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 T53°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.     

Critical behavior of betaine arsenate

The critical exponents , and of undeuterated and partially deuterated ferroelectric betaine arsenate are estimated. Small but remarkable deviations from the tricritical values are observed. The obtained values are tested via scaling of the isothermals.At some distance aboveT _c a cross-over of the effective critical exponent to a value typically for short-range forces is observed. A suitably defined cross-over temperature range decreases with increasing deuteration and seems to vanish near the antiferroelectric phase boundary.     

Critical wetting in the square Ising model with a boundary field

The Ising square lattice with nearest-neighbor exchangeJ>0 and a free surface at which a boundary magnetic fieldH ₁ acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surface steps are briefly discussed.Alexander von Humboldt-Fellow     

Critical behavior at dirty surfaces

The influence of quenched surface disorder — i.e. quenched disorder that is located at the bounding surface of a macroscopic system — on the surface critical behavior of such systems is investigated. To this end a class of semi-infinite continuum models of then-vector type with random surface interactions is studied. Both the case of surface transitions at a bulk critical point as well as that of surface transitions at a bulk tricritical point is considered. General irrelevance/relevance criteria of the Harris type are derived for both short-range and long-range correlated random surface interactions. These are used to assess the stability of the pure system critical behavior and to point out when random surface field or enhancement disorder is expected to be relevant.     

Wetting transition on grain boundaries in Al contacting with a Sn-rich melt

The contact angle at the intersection of a grain boundary in Al bicrystals with the solid Al/liquid Al–Sn interphase boundary has been measured for two symmetric tilt <011> {001} grain boundaries with tilt angles of 32° and 38.5°. The temperature dependencies (T) present the evidence of the grain boundary wetting phase transition at T_w. The observed hysteresis is consistent with the assumption that the wetting transition is of first order. The determined discontinuity in the temperature derivative of the grain boundary energy is–5.6 J/m²K (T w1=617°C) for the boundary with a low energy (=38.5°) and –17 J/m²K (T w2=604°C) for the grain boundary with a high energy (=32°).     

Critical point wetting in NbH0.31

The local α-α' phase distribution in a thin Nb single crystal loaded with the critical H-concentration was investigated with X-rays. The sample used in the experiment showed a macroscopic hydrogen density mode, leading to a curvature of the whole crystal plate with the α-phase on the concave side and the α'-phase on the convex side. In addition an α-phase wetting layer was found on top of the α'-phase separated from the bulk α'-phase by a mixed α-α' phase region. In a simple model their thickness were determined to about $\text{\$}\text{?}$1.0 and 7?0μm, resp. This thin wetting layer leads to a new interpretation of the phase transition of H and Nb, involving the familiar long-range elastic interaction as well as a short-range surface free energy contribution.     

Determination of the Breakage and Wetting Parameters of Calcite and Their Correlations

This paper presents the breakage and wetting parameters of calcite mineral obtained experimentally and establishes a correlation between these characteristic parameters. The breakage parameter obtained from the different feed sizes of grinding is the specific rate of breakage (S_i). The wettability parameter, obtained from surface chemistry‐based processes such as contact angle measurements or flotation methods, is the critical surface tension of wetting of a solid or mineral (γ_c). Calcite mineral, studied for the determination of the above parameters and their correlations, was ground in a laboratory‐size ceramic ball mill with dry, wet and chemically aided grindings and tested extensively to determine the γ_c values by using a contact angle goniometer and a newly designed micro‐column flotation cell. The highest S_i value obtained was 0.35 min^?1 for sodium dodecyl sulfate (SDDS)‐aided grinding, and the lowest S_i value was 0.26 min^?1 for dry grinding of the ?600+425 feed in the mill. The γ_c values for calcite were obtained as 34.0–34.9 mN/m for SDDS‐treated calcite surfaces, 29.9–31.4 mN/m for sodium oleate‐treated surfaces and >72 mN/m for both dry and wet ground products whose surfaces were not treated chemically. Some correlations were established between the S_i and γ_c parameters; as the S_i increases, γ_c decreases, indicating that relatively more hydrophobic surfaces are broken faster for the largest sizes, resulting in higher S_i values with more fines (lower γ of B_{i, j}) in the finer size distribution region (i.e. ?150 μm).     

Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions

We perform a comparative Monte Carlo study of the easy-plane deconfined critical point (DCP) action and its short-range counterpart to reveal close similarities between the two models for intermediate and strong coupling regimes. For weak coupling, the structure of the phase diagram depends on the interaction range: while the short-range model features a tricritical point and a continuous U(1) × U(1) transition, the long-range DCP action is characterized by the runaway renormalization flow of coupling into a first (I) order phase transition. We develop a “numerical flowgram” method for high precision studies of the runaway effect, weakly I-order transitions, and polycritical points. We prove that the easy-plane DCP action is the field theory of a weakly I-order phase transition between the valence bond solid and the easy-plane antiferromagnet (or superfluid, in particle language) for any value of the weak coupling strength. Our analysis also solves the long standing problem of what is the ultimate fate of the runaway flow to strong coupling in the theory of scalar electrodynamics in three dimensions with U(1) × U(1) symmetry of quartic interactions.     

Nonlinearity in cooperative systems-dynamical Bethe-Ising model

The dynamics of the short-range order as well as the long-range order in the nonlinear cooperative system is investigated specifically for a kinetic Ising model in the Bethe approximation. The phenomena of critical slowing down near the transition temperatureT _c and anomalous fluctuation belowT _c are directly related to the instability of the long-range order. The dynamics of the short-range order is essentially a fast mode and is noncritical. However, through the nonlinear coupling the short-range order is also influenced by the critical behavior of the long-range order.     

Pressure effect on grain boundary wetting at various temperatures

Bicrystals of Fe-6 at.% Si alloy containing <001> 5 tilt grain boundaries with a deposited zinc layer have been annealed at various hydrostatic pressure at four temperatures between 700° and 905°C. After the anneals the dihedral angle of the grain boundary groove formed at the site of the grain boundary intersection with the solid-melt interphase boundary has been measured. The transition from complete to incomplete wetting of the grain boundary by the zinc-rich melt (dewetting phase transition) has been found to occur as the pressure increased at all temperatures studied. The temperature dependence of the dewetting transition pressure p _w has been determined. That dependence has a minimum at a temperature of 790°C, which is close to the peritectic temperature in the Fe–Zn system (782°C). A thermodynamic analysis of the wetting phenomena in the two-component system, based on Becker's regular solution model for the surface tension of the interphase boundary, explains the minimum in the p _w (T) dependence.     

What controls the thickness of wetting layers near bulk criticality?

We study the thickness of wetting layers in the binary-liquid mixture cyclohexane methanol. Far from the bulk critical point, the wetting layer thickness is independent of temperature, resulting from the competition between van der Waals and gravitational forces. Upon approaching the bulk critical temperature [t=(T(c)-T)/T(c)-->0], we observe that the wetting layer thickness diverges as t(-beta) with effective critical exponent beta=0.23+/-0.06. This is characteristic of a broad, intermediate scaling regime for the crossover from van der Waals wetting to critical scaling. We predict beta=beta/3 approximately 0.11, with beta the usual bulk-order parameter critical exponent, showing a small but significant difference with experiment.     

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

We explore the tricritical points and the critical lines of both Blume-Emery-Griffiths and Ising model within long-range interactions in the microcanonical ensemble. For K=K_MTP, the tricritical exponents take the values β=1/4, 1=γ^-≠γ⁺=1/2 and 0=α^-≠α⁺=-1/2, which disagree with classical (mean field) values. When K>K_MTP, the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K_CTP), where the values of the critical expoents become β=1/2, 1=γ^-≠γ⁺=2 and 0=α⁺≠α⁺=1.     

Wetting and Phase Separation in Polymer Blend Films: Identification of Four Thickness Regimes with Distinct Morphological Pathways

Using forward recoil spectrometry and atomic force microscopy, the phase evolution of a critical blend thin film of deuterated poly(methyl methacrylate) (dPMMA) and poly(styrene-ran-acrylonitrile) (SAN) is found to depend on film thickness. Four regimes are identified as film thickness l ₀ decreases from semi-infinite to below the radius of gyration, R _g. In the semi-infinite limit or regime IV (l ₀ R _g), surface directed spinodal decomposition is observed and found to agree with cell dynamic simulations. In regime III (10 R _g < l ₀ < 150 R _g), three stages of evolution are observed. During the early stage, wetting dominates and produces a dPMMA-rich/SAN-rich/dPMMA-rich structure. During the intermediate stage, the surface phase flows back into the middle layer inducing lateral phase coarsening. During the late stage, capillary fluctuations rupture the middle layer by spinodal dewetting, resulting in a final morphology with SAN-rich droplets encapsulated by dPMMA-rich wetting layers. Although regime II (R _g < l ₀ < 10 R _g) films also exhibit a tri-layer early stage, correlated holes in the middle layer spontaneously grow suggesting that this layer is too thin to support fully developed capillary fluctuations. Three stages of roughening are observed with a final morphology similar to regime III. In regime I (l ₀ < R _g), films roughen almost immediately after annealing in contrast to the other regimes. Initially, the surface roughness increases logarithmically with time before reaching a constant value of 2 R _g. The final average droplet height, 29.5 nm, is in good agreement with a simple interfacial energy model. Whereas the final morphology for regimes I, II and III are identical, the pathways by which films roughen are distinct suggesting that erroneous conclusions can be made by simply analyzing the final morphology.     

Lee-Yang zeros and stokes phenomenon in a model with a wetting transition

We consider the statistical mechanics of a fluctuating string (1D solid-on-solid model) ofN columns with a contact energy term displaying a critical wetting transition. For this model we derive a contour integral representation for the finite-size partition function. From this representation we derive a polynomial representation and obtain the Lee-Yang zeros forN , 100. Through the asymptotic evaluation of the contour integral we evaluate the zeros for higherN. This asymptotic evaluation displays a Stokes phenomenon providing a different viewpoint of the mechanism by which a phase transition can arise, supplementing the picture of Lee and Yang. We also reproduce and extend somewhat the results of Smith for the finite-size scaling limit of the partition function.     

Nonuniform van der Waals theory

The liquid-vapor interface of a confined fluid at the condensation phase transition is studied in a combined hydrostatic/mean-field limit of classical statistical mechanics. Rigorous and numerical results are presented. The limit accounts for strongly repulsive short-range forces in terms of local thermodynamics. Weak attractive longer-range ones, like gravitational or van der Waals forces, contribute a self-consistent mean potential. Although the limit is fluctuationfree, the interface is not a sharp Gibbs interface, but its structure is resolved over the range of the attractive potential. For a fluid of hard balls with –r ^–6 interactions the traditional condensation phase transition with critical point is exhibited in the grand ensemble: A vapor state coexists with a liquid state. Both states are quasiuniform well inside the container, but wall-induced inhomogeneities show up close to the boundary of the container. The condensation phase transition of the grand ensemble bridges a region of negative total compressibility in the canonical ensemble which contains canonically stable proper liquid-vapor interface solutions. Embedded in this region is a new, strictly canonical phase transition between a quasiuniform vapor state and a small droplet with extended vapor atmosphere. This canonical transition, in turn, bridges a region of negative total specific heat in the microanonical ensemble. That region contains subcooled vapor states as well as superheated very small droplets which are microcanonically stable.     

Correlation of Grain Boundary Character with Wetting Behavior

Wetting of 975 grain boundaries (GB's) by liquid Cu in an iron-based alloy has been studied as a function of the five macroscopic degrees of freedom (DoF's) of grain boundary character. In addition, models of GB energy in terms of all five DoF's, and of anisotropic solid-liquid interfacial energy have been developed. The experimentally observed wetting behavior is interpreted in terms of the model, and it is shown that reasonable overall agreement is obtained between experimental results and model predictions.     

Finite-size scaling approach for critical wetting: rationalization in terms of a bulk transition with an order parameter exponent equal to zero

Clarification of critical wetting with short-range forces by simulations has been hampered by the lack of accurate methods to locate where the transition occurs. We solve this problem by developing an anisotropic finite-size scaling approach and show that then the wetting transition is a "bulk" critical phenomenon with order parameter exponent equal to zero. For the Ising model in two dimensions, known exact results are straightforwardly reproduced. In three dimensions, it is shown that previous estimates for the location of the transition need revision, but the conclusions about a slow crossover away from mean-field behavior remain unaltered.     

Renormalized tricritical behaviour for wetting transitions

In this paper we study tricritical wetting behaviour in three dimensions. In particular we concentrate on systems with short-ranged forces and apply linear functional renormalization group techniques to elucidate the effect of fluctuations upon tricriticality. In comparison with studies of critical wetting we identify an additional fluctuation regime which is relevant for values of the capillary parameter between 2/9 and 1/2. We demonstrate that this regime essentially provides a crossover from mean-field like behaviour, in which tricritical exponents are always distinct from their critical counterparts, from intermediate- and strong-fluctuation behaviour where the critical exponents for tricritical and critical wetting are found to always coincide. We conclude by discussing briefly the possible relevance of these results for experimental studies of wetting. Received 4 January 2001 and Received in final form 11 May 2001     

Critical Properties and Finite-Size Estimates for the Depinning Transition of Directed Random Polymers

We consider models of directed random polymers interacting with a defect line, which are known to undergo a pinning/depinning (or localization/delocalization) phase transition. We are interested in critical properties and we prove, in particular, finite-size upper bounds on the order parameter (the contact fraction) in a window around the critical point, shrinking with the system size. Moreover, we derive a new inequality relating the free energy F and an annealed exponent μ which describes extreme fluctuations of the polymer in the localized region. For the particular case of a (1+1)-dimensional interface wetting model, we show that this implies an inequality between the critical exponents which govern the divergence of the disorder-averaged correlation length and of the typical one. Our results are based on the recently proven smoothness property of the depinning transition in presence of quenched disorder and on concentration of measure ideas.