Apparent First-Order Wetting and Anomalous Scaling in the Two-Dimensional Ising Model.

The global phase diagram of wetting in the two-dimensional Ising model is obtained through the exact calculation of the surface excess free energy. In addition to a surface field for inducing wetting, a surface-coupling enhancement is also included. The wetting transition (of second order) is critical for any finite ratio of surface coupling J_{s} to bulk coupling J, and becomes of first order in the limit J_{s}/J→∞. However, for J_{s}/J≫1, the critical region is exponentially small and is practically invisible to numerical studies. A distinct preasymptotic regime exists in which the transition displays first-order character. In this regime, surprisingly, the surface susceptibility and surface specific heat develop a divergence and show anomalous scaling with an exponent equal to 3/2.

Renormalization group calculations for wetting transitions of infinite order and continuously varying order: local interface Hamiltonian approach.

We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying 2-α(s)=∞) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with ß(s)=-1) of the wetting layer thickness are not modified as long as ω<2, with ω the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with ν([perpendicular])=1/2). In contrast, the nonuniversal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate, and strong fluctuation regimes.

How much does the core structure of a three-phase contact line contribute to the line tension near a wetting transition?

We initially simplify a three-phase contact line to a 'primitive' star-shaped structure formed by three planar interfaces meeting at a common line of intersection, and calculate the line tension associated with this primitive picture. Next, we consider the well-known more refined picture of the contact line that includes a 'core structure' consisting of interface deviations away from the planar interface picture. The corresponding contact line properties were calculated earlier, within mean-field theory, using an interface displacement model or a more microscopic density-functional theory. The question we ask is to what extent the thermodynamic line tension of the contact line near a wetting phase transition can be attributed to the core structure. To answer it we compare our result for the line tension contribution associated with the primitive structure to the known line tension of the full structure (within mean-field theory). While our primitive structure calculation provides a surprisingly useful upper bound to the known line tension near a critical wetting transition, the nontrivial core structure of the contact line near first-order wetting is found to be responsible for an important difference between the known line tension and the upper bound provided by the primitive picture calculation. This accounts also for the discrepancy between the line tensions calculated by two different methods in an earlier mean-field density-functional model of a first-order wetting transition.

First- and second-order wetting transitions at liquid-vapor interfaces.

Wetting transitions, in which one liquid wets, or spreads at, the interface between a second liquid and their common vapor, are defined and first- and second-order transitions are distinguished. The mean-field density-functional models of fluid interfaces are recalled. A criterion is noted for determining when the wetting transitions in those models are required to be of first order or may be of second order. It is seen how two examples of such density-functional models that have been treated in the past, one leading to a first-order and the other to a second-order wetting transition, provide examples of the application of the criterion.

Thermal fluctuation forces and wetting layers in colloid-polymer mixtures: derivation of an interface potential.

We discuss wetting layers in phase-separated colloid-polymer mixtures adsorbed at a vertical wall, observed in recent laser scanning confocal microscopy experiments. Matching of colloid and solvent dielectric properties renders van der Waals forces negligible and provides a system governed by short-range forces and thermal fluctuations on which the subtle predictions of renormalization group (RG) theory for wetting can be tested. The width w of the fluid-fluid ("liquid-gas") interface bounding the wetting layer scales with the square root of the wetting layer thickness l, in qualitative agreement with RG theory for short-range complete wetting in three dimensions. The measured wetting layer thickness l as a function of the height h above the horizontal plane of bulk phase separation is compared with two distinct theoretical predictions. A simple heuristic interface potential V(l), first proposed in a previous report, is now fully derived, and confronted here with the interface potential based on the linear RG theory. The heuristic approach does not capture fully the RG treatment. While fundamental differences exist between the two approaches, the resulting predictions for l(h) are almost identical. However, the theory does not follow the precise shape of the experimental curve of l(h).

Infinite-order transitions in density-functional models of wetting.

A class of density-functional models for wetting transitions is defined. A necessary condition for the transitions to be of higher than first order is derived. A locus of wetting transitions in the plane of two model field variables is determined on which there are states of first-order and of higher-order, including infinite-order, transitions. The observed behavior is rationalized via a different but related, analytically soluble model.

Fluctuation forces and wetting layers in colloid-polymer mixtures.

We present confocal microscopy experiments on the wetting of phase-separated colloid-polymer mixtures. We observe that an unusually thick wetting layer of the colloid-rich phase forms at the walls of the glass container that holds the mixture. Because of the ultralow interfacial tension between the colloid-rich and the polymer-rich phases, the thermally activated roughness of the interfaces becomes very big and measurable. We observe that close to the critical point the roughness of the interface between the wetting layer and the polymer-rich phase decreases with decreasing layer thickness: large excursions of the interface are confined in the wetting layer. The measured relationship between the roughness and the thickness of the wetting layer is in qualitative agreement with the predictions of renormalization group theory for short-range forces and complete wetting.

Criticality on networks with topology-dependent interactions.

Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behavior, which are known to depend on topology, can also be explored by tuning the form of the interactions at fixed topology. For a model of opinion formation, simple mean field and scaling arguments show that a mapping gamma'=(gamma-mu)(1-mu) describes how a shift of the standard exponent gamma of the degree distribution can absorb the effect of degree-dependent pair interactions J(ij) proportional to (k(i)k(j))(-mu), where k(i) stands for the degree of vertex i. This prediction is verified by extensive numerical investigations using the cavity method and Monte Carlo simulations. The critical temperature of the model is obtained through the Bethe-Peierls approximation and with the replica technique. The mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network.

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)proportional to(q(i)q(j))(-mu). The 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 nonequilibrium systems, and is illustrated with interdisciplinary applications.

Extraordinary wetting phase diagram for mixtures of Bose-Einstein condensates.

The possibility of wetting phase transitions in Bose-Einstein condensed gases is predicted on the basis of Gross-Pitaevskii theory. The surface of a binary mixture of Bose-Einstein condensates can undergo a first-order wetting phase transition upon varying the interparticle interactions, using, e.g., Feshbach resonances. Interesting ultra-low-temperature effects shape the wetting phase diagram. The prewetting transition is, contrary to general expectations, not of first order but critical, and the prewetting line does not meet the bulk phase coexistence line tangentially. Experimental verification of these extraordinary results is called for, especially now that it has become possible, using optical methods, to realize a planar "hard wall" boundary for the condensates.

Hierarchical population model with a carrying capacity distribution for bacterial biofilms.

In order to describe biological colonies with a conspicuous hierarchical structure, a time- and space-discrete model for the growth of a rapidly saturating local biological population N(x,t) is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant parameters, the probabilities of birth, B, and of death, D, determine the carrying capacity K. Due to the randomness the population depends strongly on position x and there is a distribution of carrying capacities, Pi(K). This distribution has self-similar character owing to the exponential slowing down of the growth, assumed in this hierarchical model. The most probable carrying capacity and its probability are studied as a function of B and D. The effective growth rate decreases with time, roughly as in a Verhulst process. The model is possibly applicable, for example, to bacteria forming a "towering pillar" biofilm, a structure poorly described by standard Eden or diffusion-limited-aggregation models. The bacteria divide on randomly distributed nutrient-rich regions and are exposed to a random local bactericidal agent (antibiotic spray). A gradual overall temperature or chemical change away from optimal growth conditions reduces bacterial reproduction, while biofilm development degrades antimicrobial susceptibility, causing stagnation into a stationary state.

Crossover from first-order to critical wetting: short-range tricritical wetting.

We study wetting in liquid mixtures of methanol and the n-alkanes. Mixing alkanes of different chain lengths, we can examine the crossover between critical (continuous) and first-order (discontinuous) wetting transitions. Measurements of the film thickness and surface specific heat exponent indicate that for carbon number n between 11 (undecane) and 9 (nonane), there is a crossover from first-order to critical wetting with a tricritical wetting point between an effective alkane carbon number of 9.6 and 10. The observed variation of the specific heat exponent in the tricritical region agrees fairly well with the predictions of a simple mean-field model with only short-range interactions.