Marek Napiórkowski

Conceptual aspects of line tensions

We analyze two representative systems containing a three-phase-contact line: a liquid lens at a fluid-fluid interface and a liquid drop in contact with a gas phase residing on a solid substrate. In addition we study a system containing a planar liquid-gas interface in contact with a solid substrate. We discuss to which extent the decomposition of the grand canonical free energy of such systems into volume, surface, and line contributions is unique in spite of the freedom one has in positioning the Gibbs dividing interfaces. Curvatures of interfaces are taken into account. In the case of a lens it is found that the line tension is independent of arbitrary choices of the Gibbs dividing interfaces. In the case of a drop, however, one arrives at two different possible definitions of the line tension. One of them corresponds seamlessly to that applicable to the lens. The line tension defined this way turns out to be independent of choices of the Gibbs dividing interfaces. In the case of the second definition, however, the line tension does depend on the choice of the Gibbs dividing interfaces. We also provide form invariant equations for the equilibrium contact angles which properly transform under notional shifts of dividing interfaces which change the description of the system but leave the density configurations unchanged. It is shown that in order to accomplish this form invariance, additional stiffness coefficients attributed to the contact line must be introduced. The choice of the dividing interfaces influences the actual values of the stiffness coefficients. We show how these coefficients transform as a function of the relative displacements of the dividing interfaces. Our formulation provides a clearly defined scheme to determine line properties from measured dependences of the contact angles on lens or drop volumes. This scheme implies relations different from the modified Neumann or Young equations, which currently are the basis for extracting line tensions from experimental data. These relations show that the experiments do not render the line tension alone but a combination of the line tension, the Tolman length, and the stiffness coefficients of the line. In contrast to previous approaches our scheme works consistently for any choice of the dividing interfaces. It further allows us to compare results obtained by different experimental or theoretical methods, based on different conventions of choosing the dividing interfaces.

FILLING TRANSITION FOR A WEDGE

We study the formation and the shape of a liquid meniscus in a wedge with opening angle 2phi which is exposed to a vapor phase. By applying a suitable effective interface model, at liquid-vapor coexistence and at a temperature Tphi we find a filling transition at which the height of the meniscus becomes macroscopically large while the planar walls of the wedge far away from its center remain nonwet up to the wetting transition occurring at Tw>Tphi. Depending on the fluid and the substrate potential the filling transition can be either continuous or discontinuous. In the latter case it is accompanied by a prefilling line extending into the vapor phase of the bulk phase diagram and describing a transition from a small to a large, but finite, meniscus height. The filling and the prefilling transitions correspond to nonanalyticities in the surface and line contributions to the free energy of the fluid, respectively.

The three‐state lattice gas as model for binary gas–liquid systems

This paper deals with the three‐state lattice model as applied to binary liquid–gas systems. Schouten, ten Seldam, and Trappeniers [Physica 73, 556 (1974)] used this model to describe the transition between the liquid phases as well as the gas–gas separation when varying the interaction parameters of the model. Our analysis is aimed at the behavior of the system in the vicinity of its tricritical point in the generalized field space. Different shapes of the critical lines are calculated by using the molecular field method as well as by using the lowest approximation of the cluster variation method. The equivalence between the two approaches is demonstrated. In the immediate neighborhood of the tricritical point the shapes of the critical lines are also determined analytically.

Properties of the solvation force of a two-dimensional Ising strip in scaling regimes

We consider the d = 2 Ising strip with surface fields acting on boundary spins. Using the properties of the transfer matrix spectrum we identify two pseudotransition temperatures and show that they satisfy similar scaling relations as expected for real transition temperatures in strips with d>2. The solvation force between the boundaries of the strip is analysed as a function of temperature, surface fields and the width of the strip. For large widths, the solvation force can be described by scaling functions in three different regimes: in the vicinity of the critical wetting temperature of the 2D semi-infinite system, in the vicinity of the bulk critical temperature and in the regime of weak surface fields, where the critical wetting temperature tends towards the bulk critical temperature. The properties of the relevant scaling functions are discussed.

A liquid drop in a cone - line tension effects

The shape of a liquid drop placed in a cone is analysed macroscopically. Depending on the values of the cone opening angle, the Young angle and the line tension, four different interfacial configurations may be realized. The phase diagram in these variables is constructed and discussed; it contains both the first- and the second-order transition lines. In particular, the tricritical point is found and the value of the critical exponent characterizing the behaviour of the system along the line of the first-order transitions in the neighbourhood of this point is determined.

Adsorption on a periodically corrugated substrate

Mean field analysis of the effective interfacial Hamiltonian shows that with increasing temperature the adsorption on a periodically corrugated substrate can proceed in two steps: first, there is the filling transition in which the depressions of the substrate become partially or completely filled; then there is the wetting transition at which the substrate as a whole becomes covered with a macroscopically thick wetting layer. The actual order and location of both transitions are related to the wetting properties of the corresponding planar substrate and to the form of corrugation. Certain morphological properties of the liquid-vapor interface in the case of a saw-like corrugated substrate are discussed analytically

The influence of line tension on the formation of liquid bridges in atomic force microscope-like geometry

We investigate thermodynamic and geometrical conditions for the formation of a liquid bridge between a planar and conical walls modeling atomic force microscope (AFM). Our macroscopic analysis is based on the grand canonical functional of the shape of the liquid?vapor interface which contains the relevant bulk, surface and line free energies. The phase diagram of such a confined fluid displays the existence of two phases: one with a liquid bridge connecting the walls, and the other without a bridge. The structure of the corresponding coexistence line is determined and its dependence on the value of the line tension coefficient is discussed.

Interfacial fluctuations near the critical filling transition.

We advance a method to describe the short-distance fluctuations of an interface spanning a wedge-shaped substrate near the critical filling transition. Two different length scales determined by the average distance of the interface from the substrate at the wedge center can be identified. On one length scale, the one-dimensional approximation of A. O. Parry, C. Rascon, and A. J. Wood [Phys. Rev. Lett. 85, 345 (2000)], which allows one to determine the interfacial critical exponents, is extracted from the full description. On the other scale, the short-distance fluctuations are analyzed by mean-field theory.

Influence of Van Der Waals Tails on Interfaces

We present analytical results for the grand canonical density functional of inhomogeneous fluids by explicitly taking into account the van der Waals tails of interfacial density profiles which are characteristic for systems with long-range forces. Two cases are considered: wetting of a wall by a one-component fluid near its liquid-gas coexistence line and interfacial wetting in a binary liquid mixture along its triple line. We discuss the influence of these van der Waals tails of the order of wetting transition as well as their relevance for the onset of critical adsorption.

Lateral critical Casimir force in 2D Ising strip with inhomogeneous walls

We analyze the lateral critical Casimir force acting between two planar, chemically inhomogeneous walls confining an infinite 2D Ising strip of width M. The inhomogeneity of each of the walls has size N1; they are shifted by the distance L along the strip. Using the exact diagonalization of the transfer matrix, we calculate the lateral critical Casimir force and discuss its properties, in particular its scaling close to the 2D bulk critical point, as a function of temperature, surface magnetic field, and the geometric parameters M, N1, L. We determine the magnetization profiles which display the formation of the bridge joining the inhomogeneities on the walls and establish the relation between the characteristic properties of the lateral Casimir force and magnetization morphologies. We check numerically that breaking of the bridge is related to the inflection point of the lateral force.