Joseph Indekeu

Line tension near the wetting transition: results from an interface displacement model

An interface displacement model is employed for calculating the line tension of a contact line where three phases meet. At a first-order wetting transition the line tension reaches a positive and finite limit if the intermolecular potentials decay faster than r−6. In contrast, for non-retarder Van der Waals forces, and forces of still longer range, the line tension diverges at first-order wetting. The boundary tension along the prewetting line is positive and finite. Approaching wetting, it increases (with diverging slope) and converges to the value of the line tension at first-order wetting. Approaching first-order wetting at bulk phase coexistence, the line tension is finite provided the potentials decay faster than r−5, and increases (with diverging slope) towards its limit at wetting. In contrast, at a critical wetting transition the line tension vanishes. Comparison with recent results from alternative microscopic mean-field approximations is favourable.

LINE TENSION AT WETTING

A review is presented of recent theoretical advances on a fundamental problem in statistical mechanics that concerns the three-phase contact line ℒ and its tension τ near a wetting phase transition. In addition to answering the intriguing question whether or not ℒ and τ vanish at wetting, recent work has also revealed that τ displays universal singular behavior, reflecting critical phenomena associated with the wetting transition. Three factors are crucial for determining the fate of ℒ and τ at wetting: the order of the wetting transition, the range of the intermolecular forces, and the upper critical dimension du, above which mean-field theory holds and below which fluctuations dominate. For most systems studied experimentally, du < 3, so that the mean-field predictions should be correct in d = 3. In the thermal fluctuation regime, for d < du, hyperscaling predicts the value 2(d – 2)/(d – 1) for the critical exponent of τ(θ), in the limit that the contact angle θ approaches 0.

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.

SIMULATION OF WETTING AND DRYING AT SOLID-FLUID INTERFACES ON THE DELFT MOLECULAR DYNAMICS PROCESSOR

The adsorption is studied of a fluid at a structured solid substrate by means of computer simulations on the Delft Molecular Dynamics Processor. Two types of particles are present, 2904 of one type for building a three-layer substrate and about 8500 of another type for composing the fluid. Interactions between like and unlike atoms are modeled by pair potentials of Lennard-Jones form cut off at 2.5σ. Simulations are performed at constant temperature and variable ratio of substrate-adsorbate to adsorbate-adsorbate attraction. On the basis of measurements of density profiles, coverages, surface tensions, and contact angles, a wetting as well as a drying phase transition have been identified. Both transitions are of first order.

Capturing Wetting States in Nanopatterned Silicon

Spectacular progress in developing advanced Si circuits with reduced size, along the track of Moores law, has been relying on necessary developments in wet cleaning of nanopatterned Si wafers to provide contaminant free surfaces. The most efficient cleaning is achieved when complete wetting can be realized. In this work, ordered arrays of silicon nanopillars on a hitherto unexplored small scale have been used to study the wetting behavior on nanomodulated surfaces in a substantial range of surface treatments and geometrical parameters. With the use of optical reflectance measurements, the nanoscale water imbibition depths have been measured and the transition to the superhydrophobic Cassie-Baxter state has been accurately determined. For pillars of high aspect ratio (about 15), the transition occurs even when the surface is grafted with a hydrophilic functional group. We have found a striking consistent deviation between the contact angle measurements and the straightforward application of the classical wetting models. Molecular dynamics simulations show that these deviations can be attributed to the long overlooked atomic-scale surface perturbations that are introduced during the nanofabrication process. When the transition condition is approached, transient states of partial imbibition that characterize intermediate states between the Wenzel and Cassie-Baxter states are revealed in our experiments.

Surface enhancement of superconductivity in tin

The possibility of surface enhancement of superconductivity is examined experimentally. It is shown that single crystal tin samples with cold-worked surfaces represent a superconductor with a surface-enhanced order parameter (or negative surface extrapolation length b), whose magnitude can be controlled.

Wetting of Alkanes on Water from a Cahn-Type Theory: Effects of Long-Range Forces

We apply the phenomenological wetting theory of Cahn to fluids with van der Waals forces, and in particular to the wetting of pentane on water. Taking into account explicitly the long-range substrate–adsorbate interaction allows us to reproduce the experimentally observed critical wetting transition, which arises from the vanishing of the Hamaker constant at T≈53°C. This transition is preceded by a first-order transition between a thin and a thick film at a (much) lower temperature. If long-range forces are neglected, this thin–thick transition is the only wetting transition and critical wetting is missed. Our study focuses on the development of useful theoretical tools, such as phase portraits and interface potentials adapted to systems with van der Waals forces.

Special attention network

In this Note a social network model for opinion formation is proposed in which a person connected to q partners pays an attention 1/q to each partner. The mutual attention between two connected persons i and j is taken equal to the geometric mean 1/qiqj. Opinion is represented as usual by an Ising spin s=±1 and mutual attention is given through a two-spin coupling Jij=JQ/qiqj, Q being the average connectivity in the network. Connectivity diminishes attention and only persons with low connectivity can pay special attention to each other leading to a durable common (or opposing) opinion. The model is solved in “mean-field” approximation and a critical “temperature” Tc proportional to JQ is found, which is independent of the number of persons N, for large N.

Wetting of alkanes on water

The wetting behavior of oil on water (or brine) has important consequences for the transport properties of oil in water-containing porous reservoirs, and consequently for oil recovery. The equilibrium wetting behavior of model oils composed of pure alkanes or alkane mixtures on brine is reviewed in this paper. Intermediate between the partial wetting state, in which oil lenses coexist on water with a thin film of adsorbed alkane molecules, and the complete wetting state, in which a macroscopically thick oil layer covers the water, these systems display a third, novel wetting state, in which oil lenses coexist with a mesoscopic (a few-nanometers-thick) oil film. The nature and location of the transitions between these wetting regimes depend on oil and brine compositions, temperature and pressure.

Molecular tail lengths, dipole pairings, and multiple reentrance mechanisms of liquid crystals

Employing the “spin-gas” model which incorporates the inherent microscopic frustration of dipoles, observed sequences of reentrant nematic and smectic phases are reproduced. In particular, the quadruple reentrance (nematic ↔ smecticAd ↔ nematic ↔ smecticAd ↔ nematic ↔ smecticA1) is explained. The molecular tail length theoretically required for this phenomenon agrees with experiment. In the theory, associations if correlated triplets of molecules propagate smectic order. By contrast, dipole pairings giving rise to dimers of molecules frustrate smectic order and favor the nematic phase. Calculated dimer concentrations are insensitive to N ↔ Ad transitions, consistently with dielectric measurements, whereas dimers break up at the N ↔ A1 transition, causing the large transition enthalpy.