Shapes, contact angles, and line tensions of droplets on cylinders

Using an interface displacement model we calculate the shapes of nanometer-size liquid droplets on homogeneous cylindrical surfaces. We determine effective contact angles and line tensions, the latter defined as excess free energies per unit length associated with the two contact lines at the ends of the droplet. The dependences of these quantities on the cylinder radius and on the volume of the droplets are analyzed.Comment: 26 pages, RevTeX, 10 Figure

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

Oberflaechen- und Linienspannungen bei Benetzungsphasenuebergaengen

Within the first part the interfacial wetting behaviour of binary liquid mixtures at their liquid-vapor interface is classified. The criteria with respect to the atomic interactions between the two species are whether the Hamaker constant of that interface fulfills either the sufficient conditions for the absence of a wetting transition, or the necessary conditions for critical wetting, or the necessary conditions either for being wet already at low temperatures or for undergoing a first-order wetting transition upon approaching the critical end point along the triple line. Based on the Blume-Emery-Griffiths model and on the Percus-Yevick theory we scan the parameter space which determines the structure of the bulk phase diagrams. By analyzing the absolute values of the Hamaker constant particular attention is paid to interfacial wetting induced by tricritical points. In addition a comparison of the predictions of the Percus-Yevick theory for the bulk phase diagrams and the number densities of the fluid bulk phases with experimental and simulation data as well as with different theoretical approaches is given. In the second part we analyze the behavior of the line tension at the wetting transition of a fluid on a solid substrate. Using a non-local approach depending only on interaction potentials within the microscopic density functional theory for inhomogeneous fluids and in a local approximation the interface profiles between the non-wetted and the wetted parts of a partial wetted system are calculated for both the cases of first-order wetting transitions and critical wetting transitions. By dividing the density functional for the grand canonical free energy into bulk, surface and line contributions one is able to estimate the microscopic expression for the physical line tension of this system. We insert the obtained interface profiles into the line contribution and calculate numerical values for the line tension, which can be compared for the non-local and local approach. (orig.)SIGLEAvailable from TIB Hannover: RO 9740(96-20) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman