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# Contact angle and wetting in the intermediate state of superconducting lead

The geometry of superconducting domains (laminae) near the rim of disk-shaped lead samples has been studied experimentally using a magneto-optical technique and theoretically on the basis of the Ginzburg-Landau theory. Magnetization measurements versus magnetic field at different sample-field angles and temperatures have been performed as well. The laminae make a non-zero contact angle with the rim of the sample, similar to the contact

angle of a fluid-fluid interface with a substrate at partial wetting. For each temperature there is a specific value of field at which the contact angle decreases so that the laminae overlap producing a continuous surface superconducting sheath along the sample perimeter, similar to spreading drops at wetting. The magnetic flux remaining in the normal regions of the sample is then trapped and a persistent current starts circulating over the sheath, resulting in a characteristic hysteresis loop in the field dependence of the magnetic moment. Results from magneto-optical observations are in good agreement with the magnetization data, allowing one to visualize the process of development of the persistent current in the intermediate state. Results from theoretical calculations of the contact angle and threshold field for the wetting transition are compared with the observations.

**This research has been supported in part by K.U.Leuven fellowship F/03/066 for V.F.K. and by FWO-Project G.0237.05.**

# Dual scale modelling approach to study organic molecule adsorption at metal/water interfaces

Multiscale simulation methods are indispensable in studies of phenomena where on the one hand quantum mechanical and atomistic detail must be explicitly treated while on the other hand large enough systems must be simulated on long enough time scales. We present a newly developed method for studying surface adsorption phenomena in aqueous systems by combination of ab initio DFT methods and classical atomistic simulations. In our method, surface interactions are obtained from ab initio DFT calculations while solute-solvent and solventsolvent interactions are described with classical force fields. The method is applied to study adsorption of organic molecules onto transition metal surfaces ([111]-surfaces of Au, Ni, Pd, Pt, and Rh) in water. In addition to adsorption on these atomistically flat metal surfaces, we present studies of adsorption onto surfaces with step defects. The multiscale method offers the opportunity to study systems that were impossible to deal with before

with alternative simulation methods. We currently extend our ethodologies to simulate the adsorption of small biomolecules.

(1) Pim Schravendijk, Nico F.A. van der Vegt, Luigi Delle Site, Kurt Kremer, ChemPhysChem. in press (2005)

# Corresponding-states analysis of the surface tension of simple, polar, and ionic fluids

The liquid–vapor interfacial tension of various simple, polar, and ionic luids is studied in a corresponding-states analysis originally suggested by Guggenheim (1). The results for real fluids are compared to the corresponding ones for model fluids of each of the three types. For simple and weakly polar fluids (both real and model), the data map onto a master curve, as already demonstrated by Guggenheim. For strongly dipolar, associating fluids, which also exhibit hydrogen-bonding (e.g. water and ethanol), one finds deviations from this master curve at low temperatures. These associating fluids display a characteristic sigmoid behavior of the reduced surface tension as a function of temperature. A similar behavior is found from simulations (2) of an ionic model fluid, the restricted primitive model (RPM), but not (yet) from available electrolyte theories (3). Truly exceptionally low values of the reduced surface tension are obtained for hydrogen fluoride (HF) and for the Onsager model of dipolar fluids, the surface tension of which we evaluate using an approximate hypernetted chain relation to calculate the square-gradient term in a modified van der Waals theory (4). Remarkably, in the correspondingstates plot, the surface tensions of HF and of the Onsager model agree very closely, while being well separated from the values for the other fluids. We also study the gradual transition of a model fluid from a simple fluid to a strongly dipolar one by varying the relative strength of dipolar and dispersion forces, as suggested by van Leeuwen and Smit (5), and discuss the consequences for the reduced surface tension (4).

(1) E.A. Guggenheim, J. Chem. Phys. 13, 253 (1945); Proc. Phys. Soc. 85, 811 (1965)

(2) M. Gonz´alez-Melchor, J. Alejandre, and F. Bresme, Phys. Rev. Lett. 90, 135506 (2003); M. Gonz´alez-Melchor,

F. Bresme, and J. Alejandre, J. Chem. Phys., in press

(3) M.M. Telo da Gama, R. Evans, and T.J. Sluckin, Mol. Phys. 41, 1355 1980); B. Groh, R. Evans, and S. Dietrich, Phys. Rev. E 57, 6944 (1998); V.C. Weiss and W. Schr¨oer, J. Phys.: Condens. Matter 12, 2637 (2000)

(4) Deltion festival Netherlands

(5) M.E. van Leeuwen and B. Smit, Phys. Rev. Lett. 71, 3991 (1993); Y. Levin, P.S. Kuhn, and M.C. Barbosa, Physica A 292, 129 (2001

# Density functional theory for fluids in random inhomogeneous external potentials

The model we study in this work is a classical fluid whose particles are under the action of a random inhomogeneous external potential which is distributed after certain probability distribution. This model is a generalization of the quenched-annealed (QA) model, which is the paradigm for studying fluids in porous media. The theory of integral equations was extended for this particular case and many achievements have been reached by using the so called ROZ (replica Ornstein-Zernike) equations. Recently [M. Schmidt, Phys. Rev. E 66, 041108 (2002)], a density functional approach has been proposed. The fundamental idea is to describe the system by means of a functional of the average (over disorder) density profile. In this work, we rigorously prove that the density functional formalism can be extended to deal with the models described above. The main result is that for a given interaction and probabilty distribution of the external potential, there exists a functional of the average density profile whose minimum is the equilibrium average density profile of the system corresponding to the external fixed parameters. As in classical density fnuctional theory, we can define a hierarchy of correlation functionals through the derivatives of this functional with respect the average density profile. Also, an Ornstein-Zernike equation can be derived and we should remark that it is not possible to deduce all direct correlation functionsfrom the functional, in particular those related with the fluctuations of the density profile due to the disorder (which is known as the blocking part). Finally, we proposed an approximation scheme based upon the latticePosters fundamental measure theory which improves previous like-based approches. Results are shown for some specific models which concern the freezing transition in the present of disorder.