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

Free energies, vacancy concentrations and density distribution anisotropies in hard--sphere crystals: A combined density functional and simulation study

We perform a comparative study of the free energies and the density distributions in hard sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009)) we obtain crystal free energies to a high precision. The free energies from Fundamental Measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between FMT and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that Fundamental Measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of Fundamental Measure functionals studied, only the White Bear II functional (Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)) exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.Comment: 17 pages, submitted to Phys. Rev.

Production Processes as a Tool to Study Parameterizations of Quark Confinement

We introduce diquarks as separable correlations in the two-quark Green's function to facilitate the description of baryons as relativistic three-quark bound states. These states then emerge as solutions of Bethe-Salpeter equations for quarks and diquarks that interact via quark exchange. When solving these equations we consider various dressing functions for the free quark and diquark propagators that prohibit the existence of corresponding asymptotic states and thus effectively parameterize confinement. We study the implications of qualitatively different dressing functions on the model predictions for the masses of the octet baryons as well as the electromagnetic and strong form factors of the nucleon. For different dressing functions we in particular compare the predictions for kaon photoproduction, $\gamma p\to K\Lambda$, and associated strangeness production, $pp\to pK\Lambda$ with experimental data. This leads to conclusions on the permissibility of different dressing functions.Comment: 43 pages, Latex, 28 eps files included via epsfig; version to be published in Physical Review

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.Comment: 13 pages, accepted by EPJ

Mesons in a Poincare Covariant Bethe-Salpeter Approach

We develop a covariant approach to describe the low-lying scalar, pseudoscalar, vector and axialvector mesons as quark-antiquark bound states. This approach is based on an effective interaction modeling of the non--perturbative structure of the gluon propagator that enters the quark Schwinger-Dyson and meson Bethe-Salpeter equations. We consistently treat these integral equations by precisely implementing the quark propagator functions that solve the Schwinger-Dyson equations into the Bethe-Salpeter equations in the relevant kinematical region. We extract the meson masses and compute the pion and kaon decay constants. We obtain a quantitatively correct description for pions, kaons and vector mesons while the calculated spectra of scalar and axialvector mesons suggest that their structure is more complex than being quark-antiquark bound states.Comment: 18 pages LaTeX, 5 figures; some changes in the presentation, new results on axial vector mesons in enlarged mixing scheme; version to be published in Physical Review

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 LxLxL 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 rho 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 slab-like configuration of two parallel flat interfaces. Extending the analysis of M. Schrader, P. Virnau, and K. Binder [Phys. Rev. E 79, 061104 (2009)], we extract the surface free energy gamma (R) of both spherical and cylindrical droplets and bubbles in the vapor-liquid case, and present evidence that for R -> Infinity 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 non-existence of the Tolman length is confirmed. In all cases {and for a range of radii} R relevant for nucleation theory, gamma(R) deviates strongly from gamma (Infinity) which can be accounted for by a term of order gamma(Infinity)/gamma(R)-1 ~ 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 gamma(R) as well as in the sign and magnitude of the Tolman length.Comment: 25 pages, submitted to J. Chem. Phy

Free energy of colloidal particles at the surface of sessile drops

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals $\pi/2$ a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.Comment: 24 pages, 19 figure

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.Comment: 29 page

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 $\Delta$. 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.Comment: 14 pages, 6 figure

Diquarks: condensation without bound states

We employ a bispinor gap equation to study superfluidity at nonzero chemical potential: mu .neq. 0, in two- and three-colour QCD. The two-colour theory, QC2D, is an excellent exemplar: the order of truncation of the quark-quark scattering kernel: K, has no qualitative impact, which allows a straightforward elucidation of the effects of mu when the coupling is strong. In rainbow-ladder truncation, diquark bound states appear in the spectrum of the three-colour theory, a defect that is eliminated by an improvement of K. The corrected gap equation describes a superfluid phase that is semi-quantitatively similar to that obtained using the rainbow truncation. A model study suggests that the width of the superfluid gap and the transition point in QC2D provide reliable quantitative estimates of those quantities in QCD.Comment: 7 pages, 3 figures, REVTEX, epsfi