arXiv subjects

M. Oettel

Publications and source records attributed to M. Oettel.

At least 37 records · Page 2Linked to original sources

arXiv2009

Hard sphere fluids in annular wedges: density distributions and depletion potentials

We analyze the density distribution and the adsorption of solvent hard spheres in an annular slit formed by two large solute spheres or a large solute and a wall at close distances by means of fundamental measure density functional theory, anisotropic integral equations and simulations. We find that the main features of the density distribution in the slit are described by an effective, two--dimensional system of disks in the vicinity of a central obstacle. For large solute--solvent size ratios, the resulting depletion force has a straightforward geometrical interpretation which gives a precise "colloidal" limit for the depletion interaction. For intermediate size ratios 5...10 and high solvent packing fractions larger than 0.4, the explicit density functional results show a deep attractive well for the depletion potential at solute contact, possibly indicating demixing in a binary mixture at low solute and high solvent packing fraction.

cond-mat.soft↗

arXiv2008

Stability and interactions of nanocolloids at fluid interfaces: effects of capillary waves and line tensions

We analyze the effective potential for nanoparticles trapped at a fluid interface within a simple model which incorporates surface and line tensions as well as a thermal average over interface fluctuations (capillary waves). For a single colloid, a reduced steepness of the potential well hindering movements out of the interface plane compared to rigid interface models is observed, and an instability of the capillary wave partition sum in case of negative line tensions is pointed out. For two colloids, averaging over the capillary waves leads to an effective Casimir--type interaction which is long--ranged, power-like in the inverse distance but whose power sensitively depends on possible restrictions of the colloid degress of freedom. A nonzero line tension leads to changes in the magnitude but not in the functional form of the effective potential asymptotics.

cond-mat.soft↗

arXiv2008

Effective interactions of colloids on nematic films

The elastic and capillary interactions between a pair of colloidal particles trapped on top of a nematic film are studied theoretically for large separations $d$. The elastic interaction is repulsive and of quadrupolar type, varying as $d^{-5}$. For macroscopically thick films, the capillary interaction is likewise repulsive and proportional to $d^{-5}$ as a consequence of mechanical isolation of the system comprised of the colloids and the interface. A finite film thickness introduces a nonvanishing force on the system (exerted by the substrate supporting the film) leading to logarithmically varying capillary attractions. However, their strength turns out to be too small to be of importance for the recently observed pattern formation of colloidal droplets on nematic films.

cond-mat.soft↗

arXiv2008

Ellipsoidal particles at fluid interfaces

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$^o$, 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.

cond-mat.soft↗

arXiv2007

Multipolar expansion of the electrostatic interaction between charged colloids at interfaces

The general form of the electrostatic potential around an arbitrarily charged colloid at an interface between a dielectric and a screening phase (such as air and water, respectively) is analyzed in terms of a multipole expansion. The leading term is isotropic in the interfacial plane and varies with $d^{-3}$ where $d$ is the in--plane distance from the colloid. The electrostatic interaction potential between two arbitrarily charged colloids is likewise isotropic and $\propto d^{-3}$, corresponding to the dipole--dipole interaction first found for point charges at water interfaces. Anisotropic interaction terms arise only for higher powers $d^{-n}$ with $n \ge 4$.

cond-mat.soft↗

arXiv2007

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 of the surfactant sodium dodecylsulfate (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 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.

cond-mat.soft↗

arXiv2007

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 air-water interfaces with arbitrarily shaped colloids.

cond-mat.soft↗

arXiv2006

The Importance of Boundary Conditions for Fluctuation Induced Forces between Colloids at Interfaces

We calculate the effective fluctuation induced force between spherical or disk-like colloids trapped at a flat, fluid interface mediated by thermally excited capillary waves. This Casimir type force is determined by the partition function of the system which in turn is calculated in a functional integral approach, where the restrictions on the capillary waves imposed by the colloids are incorporated by auxiliary fields. In the long-range regime the fluctuation induced force is shown to depend sensitively on the boundary conditions imposed at the three-phase contact line between the colloids and the two fluid phases. The splitting of the fluctuating capillary wave field into a mean-field and a fluctuation part leads to competing repulsive and attractive contributions, respectively, which give rise to cancellations of the leading terms. In a second approach based on multipole expansion of the Casimir interaction, these cancellations can be understood from the vanishing of certain multipole moments enforced by the boundary conditions. We also discuss the connection of the different types of boundary conditions to certain external fields acting on the colloids which appear to be realizable by experimental techniques such as the laser tweezer method.

cond-mat.soft↗

arXiv2006

Effective forces between colloids at interfaces induced by capillary wave-like fluctuations

We calculate the effective force mediated by thermally excited capillary waves between spherical or disklike colloids trapped at a fluid interface. This Casimir type interaction is shown to depend sensitively on the boundary conditions imposed at the three-phase contact line. For large distances between the colloids an unexpected cancellation of attractive and repulsive contributions is observed leading to a fluctuation force which decays algebraically very rapidly. For small separations the resulting force is rather strong and it may play an important role in two-dimensional colloid aggregation if direct van der Waals forces are weak.

cond-mat.soft↗

arXiv2005

Attractions between charged colloids at water interfaces

The effective potential between charged colloids trapped at water interfaces is analyzed. It consists of a repulsive electrostatic and an attractive capillary part which asymptotically both show dipole--like behavior. For sufficiently large colloid charges, the capillary attraction dominates at large separations. The total effective potential exhibits a minimum at intermediate separations if the Debye screening length of water and the colloid radius are of comparable size.

cond-mat.soft↗

arXiv2004

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed `wetting' film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a `bridging' transition as the wetting films join to form a fluid bridge. The potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a non-zero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.

cond-mat.soft↗

arXiv2004

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. 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.

cond-mat.soft↗

arXiv2004

Integral equations for simple fluids in a general reference functional approach

The integral equations for the correlation functions of an inhomogeneous fluid mixture are derived using a functional Taylor expansion of the free energy around an inhomogeneous equilibrium distribution. The system of equations is closed by the introduction of a reference functional for the correlations beyond second order in the density difference from the equilibrium distribution. Explicit expressions are obtained for energies required to insert particles of the fluid mixture into the inhomogeneous system. The approach is illustrated by the determination of the equation of state of a simple, truncated Lennard--Jones fluid and the analysis of the behavior of this fluid near a hard wall. The wall--fluid integral equation exhibits complete drying and the corresponding coexisting densities are in good agreement with those obtained from the standard (Maxwell) construction applied to the bulk fluid. Self--consistency of the approach is examined by analyzing the virial/compressibility routes to the equation of state and the Gibbs--Duhem relation for the bulk fluid, and the contact density sum rule and the Gibbs adsorption equation for the hard wall problem. For the bulk fluid, we find good self--consistency for stable states outside the critical region. For the hard wall problem, the Gibbs adsorption equation is fulfilled very well near phase coexistence where the adsorption is large.For the contact density sum rule, we find some deviationsnear coexistence due to a slight disagreement between the coexisting density for the gas phase obtained from the Maxwell construction and from complete drying at the hard wall.

cond-mat.soft↗

arXiv2003

Depletion force between two large spheres suspended in a bath of small spheres: Onset of the Derjaguin limit

We analyze the depletion interaction between two hard colloids in a hard--sphere solvent and pay special attention to the limit of large size ratio between colloids and solvent particles which is governed by the well--known Derjaguin approximation. For separations between the colloids of less than the diameter of the solvent particles (defining the depletion region), the solvent structure between the colloids can be analyzed in terms of an effective two--dimensional gas. Thereby we find that the Derjaguin limit is approached more slowly than previously thought. This analysis is in good agreement with simulation data which are available for a moderate size ratio of 10. Small discrepancies to results from density functional theory (DFT) at this size ratio become amplified for larger size ratios. Therefore we have improved upon previous DFT techniques by imposing test particle consistency which connects DFT to integral equations. However, the improved results show no convergence towards the Derjaguin limit and thus we conclude that this implementation of DFT together with previous ones which rely on test particle insertion become unreliable in predicting the force in the depletion region for size ratios larger than 10.

cond-mat.soft↗

arXiv2002

Nucleon form factors from a covariant quark core: limits in their description

In treating the relativistic three-quark problem, a dressed-quark propagator parameterization is used which is compatible with recent lattice data and pion observables. Furthermore two-quark correlations are modeled as a series of quark loops in the scalar and axialvector channel. The resulting reduced Faddeev equations are solved for nucleon and delta. Nucleon electromagnetic form factors are calculated in a fully covariant and gauge--invariant scheme. Whereas the proton electric form factor $G_E$ and the nucleon magnetic moments are described correctly, the neutron electric form factor and the ratio $G_E/G_M$ for the proton appear to be quenched. The influence of vector mesons on the form factors is investigated which amounts to a 25 percent modification of the electromagnetic proton radii within this framework.

hep-ph↗

arXiv2002

Nucleon mass and pion loops: Renormalization

Using Dyson--Schwinger equations, the nucleon propagator is analyzed nonperturbatively in a field--theoretical model for the pion--nucleon interaction. Infinities are circumvented by using pion--nucleon form factors which define the physical scale. It is shown that the correct, finite, on--shell nucleon renormalization is important for the value of the mass--shift and the propagator. For physically acceptable forms of the pion--nucleon form factor the rainbow approximation together with renormalization is inconsistent. Going beyond the rainbow approximation, the full pion--nucleon vertex is modelled by its bare part plus a one--loop correction including an effective $Δ$. It is found that a consistent value for the nucleon mass--shift can be obtained as a consequence of a subtle interplay between wave function and vertex renormalization. Furthermore, the bare and renormalized pion--nucleon coupling constant are approximately equal, consistent with results from the Cloudy Bag Model.

nucl-th↗

arXiv2002

Nucleon mass and pion loops

Poincare' covariant Faddeev equations for the nucleon and Delta are solved to illustrate that an internally consistent description in terms of confined-quark and nonpointlike confined-diquark-correlations can be obtained. pi N-loop induced self-energy corrections to the nucleon's mass are analysed and shown to be independent of whether a pseudoscalar or pseudovector coupling is used. Phenomenological constraints suggest that this self-energy correction reduces the nucleon's mass by up to several hundred MeV. That effect does not qualitatively alter the picture, suggested by the Faddeev equation, that baryons are quark-diquark composites. However, neglecting the pi-loops leads to a quantitative overestimate of the nucleon's axial-vector diquark component.

nucl-th↗

arXiv2001

Relativistic Three-Quark Bound States in Separable Two-Quark Approximation

Baryons as relativistic bound states in 3-quark correlations are described by an effective Bethe-Salpeter equation when irreducible 3-quark interactions are neglected and separable 2-quark correlations are assumed. We present an efficient numerical method to calculate the nucleon mass and its covariant wave function in this quantum field theoretic quark-diquark model with quark-exchange interaction. Expanding the components of the spinorial wave function in terms of Chebyshev polynomials, the four-dimensional integral equations are in a first step reduced to a coupled set of one-dimensional ones. This set of linear and homogeneous equations defines a generalised eigenvalue problem. Representing the eigenvector corresponding to the largest eigenvalue, the Chebyshev moments are then obtained by iteration. The nucleon mass is implicitly determined by the eigenvalue, and its covariant wave function is reconstructed from the moments within the Chebyshev approximation.

hep-ph↗