Liquid drop in a cone - line tension effects

The shape of a liquid drop placed in a cone is analyzed 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.Comment: 11 pages, 4 figure

Fluctuations of a driven membrane in an electrolyte

We develop a model for a driven cell- or artificial membrane in an electrolyte. The system is kept far from equilibrium by the application of a DC electric field or by concentration gradients, which causes ions to flow through specific ion-conducting units (representing pumps, channels or natural pores). We consider the case of planar geometry and Debye-H\"{u}ckel regime, and obtain the membrane equation of motion within Stokes hydrodynamics. At steady state, the applied field causes an accumulation of charges close to the membrane, which, similarly to the equilibrium case, can be described with renormalized membrane tension and bending modulus. However, as opposed to the equilibrium situation, we find new terms in the membrane equation of motion, which arise specifically in the out-of-equilibrium case. We show that these terms lead in certain conditions to instabilities.Comment: 7 pages, 2 figures. submitted to Europhys. Let

Scaling for Interfacial Tensions near Critical Endpoints

Parametric scaling representations are obtained and studied for the asymptotic behavior of interfacial tensions in the \textit{full} neighborhood of a fluid (or Ising-type) critical endpoint, i.e., as a function \textit{both} of temperature \textit{and} of density/order parameter \textit{or} chemical potential/ordering field. Accurate \textit{nonclassical critical exponents} and reliable estimates for the \textit{universal amplitude ratios} are included naturally on the basis of the ``extended de Gennes-Fisher'' local-functional theory. Serious defects in previous scaling treatments are rectified and complete wetting behavior is represented; however, quantitatively small, but unphysical residual nonanalyticities on the wetting side of the critical isotherm are smoothed out ``manually.'' Comparisons with the limited available observations are presented elsewhere but the theory invites new, searching experiments and simulations, e.g., for the vapor-liquid interfacial tension on the two sides of the critical endpoint isotherm for which an amplitude ratio $-3.25 \pm 0.05$ is predicted.Comment: 42 pages, 6 figures, to appear in Physical Review

Line and boundary tensions on approach to the wetting transition

A mean-field density-functional model often used in the past in the study of line and boundary tensions at wetting and prewetting transitions is reanalyzed by extensive numerical calculations, approaching the wetting transition much more closely than had previously been possible. The results are what are now believed to be definitive for the model. They include strong numerical evidence for the presence of the logarithmic factors predicted by theory both in the mode of approach of the prewetting line to the triple-point line at the point of the first-order wetting transition and in the line tension itself on approach to that point. It is also demonstrated with convincing numerical precision that the boundary tension on the prewetting line and the line tension on the triple-point line have a common limiting value at the wetting transition, again as predicted by theory. As a by product of the calculations, in the model's symmetric three-phase state, far from wetting, it is found that certain properties of the model's line tension and densities are almost surely given by simple numbers arising from the symmetries, but proving that these are exact for the model remains a challenge to analytical theory

Mean-field Density Functional Theory of a Three-Phase Contact Line

A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive over-relaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.Comment: 14 pages, 13 figures, submitted to PR

Beware of density dependent pair potentials

Density (or state) dependent pair potentials arise naturally from coarse-graining procedures in many areas of condensed matter science. However, correctly using them to calculate physical properties of interest is subtle and cannot be uncoupled from the route by which they were derived. Furthermore, there is usually no unique way to coarse-grain to an effective pair potential. Even for simple systems like liquid Argon, the pair potential that correctly reproduces the pair structure will not generate the right virial pressure. Ignoring these issues in naive applications of density dependent pair potentials can lead to an apparent dependence of thermodynamic properties on the ensemble within which they are calculated, as well as other inconsistencies. These concepts are illustrated by several pedagogical examples, including: effective pair potentials for systems with many-body interactions, and the mapping of charged (Debye-H\"{u}ckel) and uncharged (Asakura-Oosawa) two-component systems onto effective one-component ones.Comment: 22 pages, uses iopart.cls and iopart10.clo; submitted to Journal of Physics Condensed Matter, special issue in honour of professor Jean-Pierre Hanse

Interfaces of Modulated Phases

Numerically minimizing a continuous free-energy functional which yields several modulated phases, we obtain the order-parameter profiles and interfacial free energies of symmetric and non-symmetric tilt boundaries within the lamellar phase, and of interfaces between coexisting lamellar, hexagonal, and disordered phases. Our findings agree well with chevron, omega, and T-junction tilt-boundary morphologies observed in diblock copolymers and magnetic garnet films.Comment: 4 page

Interfacial Tensions near Critical Endpoints: Experimental Checks of EdGF Theory

Predictions of the extended de Gennes-Fisher local-functional theory for the universal scaling functions of interfacial tensions near critical endpoints are compared with experimental data. Various observations of the binary mixture isobutyric acid $+$ water are correlated to facilitate an analysis of the experiments of Nagarajan, Webb and Widom who observed the vapor-liquid interfacial tension as a function of {\it both} temperature and density. Antonow's rule is confirmed and, with the aid of previously studied {\it universal amplitude ratios}, the crucial analytic ``background'' contribution to the surface tension near the endpoint is estimated. The residual singular behavior thus uncovered is consistent with the theoretical scaling predictions and confirms the expected lack of symmetry in $(T-T_c)$. A searching test of theory, however, demands more precise and extensive experiments; furthermore, the analysis highlights, a previously noted but surprising, three-fold discrepancy in the magnitude of the surface tension of isobutyric acid $+$ water relative to other systems.Comment: 6 figure

From Capillary Condensation to Interface Localization Transitions in Colloid Polymer Mixtures Confined in Thin Film Geometry

Monte Carlo simulations of the Asakura-Oosawa (AO) model for colloid-polymer mixtures confined between two parallel repulsive structureless walls are presented and analyzed in the light of current theories on capillary condensation and interface localization transitions. Choosing a polymer to colloid size ratio of q=0.8 and studying ultrathin films in the range of D=3 to D=10 colloid diameters thickness, grand canonical Monte Carlo methods are used; phase transitions are analyzed via finite size scaling, as in previous work on bulk systems and under confinement between identical types of walls. Unlike the latter work, inequivalent walls are used here: while the left wall has a hard-core repulsion for both polymers and colloids, at the right wall an additional square-well repulsion of variable strength acting only on the colloids is present. We study how the phase separation into colloid-rich and colloid-poor phases occurring already in the bulk is modified by such a confinement. When the asymmetry of the wall-colloid interaction increases, the character of the transition smoothly changes from capillary condensation-type to interface localization-type. The critical behavior of these transitions is discussed, as well as the colloid and polymer density profiles across the film in the various phases, and the correlation of interfacial fluctuations in the direction parallel to the confining walls. The experimental observability of these phenomena also is briefly discussed.Comment: 36 pages, 15 figure