Complete wetting on a linear wedge

Capillary condensation between nonparallel walls

We study the condensation of fluids confined by a pair of nonparallel plates of finite height H. We show that such a system experiences two types of condensation, termed single and double pinning, which can be characterized by one (single-pinning) or two (double-pinning) edge contact angles describing the shape of menisci pinned at the system edges. For both types of capillary condensation, we formulate the Kelvin-like equation and determine the conditions under which the given type of condensation occurs. We construct the global phase diagram revealing a reentrant phenomenon pertinent to the change of the capillary condensation type upon varying the inclination of the walls. Asymptotic properties of the system are discussed and a link with related phase phenomena in different systems is made. Finally, we show that the change from a single- to a double-pinned state is a continuous transition, the character of which depends on the wetting properties of the walls.

Kelvin equation for bridging transitions

We study bridging transitions between a pair of nonplanar surfaces. We show that the transition can be described using a generalized Kelvin equation by mapping the system to a slit of finite length. The proposed equation is applied to analyze the asymptotic behavior of the growth of the bridging film, which occurs when the confining walls are gradually flattened. This phenomenon is characterized by a power-law divergence with geometry-dependent critical exponents that we determine for a wide class of walls' geometries. In particular, for a linear-wedge model, a covariance law revealing a relation between a geometric and Young's contact angle is presented. These predictions are shown to be fully in line with the numerical results obtained from a microscopic (classical) density functional theory.

Critical behaviour of the contact angle within nonwetting gaps

Recent density functional theory and simulation studies of fluid adsorption near planar walls in systems where the wall-fluid and fluid-fluid interactions have different ranges, have shown that critical point wetting may not occur and instead nonwetting gaps appear in the surface phase diagram, separating lines of wetting and drying transitions, that extend up to the critical temperatureTc. Here we clarify the features of the surface phase diagrams that are common, regardless of the range and balance of the forces, showing, in particular, that the lines of temperature driven wetting and drying transitions, as well as lines of constant contact angleπ>θ>0, always converge to an ordinary surface phase transition atTc. When nonwetting gaps appear the contact angle either vanishes or tends toπast≡(Tc-T)/Tc→0. More specifically, when the wall-fluid interaction is long-ranged (dispersion-like) and the fluid-fluid short-ranged we estimateπ-θ∝t0.16, compared withθ∝t0.77when the wall-fluid interaction is short-ranged and the fluid-fluid dispersion-like, allowing for the effects of bulk critical fluctuations. The universal convergence of the lines of constant contact angle implies that critical point filling always occurs for fluids adsorbed in wedges.

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.

Meniscus osculation and adsorption on geometrically structured walls

We study the adsorption of simple fluids at smoothly structured, completely wet walls and show that a meniscus osculation transition occurs when the Laplace and geometrical radii of curvature of locally parabolic regions coincide. Macroscopically, the osculation transition is of fractional, 7/2, order and separates regimes in which the adsorption is microscopic, containing only a thin wetting layer, and mesoscopic, in which a meniscus exists. We develop a scaling theory for the rounding of the transition due to thin wetting layers and derive critical exponent relations that determine how the interfacial height scales with the geometrical radius of curvature. Connection with the general geometric construction proposed by Rascón and Parry is made. Our predictions are supported by a microscopic model density functional theory for drying at a sinusoidally shaped hard wall where we confirm the order of the transition and also an exact sum rule for the generalized contact theorem due to Upton. We show that as bulk coexistence is approached the adsorption isotherm separates into three regimes: A preosculation regime where it is microscopic, containing only a thin wetting layer; a mesoscopic regime, in which a meniscus sits within the troughs; and finally another microscopic regime where the liquid-gas interface unbinds from the crests of the substrate.

Bridging of liquid drops at chemically structured walls

Using mesoscopic interfacial models and microscopic density functional theory we study fluid adsorption at a dry wall decorated with three completely wet stripes of width L separated by distances D_{1} and D_{2}. The stripes interact with the fluid with long-range forces inducing a large finite-size contribution to the surface free energy. We show that this nonextensive free-energy contribution scales with lnL and drives different types of bridging transition corresponding to the merging of liquid drops adsorbed at neighboring wetting stripes when the separation between them is molecularly small. We determine the surface phase diagram and show that this exhibits two triple points, where isolated drops, double drops, and triple drops coexist. For the symmetric case, D_{1}=D_{2}≡D, our results also confirm that the equilibrium droplet configuration always has the symmetry of the substrate corresponding to either three isolated drops when D is large or a single triple drop when D is small; however, symmetry-broken configurations do occur in a metastable part of the phase diagram which lies very close to the equilibrium-bridging phase boundary. Implications for phase transitions on other types of patterned surface are considered.

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.

Influence of intermolecular forces at critical-point wedge filling

We use microscopic density functional theory to study filling transitions in systems with long-ranged wall-fluid and short-ranged fluid-fluid forces occurring in a right-angle wedge. By changing the strength of the wall-fluid interaction we can induce both wetting and filling transitions over a wide range of temperatures and study the order of these transitions. At low temperatures we find that both wetting and filling transitions are first order in keeping with predictions of simple local effective Hamiltonian models. However close to the bulk critical point the filling transition is observed to be continuous even though the wetting transition remains first order and the wetting binding potential still exhibits a small activation barrier. The critical singularities for adsorption for the continuous filling transitions depend on whether retarded or nonretarded wall-fluid forces are present and are in excellent agreement with predictions of effective Hamiltonian theory even though the change in the order of the transition was not anticipated.

Filling and wetting transitions on sinusoidal substrates: a mean-field study of the Landau-Ginzburg model

We study the interfacial phenomenology of a fluid in contact with a one-dimensional array of infinitely long grooves of sinusoidal section, characterized by the periodicity length L and amplitude A. The system is modelled by the Landau-Ginzburg-Wilson functional, with fluid-substrate couplings which control the wettability of the substrate. We investigate the filling and wetting phenomena within the mean-field approximation, and compare with the predictions of the macroscopic and interfacial Hamiltonian theories. For large values of L and under bulk coexistence conditions, we observe first-order filling transitions between dry (D) and partially filled (F) interfacial states, and wetting transitions between partially filled F and completely wet (W) interfacial states of the same order as for the flat substrate. Depending on the order of the wetting transition, the transition temperature is either shifted towards lower temperatures for first-order wetting or it coincides with the wetting temperature on the flat substrate for continuous wetting. On the other hand, if the groove height is of order of the correlation length, only wetting transitions between D and W states are observed under bulk coexistence conditions. For this case, the transition temperature shift obeys approximately Wenzel's phenomenological law if the substrate favors first-order wetting, but it remains unshifted for continuous wetting. The borderline between the small and large L regimes correspond to a D - F - W triple point if wetting is first-order, and a D - F critical point for continuous wetting. Beyond bulk coexistence conditions, filling and first-order wetting transitions continue into off-coexistence filling and prewetting lines, which end up at critical points. Our findings show that the macroscopic theory only describes accurately the filling transition close to bulk coexistence and large L, while microscopic structure of the fluid is essential to understand wetting and filling away from bulk coexistence.

Capillary contact angle in a completely wet groove

We consider the phase equilibria of a fluid confined in a deep capillary groove of width L with identical side walls and a bottom made of a different material. All walls are completely wet by the liquid. Using density functional theory and interfacial models, we show that the meniscus separating liquid and gas phases at two phase capillary coexistence meets the bottom capped end of the groove at a capillary contact angle θ(cap)(L) which depends on the difference between the Hamaker constants. If the bottom wall has a weaker wall-fluid attraction than the side walls, then θ(cap) > 0 even though all the isolated walls are themselves completely wet. This alters the capillary condensation transition which is now first order; this would be continuous in a capped capillary made wholly of either type of material. We show that the capillary contact angle θ(cap)(L) vanishes in two limits, corresponding to different capillary wetting transitions. These occur as the width (i) becomes macroscopically large, and (ii) is reduced to a microscopic value determined by the difference in Hamaker constants. This second wetting transition is characterized by large scale fluctuations and essential critical singularities arising from marginal interfacial interactions.

Phase separation in a wedge: exact results

The exact theory of phase separation in a two-dimensional wedge is derived from the properties of the order parameter and boundary condition changing operators in field theory. For a shallow wedge we determine the passage probability for an interface with endpoints on the boundary. For generic opening angles we exhibit the fundamental origin of the filling transition condition and of the property known as wedge covariance.

Complete wetting near an edge of a rectangular-shaped substrate

We consider fluid adsorption near a rectangular edge of a solid substrate that interacts with the fluid atoms via long range (dispersion) forces. The curved geometry of the liquid-vapour interface dictates that the local height of the interface above the edge ℓ(E) must remain finite at any subcritical temperature, even when a macroscopically thick film is formed far from the edge. Using an interfacial Hamiltonian theory and a more microscopic fundamental measure density functional theory (DFT), we study the complete wetting near a single edge and show that ℓ(E)(0)-ℓ(E)(δμ)∼δμ(β(CO)(E), as the chemical potential departure from the bulk coexistence δμ = μ(s)(T) - μ tends to zero. The exponent β(CO)(E) depends on the range of the molecular forces and in particular β(CO)(E)=2/3 for three-dimensional systems with van der Waals forces. We further show that for a substrate model that is characterised by a finite linear dimension L, the height of the interface deviates from the one at the infinite substrate as δℓE(L) ∼ L(-1) in the limit of large L. Both predictions are supported by numerical solutions of the DFT.

Filling and wetting transitions at grooved substrates

The wetting and filling properties of a fluid adsorbed on a solid grooved substrate are studied by means of a microscopic density functional theory. The grooved substrates are modelled using a solid slab, interacting with the fluid particles via long-range dispersion forces, to which a one-dimensional array of infinitely long rectangular grooves is sculpted. By investigating the effect of the groove periodicity and the width of the grooves and the ridges, a rich variety of different wetting morphologies is found. In particular, we show that for a saturated ambient gas, the adsorbent can occur in one of four wetting states characterized by (i) empty grooves, (ii) filled grooves, (iii) a formation of mesoscopic hemispherical caps (iv) a macroscopically wet surface. The character of the transition between particular regimes, that also extend off-coexistence, sensitively depends on the model geometry. The temperature at which the system becomes completely wet is considerably higher than that for a flat wall.

Density functional study of complete, first-order and critical wedge filling transitions

We present numerical studies of complete, first-order and critical wedge filling transitions, at a right angle corner, using a microscopic fundamental measure density functional theory. We consider systems with short-ranged, cut-off Lennard-Jones, fluid-fluid forces and two types of wall-fluid potential: a purely repulsive hard wall and also a long-ranged potential with three different strengths. For each of these systems we first determine the wetting properties occurring at a planar wall, including any wetting transition and the dependence of the contact angle on temperature. The hard wall corner is completely filled by vapour on approaching bulk coexistence and the numerical results for the growth of the meniscus thickness are in excellent agreement with effective Hamiltonian predictions for the critical exponents and amplitudes, at leading and next-to-leading order. In the presence of the attractive wall-fluid interaction, the corresponding planar wall-fluid interface exhibits a first-order wetting transition for each of the interaction strengths considered. In the right angle wedge geometry the two strongest interactions produce first-order filling transitions while for the weakest interaction strength, for which wetting and filling occur closest to the bulk critical point, the filling transition is second-order. For this continuous transition the critical exponent describing the divergence of the meniscus thickness is found to be in good agreement with effective Hamiltonian predictions.

Mixing-demixing phase diagram for simple liquids in nonuniform electric fields

We deduce the mixing-demixing phase diagram for binary liquid mixtures in an electric field for various electrode geometries and arbitrary constitutive relation for the dielectric constant. By focusing on the behavior of the liquid-liquid interface, we produce simple analytic expressions for the dependence of the interface location on experimental parameters. We also show that the phase diagram contains regions where liquid separation cannot occur under any applied field. The analytic expression for the boundary "electrostatic binodal" line reveals that the regions' size and shape depend strongly on the dielectric relation between the liquids. Moreover, we predict the existence of an "electrostatic spinodal" line that identifies conditions where the liquids are in a metastable state. We finally construct the phase diagram for closed systems by mapping solutions onto those of an open system via an effective liquid composition. For closed systems at a fixed temperature and mixture composition, liquid separation occurs in a finite "window" of surface potential (or charge density). Higher potentials or charge densities counterintuitively destroy the interface, leading to liquid mixing. These results give valuable guides for experiments by providing easily testable predictions for how liquids behave in nonuniform electric fields.

The order of condensation in capillary grooves

We consider capillary condensation in a deep groove of width L. The transition occurs at a pressure p(co)(L) described, for large widths, by the Kelvin equation p(sat) - p(co)(L) = 2σ cosθ/L, where θ is the contact angle at the side walls and σ is the surface tension. The order of the transition is determined by the contact angle of the capped end θcap; it is continuous if the liquid completely wets the cap, and first-order otherwise. When the transition is first-order, corner menisci at the bottom of the capillary lead to a pronounced metastability, determined by a complementary Kelvin equation Δp(L) = 2σ sinθcap/L. On approaching the wetting temperature of the capillary cap, the corner menisci merge and a single meniscus unbinds from the bottom of the groove. Finite-size scaling shifts, crossover behaviour and critical singularities are determined at mean-field level and beyond. Numerical and experimental results showing the continuous nature of condensation for θcap = 0 and the influence of corner menisci on adsorption isotherms are presented.

Critical point wedge filling

We present results of a microscopic density functional theory study of wedge filling transitions, at a right-angle wedge, in the presence of dispersionlike wall-fluid forces. Far from the corner the walls of the wedge show a first-order wetting transition at a temperature T(w) which is progressively closer to the bulk critical temperature T(c) as the strength of the wall forces is reduced. In addition, the meniscus formed near the corner undergoes a filling transition at a temperature T(f)<T(w), the value of which is found to be in excellent agreement with macroscopic predictions. We show that the filling transition is first order if it occurs far from the critical point but is continuous if T(f) is close to T(c) even though the walls still show first-order wetting behavior. For this continuous transition the distance of the meniscus from the apex grows as ℓ(w)≈(T(f)-T)(-β(w)) with the critical exponent β(w)≈0.46±0.05 in good agreement with the phenomenological effective Hamiltonian prediction. Our results suggest that critical filling transitions, with accompanying large scale universal interfacial fluctuation effects, are more generic than thought previously, and are experimentally accessible.

Complete wetting of elastically responsive substrates

We analyze theoretically complete wetting of a substrate supporting an array of parallel, vertical plates which can tilt elastically. The adsorbed liquid tilts the plates, inducing clustering, and thus modifies the substrate geometry. In turn, this change in geometry alters the wetting properties of the substrate and, consequently, the adsorption of liquid. This geometry-wetting feedback loop leads to stepped adsorption isotherms with each step corresponding to an abrupt change in the substrate geometry. We discuss how this can be used for constructing substrates with tunable wetting and adsorption properties.

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.

Fluid adsorption at the base of a cylinder

We consider the adsorption of fluid at a cylinder protruding from a flat substrate. For small contact angles θ, a liquid drop condenses at the base, the size of which is determined by macroscopic arguments. The adsorption exhibits scaling behavior related to a number of phase transitions and, for systems with short-ranged forces, shows a remarkable property: for small θ, the height and width of the drop are near identical to expressions for the thickness and parallel correlation length for microscopic wetting films. The only difference is that the bulk correlation length is replaced by the cylinder radius. 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.

Capillary condensation and evaporation in alumina nanopores with controlled modulations

Capillary condensation in nanoporous anodic aluminum oxide presenting not interconnected pores with controlled modulations is studied using adsorption experiments and molecular simulations. Both the experimental and simulation data show that capillary condensation and evaporation are driven by the smallest size of the nanopore (constriction). The adsorption isotherms for the open and closed pores are almost identical if constrictions are added to the system. The latter result implies that the type of pore ending does not matter in modulated pores. Thus, the presence of hysteresis loops observed in adsorption isotherms measured in straight nanopores with closed bottom ends can be explained in terms of geometrical inhomogeneities along the pore axis. More generally, these results provide a general picture of capillary condensation and evaporation in constricted or modulated pores that can be used for the interpretation of adsorption in disordered porous materials.

Dynamics of nanodroplets on topographically structured substrates

Mesoscopic hydrodynamic equations are solved to investigate the dynamics of nanodroplets positioned near a topographic step of the supporting substrate. Our results show that the dynamics depends on the characteristic length scales of the system given by the height of the step and the size of the nanodroplets as well as on the constituting substances of both the nanodroplets and the substrate. The lateral motion of nanodroplets far from the step can be described well in terms of a power law of the distance from the step. In general the direction of motion depends on the details of the effective laterally varying intermolecular forces. But for nanodroplets positioned far from the step it is solely given by the sign of the Hamaker constant of the system. Moreover, our study reveals that the steps always act as a barrier for transporting liquid droplets from one side of the step to the other.

Adsorption hysteresis in self-ordered nanoporous alumina

We performed systematic adsorption studies using self-ordered nanoporous anodic aluminum oxide (AAO) in an extended range of mean pore diameters and with different pore topologies. These matrices were characterized by straight cylindrical pores having a narrow pore size distribution and no interconnections. Pronounced hysteresis loops between adsorption and desorption cycles were observed even in the case of pores closed at one end. These results are in contrast with macroscopic theoretical models and detailed numerical simulations of the adsorption in a single pore. Extensive measurements involving adsorption isotherms, reversal curves, and subloops carried out in closed-bottom pores suggest that the pores do not desorb independently from one another.

Liquid-vapor coexistence at a mesoporous substrate

The condensation of hexane vapor onto a mesoporous Si substrate with a pore radius of 3.5 nm has been studied by means of volumetry and ellipsometry. The filling fraction of the pores and the coverage of the substrate have been determined. The coverage of the regime after the completion of capillary condensation has been compared to recent theoretical work.

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.

Complete wetting of pits and grooves

For one-component volatile fluids governed by dispersion forces an effective interface Hamiltonian, derived from a microscopic density functional theory, is used to study complete wetting of geometrically structured substrates. Also the long range of substrate potentials is explicitly taken into account. Four types of geometrical patterns are considered: i) one-dimensional periodic arrays of rectangular or parabolic grooves and ii) two-dimensional lattices of cylindrical or parabolic pits. We present numerical evidence that at the centers of the cavity regions the thicknesses of the adsorbed films obey precisely the same geometrical covariance relation, which has been recently reported for complete cone and wedge filling. However, this covariance does not hold for the laterally averaged wetting film thicknesses. For sufficiently deep cavities with vertical walls and close to liquid-gas phase coexistence in the bulk, the film thicknesses exhibit an effective planar scaling regime, which as a function of undersaturation is characterized by a power law with the common critical exponent -1/3 as for a flat substrate, but with the amplitude depending on the geometrical features.

Motion of nanodroplets near edges and wedges

Nanodroplets residing near wedges or edges of solid substrates exhibit a disjoining pressure induced dynamics. Our nanoscale hydrodynamic calculations reveal that nonvolatile droplets are attracted or repelled from edges or wedges depending on details of the corresponding laterally varying disjoining pressure generated, e.g., by a possible surface coating.

Complete wetting of curved microscopic channels

We have measured the adsorption of argon films on arrays of microscopic nonlinear cusps and of semicircular channels. In the former case, we observe a distinct crossover from a planarlike to a geometry dependent growth behavior near liquid-vapor bulk coexistence, characterized by a growth exponent chi equal to -0.96+/-0.04 in very good agreement with the predictions of a recent scaling theory [C. Rascon and A. O. Parry, J. Chem. Phys. 112, 5175 (2000)]. The crossover location is also consistent with theory. Instead, on the concave channels we find a much steeper growth near saturation that may signal the formation of two menisci at both sides of the channel bottom.

Complete wetting of nanosculptured substrates

Complete wetting of geometrically structured substrates by one-component fluids with long-ranged interactions is studied theoretically. We consider periodic arrays of rectangular or parabolic grooves and lattices of cylindrical or parabolic pits. We show that the midpoint interfacial heights within grooves and pits are related in the same way as for complete wedge and cone filling. For sufficiently deep cavities with vertical walls and small undersaturation, an effective planar scaling regime emerges. The scaling exponent is -1/3 in all cases studied, and only the amplitudes depend on the geometrical features. We find quantitative agreement with recent experimental data for such systems.

Extended wedge covariance for wetting and filling transitions

Fluid adsorption on nonplanar and heterogeneous substrates is studied using a simple interfacial model. For systems with short-ranged forces, we find that, by tuning the local strength of the substrate potential, it is possible to find the exact equilibrium interfacial profile as a functional of the wall shape psi x. The tuning of the local substrate potential takes the form of a gauge condition theta x=+/-psi x, where theta x can be interpreted as a local effective contact angle. For wedgelike geometries with asymptotic tilt angle alpha, the midpoint interfacial height and roughness satisfy the same covariance relations previously found for simple linear wedges. For troughlike geometries satisfying the gauge condition, covariance is also found for the two-point correlation function. Predictions for more microscopic Landau and Ising models are also discussed.

Liquids on topologically nanopatterned surfaces

We report here surface x-ray scattering studies of the adsorption of simple hydrocarbon liquid films on nanostructured surfaces-silicon patterned by an array of nanocavities. Two different regimes, filling and growing, are observed for the wetting film evolution as a function of the chemical potential offset from the bulk liquid-vapor coexistence. The strong influence of geometrical effects is manifested by a dependence of liquid adsorption in the nanocavities that is stronger than the van der Waals behavior for flat surfaces. The observed dependence is, however, much weaker than predicted for the infinitely deep parabolic cavities, suggesting that the finite-size effects contribute significantly to the observed adsorption behavior.

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.

Capillary condensation in linear mesopores of different shape

The hysteresis and kinetics of capillary condensation of N2 and Ar in linear mesopores, produced by etching of Si wafers, have been studied for different pore shapes, including the ink bottle geometry. Pore blocking has been observed in the solid state of the pore fillings, but not in the liquid state. We conclude that individual local geometries such as the pore mouth, a blind end, or a single constriction have no effect on the shape of sorption isotherms, that the pore space should be regarded as a statistical ensemble of pore segments with a lot of quenched disorder.

Wedge filling and interface delocalization in finite Ising lattices with antisymmetric surface fields

Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic LxLxL(y) Ising lattices with nearest neighbor ferromagnetic exchange and four free LxL(y) surfaces, at which antisymmetric surface fields +/-H(s) act, are studied for a wide range of linear dimensions (4</=L</=320, 30</=L(y)</=1000), in an attempt to clarify finite size effects on the wedge filling transition in this "double-wedge" geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a liquid-gas transition in a pore with quadratic cross section, where two walls favor the liquid and the other two walls favor the gas. For temperatures T below the bulk critical temperature T(c) this boundary condition (where periodic boundary conditions are used in the y direction along the wedges) leads to the formation of two domains with oppositely oriented magnetization and separated by an interface. For L,L(y)--> infinity and T larger than the filling transition temperature T(f)(H(s)), this interface runs from the one wedge where the surface planes with a different sign of the surface field meet (on average) straight to the opposite wedge, so that the average magnetization of the system is zero. For T<T(f)(H(s)), however, this interface is bound either to the wedge where the two surfaces with field -H(s) meet (then the total magnetization m of the system is positive) or to the opposite wedge (then m<0). The distance l(0) of the interface midpoint from the wedges is studied as T-->T(f)(H(s)) from below, as is the corresponding behavior of the magnetization and its moments. We consider the variation of l(0) for T>T(f)(H(s)) as a function of a bulk field and find that the associated exponents agree with theoretical predictions. The correlation length xi(y) in the y direction along the wedges is also studied, and we find no transition for finite L and L(y)--> infinity. For L--> infinity the prediction l(0) proportional, variant (H(sc)-H(s))(-1/4) is verified, where H(sc)(T) is the inverse function of T(f)(H(s)) and xi(y) proportional, variant (H(sc)-H(s))(-3/4), respectively. We also find that m vanishes discontinuously at the filling transition. When the corresponding wetting transition is first order we also obtain a first-order filling transition.

Crossover effects in the wetting of adsorbed films in linear wedges

We have measured the growth of liquid Ar adsorbed on arrays of linear wedges structured in different ways. In the most regular patterns, a clear crossover from a planarlike to a geometry-dependent growth behavior is observed. This crossover is found to depend on the characteristic wedge size and its position, in the case of a regular pattern, agrees well with theoretical predictions. Near liquid-vapor bulk coexistence, the film mass is observed to diverge as a power law of the chemical potential difference from saturation with an exponent in very good agreement with the value of -2 expected for a linear wedge. This exponent is not affected by the opening angles of the wedges. The form of the next-to-leading order singular term in the asymptotic divergence of the mass has also been investigated. The experimentally determined value of the exponent is consistent with the expected theoretical result of -4/3.

Interface localization-delocalization in a double wedge: a new universality class with strong fluctuations and anisotropic scaling

Using Monte Carlo simulations and finite-size scaling methods we study "wetting" in Ising systems in a LxLxL(y) pore with quadratic cross section. Antisymmetric surface fields H(s) act on the free LxL(y) surfaces of the opposing wedges, and periodic boundary conditions are applied along the y direction. In the limit L--> infinity, L(y)/L(3)=const, the system exhibits a new type of phase transition, which is the analog of the "filling transition" that occurs in a single wedge. It is characterized by critical exponents alpha=3/4, beta=0, and gamma=5/4 for the specific heat, order parameter, and susceptibility, respectively.

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.