymer solutions in complex geometries.Comment: 4 pages, 3 figures ReVTeX[epsfig,multicol,amssymb] references update

Influence of solvent granularity on the effective interaction between charged colloidal suspensions

We study the effect of solvent granularity on the effective force between two charged colloidal particles by computer simulations of the primitive model of strongly asymmetric electrolytes with an explicitly added hard sphere solvent. Apart from molecular oscillating forces for nearly touching colloids which arise from solvent and counterion layering, the counterions are attracted towards the colloidal surfaces by solvent depletion providing a simple statistical description of hydration. This, in turn, has an important influence on the effective forces for larger distances which are considerably reduced as compared to the prediction based on the primitive model. When these forces are repulsive, the long-distance behaviour can be described by an effective Yukawa pair potential with a solvent-renormalized charge. As a function of colloidal volume fraction and added salt concentration, this solvent-renormalized charge behaves qualitatively similar to that obtained via the Poisson-Boltzmann cell model but there are quantitative differences. For divalent counterions and nano-sized colloids, on the other hand, the hydration may lead to overscreened colloids with mutual attraction while the primitive model yields repulsive forces. All these new effects can be accounted for through a solvent-averaged primitive model (SPM) which is obtained from the full model by integrating out the solvent degrees of freedom. The SPM was used to access larger colloidal particles without simulating the solvent explicitly.Comment: 14 pages, 16 craphic