Examination of the Necessity of Complete Wetting near Critical Points in Systems with Long-Range Forces

Cahn’s general argument for complete wetting in the vicinity of critical points is critically reviewed. Critical-point wetting does occur in systems with short-range (exponentially decaying) forces. Whenever short-range forces favor wetting, while at the same time there is a tendency towards drying due to weak long-range (algebraically decaying) forces, neither critical-point wetting nor drying takes place. In this case the thickness of the partial wetting layer diverges as the bulk correlation length upon approach of the critical point

Effect of Criticality on Wetting Layers

We study wetting phenomena in which the wetting layer is (nearly) critical and intrudes between two noncritical phases. Finite-size scaling theory predicts an interaction, identical in range to that due to the van der Waals forces, between the interfaces bounding the wetting layer. This finite-size interaction leads to new wetting phenomena near critical end points, e.g., in ternary mixtures. The interaction amplitude and its possible universality can be observed directly in experiment

Effects of confinement and surface enhancement on superconductivity

Within the Ginzburg-Landau approach a theoretical study is performed of the effects of confinement on the transition to superconductivity for type-I and type-II materials with surface enhancement. The superconducting order parameter is characterized by a negative surface extrapolation length $b$. This leads to an increase of the critical field $H_{c3}$ and to a surface critical temperature in zero field, $T_{cs}$, which exceeds the bulk $T_c$. When the sample is {\em mesoscopic} of linear size $L$ the surface induces superconductivity in the interior for $T T_{cs}$. In analogy with adsorbed fluids, superconductivity in thin films of type-I materials is akin to {\em capillary condensation} and competes with the interface delocalization or "wetting" transition. The finite-size scaling properties of capillary condensation in superconductors are scrutinized in the limit that the ratio of magnetic penetration depth to superconducting coherence length, $\kappa \equiv \lambda/\xi$, goes to zero, using analytic calculations. While standard finite-size scaling holds for the transition in non-zero magnetic field $H$, an anomalous critical-point shift is found for H=0. The increase of $T_c$ for H=0 is calculated for mesoscopic films, cylindrical wires, and spherical grains of type-I and type-II materials. Surface curvature is shown to induce a significant increase of $T_c$, characterized by a shift $T_c(R)-T_c(\infty)$ inversely proportional to the radius $R$.Comment: 37 pages, 5 figures, accepted for PR

Multi-interaction mean-field renormalization group

We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of different sublattices of the given lattice and it generates as many flow equations as coupling constants without arbitrary truncations on the renormalized Hamiltonian. We obtain good results for the test case of Ising systems with an additional second-neighbor coupling in two and three dimensions. An application of the method is also done to a morphological model of interacting surfaces introduced recenlty by Likos, Mecke and Wagner [J. Chem. Phys. {\bf{102}}, 9350 (1995)]. PACS: 64.60.Ak, 64.60.Fr, 05.70.JkComment: Tex file and three macros appended at the end. Five figures available upon request to: [email protected], Fax: [+]39-40-224-60

Heterogeneous nucleation near a metastable vapour-liquid transition: the effect of wetting transitions

Phase transformations such as freezing typically start with heterogeneous nucleation. Heterogeneous nucleation near a wetting transition, of a crystalline phase is studied. The wetting transition occurs at or near a vapour-liquid transition which occurs in a metastable fluid. The fluid is metastable with respect to crystallisation, and it is the crystallisation of this fluid phase that we are interested in. At a wetting transition a thick layer of a liquid phase forms at a surface in contact with the vapour phase. The crystalline nucleus is then immersed in this liquid layer, which reduces the free energy barrier to nucleation and so dramatically increases the nucleation rate. The variation in the rate of heterogeneous nucleation close to wetting transitions is calculated for systems in which the longest-range forces are dispersion forces.Comment: 11 pages including 3 figure

Finite-Size Interaction Amplitudes and their Universality: Exact, Mean-Field, and Renormalization-Group Results

We discuss the interaction between interfaces that is mediated by critical fluctuations, and in particular the universality of the corresponding finite-size amplitudes. In the case of the two-dimensional Ising model we address the universality with respect to anisotropy. For this purpose we derive the exact free energy of a finite, anisotropic triangular lattice on a cylinder. For the rectangular Ising model we verify universality also with respect to the magnitude of the boundary fields. In mean-field theory we display the mechanism for this universality and for that with respect to the surface coupling enhancement. Numerical results, which are of experimental relevance, are obtained employing a renormalization-group approximation for three-dimensional systems

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

Trading interactions for topology in scale-free networks

Scale-free networks with topology-dependent interactions are studied. It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions. A mapping, $\gamma' = (\gamma - \mu)/(1-\mu)$, describes how a shift of the standard exponent $\gamma$ of the degree distribution $P(q)$ can absorb the effect of degree-dependent pair interactions $J_{ij} \propto (q_iq_j)^{-\mu}$. Replica technique, cavity method and Monte Carlo simulation support the physical picture suggested by Landau theory for the critical exponents and by the Bethe-Peierls approximation for the critical temperature. The equivalence of topology and interaction holds for equilibrium and non-equilibrium systems, and is illustrated with interdisciplinary applications.Comment: 4 pages, 5 figure