Mode expansion for the density profile of crystal-fluid interfaces: Hard spheres as a test case

We present a technique for analyzing the full three-dimensional density profiles of a planar crystal-fluid interface in terms of density modes. These density modes can also be related to crystallinity order parameter profiles which are used in coarse-grained, phase field type models of the statics and dynamics of crystal-fluid interfaces and are an alternative to crystallinity order parameters extracted from simulations using local crystallinity criteria. We illustrate our results for the hard sphere system using finely-resolved, three-dimensional density profiles from density functional theory of fundamental measure type.Comment: submitted for the special issue of the CODEF III conferenc

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.Comment: 7 pages, 3 figures, minor revisions, one additional figur

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.Comment: 28 pages, 10 figures, 4 table

Nucleon Form Factors in the Covariant Diquark-Quark Model

The nucleon is described as a bound state of a quark and an extended diquark. Hereby the notion ``diquark'' refers to the modelling of separable correlations in the two-quark Green's functions. Binding of quarks and diquarks takes place via an exchange interaction and is therefore related to the Pauli principle for three-quark states. Fully Poincare covariant nucleon amplitudes are calculated for free constituent propagators as well as for dressed propagators which parameterise confinement. The corresponding results for space-like form factors differ quantitatively but not qualitatively for various ans\"atze for the propagators. These results do not allow to draw definite conclusions on the permissibility of different dressing functions. Results for kaon photoproduction, on the other hand, exclude a whole class of constituent propagators.Comment: 8 pages, 4 figures; to appear in the proceedings of the workshop on Lepton scattering, Hadrons and QCD, Adelaide, March 26 to April 6, 200

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.Comment: 24 pages, 4 figure

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.Comment: 8 pages, 1 figure, revised version (one paragraph added) accepted in JPC

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 $n \ge 4$.Comment: 6 pages, mathematical details adde

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.Comment: 4 page