Wetting and Nonwetting near a Tricritical Point.

The dihedral contact angles between interfaces in three-fluid-phase equilibria must be continuous functions of the bulk thermodynamic fields. This general argument, which we propose, predicts a nonwetting gap in the phase diagram, challenging the common belief in "critical-point wetting," even for short-range forces. A demonstration is provided by exact solution of a mean-field two-density functional theory for three-phase equilibria near a tricritical point (TCP). Complete wetting is found in a tiny vicinity of the TCP. Away from it, nonwetting prevails and no wetting transition takes place, not even when a critical endpoint is approached. Far from the TCP, reentrant wetting may occur, with a different wetting phase. These findings shed light on hitherto unexplained experiments on ternary H_{2}O-oil-nonionic amphiphile mixtures in which nonwetting continues to exist as one approaches either one of the two critical endpoints.

Three-phase equilibria in density-functional theory: Interfacial tensions.

A mean-field density-functional model for three-phase equilibria in fluids (or other soft condensed matter) with two spatially varying densities is analyzed analytically and numerically. The interfacial tension between any two out of three thermodynamically coexisting phases is found to be captured by a surprisingly simple analytic expression that has a geometric interpretation in the space of the two densities. The analytic expression is based on arguments involving symmetries and invariances. It is supported by numerical computations of high precision, and it agrees with earlier conjectures obtained for special cases in the same model. An application is presented to three-phase equilibria in the vicinity of a tricritical point. Using the interfacial tension expression and employing the field variables compatible with tricritical point scaling, the expected mean-field critical exponent is derived for the vanishing of the critical interfacial tension as a function of the deviation of the noncritical interfacial tension from its limiting value, upon approach to a critical endpoint in the phase diagram. The analytic results are again confirmed by numerical computations of high precision.

Efficiency at Maximum Power of Irreversible Engines with Asymmetric Nonlinear Flux-Force Relations.

The efficiency at maximum power (EMP) is investigated for classical irreversible thermal or chemical model engines. The heat or particle transport is governed by flux-force relations of the general power-law type. Special attention is given to engines that feature asymmetric transport laws, one for input (of heat or particles) and a different one for output. It is shown that in a couple of case studies, the EMP of such engines is close to the lowest of the two EMPs that would result for symmetric implementations of the transport laws. As a consequence, ideal efficiency at maximum power is only possible in the model in which both flux-force relations are of step-function type.

Contact line of adsorbed colloid-polymer droplets in theory and experiment.

The contact line between the colloid-rich bulk liquid and an adsorbed thin film in colloid-polymer mixtures (CPM) is studied by means of an interface displacement model. The interface displacement profiles are compared to laser scanning confocal microscopy (LSCM) images. The mixtures consist of poly(methylmetacrylate) (PMMA) colloids and polystyrene (PS) polymers with polymer-to-colloid size ratio q = 1.18. Based on the experimental parameters, the theoretical model predicts a contact angle for colloid-rich liquid droplets adsorbed on glass of θ∞ = 59°, assuming a contact line with infinite radius, R = ∞. When a contact-line curvature correction and a correction for the protein-limit character of the CPM are taken into account, a modest shift is obtained. The refined theory predicts θ≈ 56°. The contact angle determined visually from the LSCM images is θ≈ 30°. The model predicts a three-phase contact-line tension of τ = -1.2 × 10(-12) N (uncorrected) and τ = -2.3 × 10(-13) N (with protein-limit correction), which is physically sound both in sign and magnitude. The line tension influences the contact angle to a small extent due to the contact line curvature. The predicted width of the transition zone between the thin film and the droplet is about 2 µm. The effect of gravity is noticeable as a deformation near the middle of the droplet.

Degree-dependent network growth: from preferential attachment to explosive percolation.

We present a simple model of network growth and solve it by writing the dynamic equations for its macroscopic characteristics such as the degree distribution and degree correlations. This allows us to study carefully the percolation transition using a generating functions theory. The model considers a network with a fixed number of nodes wherein links are introduced using degree-dependent linking probabilities pk. To illustrate the techniques and support our findings using Monte Carlo simulations, we introduce the exemplary linking rule pk∝k-α, with α between -1 and +∞. This parameter may be used to interpolate between different regimes. For negative α, links are most likely attached to high-degree nodes. On the other hand, in case α>0, nodes with low degrees are connected and the model asymptotically approaches a process undergoing explosive percolation.

Efficiency at maximum power of a chemical engine.

A cyclically operating chemical engine is considered that converts chemical energy into mechanical work. The working fluid is a gas of finite-sized spherical particles interacting through elastic hard collisions. For a generic transport law for particle uptake and release, the efficiency at maximum power η(mp) [corrected] takes the form 1/2+cΔµ+O(Δµ(2)), with 1∕2 a universal constant and Δµ the chemical potential difference between the particle reservoirs. The linear coefficient c is zero for engines featuring a so-called left/right symmetry or particle fluxes that are antisymmetric in the applied chemical potential difference. Remarkably, the leading constant in η(mp) [corrected] is non-universal with respect to an exceptional modification of the transport law. For a nonlinear transport model, we obtain η(mp) = 1/(θ + 1) [corrected], with θ > 0 the power of Δµ in the transport equation.

Biased percolation on scale-free networks.

Biased (degree-dependent) percolation was recently shown to provide strategies for turning robust networks fragile and vice versa. Here, we present more detailed results for biased edge percolation on scale-free networks. We assume a network in which the probability for an edge between nodes i and j to be retained is proportional to (k(i)k(j)(-alpha) with k(i) and k(j) the degrees of the nodes. We discuss two methods of network reconstruction, sequential and simultaneous, and investigate their properties by analytical and numerical means. The system is examined away from the percolation transition, where the size of the giant cluster is obtained, and close to the transition, where nonuniversal critical exponents are extracted using the generating-functions method. The theory is found to agree quite well with simulations. By presenting an extension of the Fortuin-Kasteleyn construction, we find that biased percolation is well-described by the q-->1 limit of the q -state Potts model with inhomogeneous couplings.

How to make a fragile network robust and vice versa.

We investigate topologically biased failure in scale-free networks with a degree distribution P(k) proportional, variantk;{-gamma}. The probability p that an edge remains intact is assumed to depend on the degree k of adjacent nodes i and j through p_{ij} proportional, variant(k_{i}k_{j});{-alpha}. By varying the exponent alpha, we interpolate between random (alpha=0) and systematic failure. For alpha>0 (<0) the most (least) connected nodes are depreciated first. This topological bias introduces a characteristic scale in P(k) of the depreciated network, marking a crossover between two distinct power laws. The critical percolation threshold, at which global connectivity is lost, depends both on gamma and on alpha. As a consequence, network robustness or fragility can be controlled through fine-tuning of the topological bias in the failure process.

Theoretical study of the three-phase contact line and its tension in adsorbed colloid-polymer mixtures.

We perform a theoretical study of the three-phase contact line and the line tension in an adsorbed colloid-polymer mixture near a first-order wetting transition, employing an interface displacement model. We use a simple free-energy functional to describe a colloid-polymer mixture near a hard wall. The bulk phase behavior and the substrate-adsorbate interaction are modeled by the free-volume theory for ideal polymers. The large size of the colloidal particles and the suppression of the van der Waals interaction by optical matching of colloid and solvent justify the planar hard wall model for the substrate. Following the Fisher-Jin scheme, we derive from the free-energy functional an interface potential V(l) for these mixtures. For a particle diameter of 10-100 nm, the calculations indicate a line tension tau approximately 10(-12)-10(-13) N at room temperature. In view of the ultralow interfacial tension in colloid-polymer mixtures, gamma approximately 10(-7) Nm, this leads to a rather large characteristic length scale taugamma in the micrometer range for the three-phase contact zone width. In contrast with molecular fluids, this zone could be studied directly with optical techniques such as confocal scanning laser microscopy.

Effective exponents in the long-range critical wetting of alkanes on aqueous substrates.

Alkanes on water show a two-stage wetting transition. Upon raising the temperature, a first-order transition from a molecularly thin to a mesoscopically thick liquid film is followed by a continuous divergence of the film thickness. This second transition is brought about by long-range interactions between adsorbate and substrate and is, therefore, referred to as long-range critical wetting. The divergence of the film thickness is theoretically expected to occur according to the asymptotic power law l approximately (Tw,c-T)betas, with betas=-1. This value has indeed been found for pentane on pure water; however, for hexane on salt solutions of different concentrations, betas=-0.73 was found for a 1.5M solution of NaCl and betas=-0.57 for a 2.5M salt solution. In addition, for hexane on a 2.5M solution of NaCl, an exponent of alphas=0.1 was found from contact-angle measurements, differing greatly from the theoretically expected value of alphas=-1. Using Dzyaloshinskii-Lifshitz-Pitaevskii theory, we calculate effective local exponents in order to explain the experimental findings. Taking into account the uncertainty of the exponents derived from experiments as well as the temperature range in which the measurements were carried out, a reasonable agreement between theory and experiment is found, thereby providing a consistent approach to resolving the apparently anomalous behavior of hexane on brine. The experimentally observed exponents betas=-0.57 and alphas=0.1 are also compatible with a long-range tricritical wetting transition, which is characterized by betas=-1/2 and alphas=0; this alternative explanation of the experimental findings is neither supported nor completely ruled out by our calculations.

Long-range critical wetting: observation of a critical end point.

Alkanes deposited on aqueous substrates exhibit two different types of wetting behavior: alternatively to the usual first-order wetting transition, a sequential-wetting scenario of a long-range critical wetting transition preceded by a first-order thin-thick transition may be observed. Here, we present the first successful experimental attempt to locate the transition point between the standard first-order wetting and the long-range critical wetting: a critical end point, observed in a mixture of pentane and hexane which is deposited on an aqueous solution of glucose. Furthermore, we present the first direct measurement of the contact angle in the intermediate wetting state (frustrated-complete wetting) in the sequential-wetting scenario of hexane on brine and compare to theoretical predictions.