Critical effects at complete wetting

Critical effects and scaling at meniscus osculation transitions

We propose a simple scaling theory describing critical effects at rounded meniscus osculation transitions which occur when the Laplace radius of a condensed macroscopic drop of liquid coincides with the local radius of curvature R_{w} in a confining parabolic geometry. We argue that the exponent β_{osc} characterizing the scale of the interfacial height ℓ_{0}∝R_{w}^{β_{osc}} at osculation, for large R_{w}, falls into two regimes representing fluctuation-dominated and mean-field-like behavior, respectively. These two regimes are separated by an upper critical dimension, which is determined here explicitly and depends on the range of the intermolecular forces. In the fluctuation-dominated regime, representing the universality class of systems with short-range forces, the exponent is related to the value of the interfacial wandering exponent ζ by β_{osc}=3ζ/(4-ζ). In contrast, in the mean-field regime, which was not previously identified and which occurs for systems with longer-range forces (and higher dimensions), the exponent β_{osc} takes the same value as the exponent β_{s}^{co} for complete wetting, which is determined directly by the intermolecular forces. The prediction β_{osc}=3/7 in d=2 for systems with short-range forces (corresponding to ζ=1/2) is confirmed using an interfacial Hamiltonian model which determines the exact scaling form for the decay of the interfacial height probability distribution function. A numerical study in d=3, based on a microscopic model density-functional theory, determines that β_{osc}≈β_{s}^{co}≈0.326 close to the predicted value of 1/3 appropriate to the mean-field regime for dispersion forces.

Edge Contact Angle, Capillary Condensation, and Meniscus Depinning

We study the phase equilibria of a fluid confined in an open capillary slit formed when a wall of finite length H is brought a distance L away from a second macroscopic surface. This system shows rich phase equilibria arising from the competition between two different types of capillary condensation, corner filling and meniscus depinning transitions depending on the value of the aspect ratio a=L/H. For long capillaries, with a<2/π, the condensation is of type I involving menisci which are pinned at the top edges at the ends of the capillary characterized by an edge contact angle. For intermediate capillaries, with 2/π<a<1, depending on the value of the contact angle the condensation may be of type I or of type II, in which the menisci overspill into the reservoir and there is no pinning. For short capillaries, with a>1, condensation is always of type II. In all regimes, capillary condensation is completely suppressed for sufficiently large contact angles. We show that there is an additional continuous phase transition in the condensed liquidlike phase, associated with the depinning of each meniscus as they round the upper open edges of the slit. Finite-size scaling predictions are developed for these transitions and phase boundaries which connect with the fluctuation theories of wetting and filling transitions. We test several of our predictions using a fully microscopic density functional theory which allows us to study the two types of capillary condensation and its suppression at the molecular level.

Breaking Cassie's Law for Condensation in a Nanopatterned Slit

We study the phase transitions of a fluid confined in a capillary slit made from two adjacent walls, each of which are a periodic composite of stripes of two different materials. For wide slits the capillary condensation occurs at a pressure which is described accurately by a combination of the Kelvin equation and the Cassie law for an averaged contact angle. However, for narrow slits the condensation occurs in two steps involving an intermediate bridging phase, with the corresponding pressures described by two new Kelvin equations. These are characterised by different contact angles due to interfacial pinning, with one larger and one smaller than the Cassie angle. We determine the triple point and predict two types of dispersion force induced Derjaguin-like corrections due to mesoscopic volume reduction and the singular free-energy contribution from nanodroplets and bubbles. We test these predictions using a fully microscopic density functional model which confirms their validity even for molecularly narrow slits. Analogous mesoscopic corrections are also predicted for two-dimensional systems arising from thermally induced interfacial wandering.

First-order wedge wetting revisited

We consider a fluid adsorbed in a wedge made from walls that exhibit a first-order wetting transition and revisit the argument as to why and how the pre-filling and pre-wetting coexistence lines merge when the opening angle is increased approaching the planar geometry. We clarify the nature of the possible surface phase diagrams, pointing out the connection with complete pre-wetting, and show that the merging of the coexistence lines lead to new interfacial transitions. These occur along the side walls and are associated with the unbinding of the thin-thick interface, rather than the liquid-gas interface (meniscus), from the wedge apex. When fluctuation effects, together with the influence of dispersion forces are included, these transitions display strong non-universal critical singularities that depend on the opening angle itself. Similar phenomena are also shown to occur for adsorption near an apex tip.

Crossover scaling of apparent first-order wetting in two-dimensional systems with short-ranged forces

Recent analyses of wetting in the semi-infinite two-dimensional Ising model, extended to include both a surface coupling enhancement and a surface field, have shown that the wetting transition may be effectively first-order and that surprisingly the surface susceptibility develops a divergence described by an anomalous exponent with value γ_{11}^{eff}=3/2. We reproduce these results using an interfacial Hamiltonian model making a connection with previous studies of two-dimensional wetting, and we show that they follow from the simple crossover scaling of the singular contribution to the surface free-energy, which describes the change from apparent first-order to continuous (critical) wetting due to interfacial tunneling. The crossover scaling functions are calculated explicitly within both the strong-fluctuation and intermediate-fluctuation regimes, and they determine uniquely and more generally the value of γ_{11}^{eff}, which is nonuniversal for the latter regime. The location and the rounding of a line of pseudo-prewetting transitions occurring above the wetting temperature and off bulk coexistence, together with the crossover scaling of the parallel correlation length, are also discussed in detail.

Complete prewetting

We study continuous interfacial transitions, analagous to two-dimensional complete wetting, associated with the first-order prewetting line, which can occur on steps, patterned walls, grooves and wedges, and which are sensitive to both the range of the intermolecular forces and interfacial fluctuation effects. These transitions compete with wetting, filling and condensation producing very rich phase diagrams even for relatively simple prototypical geometries. Using microscopic classical density functional theory to model systems with realistic Lennard-Jones fluid-fluid and fluid-substrate intermolecular potentials, we compute mean-field fluid density profiles, adsorption isotherms and phase diagrams for a variety of confining geometries.

Wetting transition in the two-dimensional Blume-Capel model: a Monte Carlo study

The wetting transition of the Blume-Capel model is studied by a finite-size scaling analysis of L×M lattices where competing boundary fields ±H_{1} act on the first or last row of the L rows in the strip, respectively. We show that using the appropriate anisotropic version of finite-size scaling, critical wetting in d=2 is equivalent to a "bulk" critical phenomenon with exponents α=-1, β=0, and γ=3. These concepts are also verified for the Ising model. For the Blume-Capel model, it is found that the field strength H_{1c}(T) where critical wetting occurs goes to zero when the bulk second-order transition is approached, while H_{1c}(T) stays nonzero in the region where in the bulk a first-order transition from the ordered phase, with nonzero spontaneous magnetization, to the disordered phase occurs. Interfaces between coexisting phases then show interfacial enrichment of a layer of the disordered phase which exhibits in the second-order case a finite thickness only. A tentative discussion of the scaling behavior of the wetting phase diagram near the tricritical point is also given.

Surface-induced weak orientational order and role of isotropic-nematic interface fluctuations in the appearance of an induced nematic film

Recently the nontrivial spatial and temperature dependence of the surface-induced weak planar orientational order parameter Q(z, T) was determined just above the isotropic-nematic (IN) phase transition point (Ji-H. Lee et al., Phys. Rev. Lett. 102, 167801 (2009)). In this paper we present a theoretical explanation of the observed behaviour. We obtain expressions for the short-range and long-range contributions to the interface potential of the induced nematic film and specify the repulsive character of the interaction between the soft IN interface and the external bounding substrate. It is shown that the small value of the IN interfacial tension results in the renormalization of the repulsive interaction potential due to the thermal fluctuations of the soft IN interface. This leads to an increase of the equilibrium thickness of the induced nematic film and the appearance of a step-like orientational order parameter profile. We find that only renormalized short-range and thermal pseudo-Casimir interactions are essential for the appearance of the induced nematic film, which provide the observed thickness, h ~ 30 nm, of this film. The long-range van der Waals interaction is shown to be negligibly small and the dominant role is played by the renormalized short-range repulsion. Fitting of the experimental order parameter profiles (Ji-H. Lee et al. (2009)) with the expressions based on these interactions makes it possible to determine the material parameters of the system, including the amplitudes of the surface interaction, the IN interfacial tension and the interfacial coherence length. The agreement between theory and experiment confirms the importance of the interface fluctuation renormalization of the interface potentials for soft interfaces.

Capillary emptying and short-range wetting

We consider a liquid trapped in a narrow horizontal capillary, under the influence of gravity. As the slit is widened, the meniscus, separating the capillary liquid from gas, deforms and develops a long tongue extending along the bottom wall. As a critical slit width is approached, the length of the tongue diverges continuously, leading to the emptying of the capillary. We show that the critical singularities characterizing emptying are the same as those at short-ranged wetting transitions, but at a scale set by the capillary length rather than the bulk correlation length. These meso- or macroscopic versions of both complete and critical wetting are observable in the laboratory and are studied here using a colloid-polymer mixture.

Scaling properties of fluid adsorption near the base of a cylinder

We consider the adsorption of fluid at the foot of a cylinder that protrudes from a flat substrate made of the same material. Provided the contact angle θ is small enough, a drop of liquid condenses near the base, the size of which can be determined using simple macroscopic arguments. The adsorption in this geometry shows scaling behavior related to a number of different interfacial phase transitions and, for systems with short-ranged forces, shows a remarkable property; for small θ, the height of the drop (measured from the base) and the width (measured from the cylinder axis) are near identical to expressions for the thickness and parallel correlation length for microscopic wetting films (at planar walls). The only difference is that the bulk correlation length is replaced by the radius of the cylinder. By taking into account the correct singular behavior of the line tension we show that this geometrical amplification of the microscopic lengths occurs for second-order, first-order, and complete wetting transitions, and is specific to three dimensions. Similar phenomena occurs for long-ranged forces, and shows crossover scaling behavior.

Interplay of complete wetting, critical adsorption, and capillary condensation

The excess adsorption Gamma in two-dimensional Ising strips (infinityxL), subject to identical boundary fields at both one-dimensional surfaces decaying in the orthogonal direction j as -h1j(-p), is studied for various values of p and along various thermodynamic paths below the bulk critical point by means of the density-matrix renormalization-group method. The crossover behavior between the complete-wetting and critical-adsorption regimes, occurring in semi-infinite systems, is strongly influenced by confinement effects. Along isotherms T=const the asymptotic power-law dependences on the external bulk field, which characterize these two regimes, are pre-empted by capillary condensation. Along the pseudo-first-order phase-coexistence line of the strips, which varies with temperature, we find a broad crossover regime in which both the thickness of the wetting film and Gamma increase as functions of the reduced temperature tau but do not follow any power law. Above the wetting temperature the order-parameter profiles are not slablike but exhibit wide interfacial variations and pronounced tails.

Domain formation in membranes caused by lipid wetting of protein

Formation of rafts and other domains in cell membranes is considered as wetting of proteins by lipids. The membrane is modeled as a continuous elastic medium. Thermodynamic functions of the lipid films that wet proteins are calculated using a mean-field theory of liquid crystals as adapted to biomembranes. This approach yields the conditions necessary for a macroscopic wetting film to form; its thickness could also be determined. It is shown that films of macroscopic thicknesses form around large (tens nanometers in diameter) lipid-protein aggregates; only thin adsorption films form around single proteins or small complexes. The means by which wetting films can facilitate the merger of these aggregates is considered. It is shown that a wetting film prevents a protein from leaving an aggregate. Using experimentally derived values of elastic moduli and spontaneous curvatures as well as height mismatch between aggregates and bulk membrane, we obtained numerical results, which can be compared with the experimental data.

Intrusion of fluids into nanogrooves: how geometry determines the shape of the gas-liquid interface

We study the shape of gas-liquid interfaces forming inside rectangular nanogrooves (i.e., slit-pores capped on one end). On account of purely repulsive fluid-substrate interactions the confining walls are dry (i.e., wet by vapor) and a liquid-vapor interface intrudes into the nanogrooves to a distance determined by the pressure (i.e., chemical potential). By means of Monte Carlo simulations in the grand-canonical ensemble (GCEMC) we obtain the density rho(z) along the midline (x = 0) of the nanogroove for various geometries (i.e., depths D and widths L) of the nanogroove. We analyze the density profiles with the aid of an analytic expression which we obtain through a transfer-matrix treatment of a one-dimensional effective interface Hamiltonian. Besides geometrical parameters such as D and L , the resulting analytic expression depends on temperature T , densities of coexisting gas and liquid phases in the bulk rho g,l(x) and the interfacial tension gamma. The latter three quantities are determined in independent molecular dynamics simulations of planar gas-liquid interfaces. Our results indicate that the analytic formula provides an excellent representation of rho(z) as long as L is sufficiently small. At larger L the meniscus of the intruding liquid flattens. Under these conditions the transfer-matrix analysis is no longer adequate and the agreement between GCEMC data and the analytic treatment is less satisfactory.

Condensation in a capped capillary is a continuous critical phenomenon

We show that condensation in a capped capillary slit is a continuous interfacial critical phenomenon, related intimately to several other surface phase transitions. In three dimensions, the adsorption and desorption branches correspond to the unbinding of the meniscus from the cap and opening, respectively, and are equivalent to 2D-like complete-wetting transitions. For dispersion forces, the singularities on the two branches are distinct, owing to the different interplay of geometry and intermolecular forces. In two dimensions we establish precise connection, or covariance, with 2D critical-wetting and wedge-filling transitions: i.e., we establish that certain interfacial properties in very different geometries are identical. Our predictions of universal scaling and covariance in finite capillaries are supported by extensive Ising model simulation studies in two and three dimensions.

Tests of nonuniversality and finite-size scaling for two-dimensional wetting with long-ranged forces

Effective Hamiltonian models predict nonuniversal critical singularities for two-dimensional wetting transitions with marginal long-ranged forces. We test these predictions by studying interfacial delocalization transitions in an infinitely long Ising strip, of width L (lattice spacings), with external fields that are long ranged and have opposite signs at each surface. Finite-size scaling suggests that the shift of the delocalization temperature T(c)(L) below the (semi-infinite) wetting temperature T(w) scales as L(-1/beta(s)) with beta(s) the adsorption critical exponent. Density-matrix renormalization-group methods allow us to study the behavior of T(c)(L) for L up to several hundred lattice spacings. For short-ranged forces the method recovers the universal value of beta(s)=1 known from the exact solution. While marginal long-ranged forces strongly influence the finite-size scaling of T(c)(L) , the extrapolated asymptotic value for the exponent beta(s) does not appear to confirm the predicted nonuniversality, but instead approaches the same universal value representative of systems with short-ranged forces.

Layered interfaces between immiscible liquids studied by density-functional theory and molecular-dynamics simulations

We present a study of the structure in the interface between two immiscible liquids by density-functional theory and molecular-dynamics calculations. The liquids are modeled by Lennard-Jones potentials, which achieve immiscibility by suppressing the attractive interaction between unlike particles. The density profiles of the liquids display oscillations only in a limited part of the simple liquid-phase diagram (rho,T). When approaching the liquid-vapor coexistence, a significant depletion appears while the layering behavior of the density profile vanishes. By analogy with the liquid-vapor interface and the analysis of the adsorption this behavior is suggested to be strongly related to the drying transition.

Covariance for cone and wedge complete filling

Interfacial phenomena associated with fluid adsorption in two dimensional systems have recently been shown to exhibit hidden symmetries, or covariances, which precisely relate local adsorption properties in different confining geometries. We show that covariance also occurs in three-dimensional systems and is likely to be verifiable experimentally and in Ising model simulations studies. Specifically, we study complete wetting in wedge (W) and cone (C) geometries as bulk coexistence is approached and show that the equilibrium midpoint heights satisfy l(c)(h,alpha)=l(w)(h / 2,alpha), where h measures the partial pressure and alpha is the tilt angle. This covariance is valid for both short-ranged and long-ranged intermolecular forces and identifies both leading and next-to-leading-order critical exponents and amplitudes in the confining geometries.

Nonlinear structures and thermodynamic instabilities in a one-dimensional lattice system

The equilibrium states of the discrete Peyrard-Bishop Hamiltonian with one end fixed are computed exactly from the two-dimensional nonlinear Morse map. These exact nonlinear structures are interpreted as domain walls, interpolating between bound and unbound segments of the chain. Their free energy is calculated to leading order beyond the Gaussian approximation. Thermodynamic instabilities (e.g., DNA unzipping and/or thermal denaturation) can be understood in terms of domain wall formation.

Kinetic wetting of a moving planar defect by a new phase

Close to a bulk phase transition, a moving planar defect can be covered by a layer of the ordered phase. This, in fact, happens above the transition point in some finite region of the temperature-velocity diagram. In the case of a first-order transition this region is furnished with a net of nonequilibrium phase-transition lines. The topology of this net resembles that of the phase diagram of a first-order wetting transition in thermal equilibrium. In particular, there appears a kinetic complete-wetting line where a significant change of the drag coefficient of the defect is predicted.

Thermodynamic instabilities in one-dimensional particle lattices: a finite-size scaling approach

One-dimensional thermodynamic instabilities are phase transitions, not prohibited by Landau's argument because the energy of the domain wall which separates the two phases is infinite. Whether they actually occur in a given system of particles must be demonstrated on a case-by-case basis by examining the properties of the corresponding singular transfer integral (TI) equation. The present work deals with the generic Peyrard-Bishop model of DNA denaturation. In the absence of exact statements about the spectrum of the singular TI equation, I use Gauss-Hermite quadratures to achieve a single-parameter-controlled approach to rounding effects; this allows me to employ finite-size scaling concepts in order to demonstrate that a phase transition occurs and to derive the critical exponents.

Fluid adsorption near an apex: covariance between complete and critical wetting

Critical wetting is an elusive phenomenon for solid-fluid interfaces. Using interfacial models we show that the diverging length scales, which characterize complete wetting at an apex, precisely mimic critical wetting with the apex angle behaving as the contact angle. Transfer matrix, renormalization group, and mean-field analysis show that this covariance is obeyed in 2D and 3D and for long- and short-ranged forces. This connection should be experimentally accessible and provides a means of checking theoretical predictions for critical wetting.

Order of the phase transition in models of DNA thermal denaturation

We examine the behavior of a model which describes the melting of double-stranded DNA chains. The model, with displacement-dependent stiffness constants and a Morse on-site potential, is analyzed numerically; depending on the stiffness parameter, it is shown to have either (i) a second-order transition with nu( perpendicular) = -beta = 1,nu(||) = gamma/2 = 2 (characteristic of short-range attractive part of the Morse potential) or (ii) a first-order transition with finite melting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents nu( perpendicular) = -beta = 1/2,nu(||) = gamma/2 = 1.

Wetting films on chemically heterogeneous substrates

Based on a microscopic density functional theory, we investigate the morphology of thin liquid-like wetting films adsorbed on substrates endowed with well-defined chemical heterogeneities. As paradigmatic cases we focus on a single chemical step and on a single stripe. In view of applications in microfluidics, the accuracy of guiding liquids by chemical microchannels is discussed. Finally we give a general prescription of how to investigate theoretically the wetting properties of substrates with arbitrary chemical structures.