Geometry-induced phase transition in fluids: capillary prewetting

Phase Transitions and Electrochemical Properties of Ionic Liquids and Ionic Liquid-Solvent Mixtures

Recent advances in studies of ionic liquids (IL) and ionic liquid-solvent mixtures are reviewed. Selected experimental, simulation, and theoretical results for electrochemical, thermodynamical, and structural properties of IL and IL-solvent mixtures are described. Special attention is paid to phenomena that are not predicted by the classical theories of the electrical double layer or disagree strongly with these theories. We focus on structural properties, especially on distribution of ions near electrodes, on electrical double layer capacitance, on effects of confinement, including decay length of a dissjoining pressure between confinig plates, and on demixing phase transition. In particular, effects of the demixing phase transition on electrochemical properties of ionic liquid-solvent mixtures for different degrees of confinement are presented.

Filling, depinning, unbinding: Three adsorption regimes for nanocorrugated substrates

We study adsorption at periodically corrugated substrates formed by scoring rectangular grooves into a planar solid wall which interacts with the fluid via long-range (dispersion) forces. The grooves are assumed to be macroscopically long but their depth, width, and separations can all be molecularly small. We show that the entire adsorption process can be divided into three parts consisting of (i) filling the grooves by a capillary liquid; (ii) depinning of the liquid-gas interface from the wall edges; and (iii) unbinding of the interface from the top of the wall, which is accompanied by a rapid but continuous flattening of its shape. Using a nonlocal density functional theory and mesoscopic interfacial models all the regimes are discussed in some detail to reveal the complexity of the entire process and subtle aspects that affect its behavior. In particular, it is shown that the nature of the depinning phenomenon is governed by the width of the wall pillars (separating grooves), while the width of the grooves only controls the location of the depinning first-order transition, if present.

Dynamics of the Desai-Zwanzig model in multiwell and random energy landscapes

We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. 19, 1 (1978)JSTPBS0022-471510.1007/BF01020331]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multiwell potential energy landscape, coupled via a Curie-Weiss type (quadratic) interaction potential. The location and depth of the local minima of the potential are either deterministic or random. We characterize the structure and nature of bifurcations and phase transitions for this system, by means of extensive numerical simulations and of analytical calculations for an explicitly solvable model. Our numerical experiments are based on Monte Carlo simulations, the numerical solution of the time-dependent nonlinear Fokker-Planck (McKean-Vlasov) equation, the minimization of the free-energy functional, and a continuation algorithm for the stationary solutions.

Microscopic aspects of wetting using classical density functional theory

Wetting is a rather efficient mechanism for nucleation of a phase (typically liquid) on the interface between two other phases (typically solid and gas). In many experimentally accessible cases of wetting, the interplay between the substrate structure, and the fluid-fluid and fluid-substrate intermolecular interactions brings about an entire 'zoo' of possible fluid configurations, such as liquid films with a thickness of a few nanometers, liquid nanodrops and liquid bridges. These fluid configurations are often associated with phase transitions occurring at the solid-gas interface and at lengths of just several molecular diameters away from the substrate. In this special issue article, we demonstrate how a fully microscopic classical density-functional framework can be applied to the efficient, rational and systematic exploration of the rich phase space of wetting phenomena. We consider a number of model prototype systems such as wetting on a planar wall, a chemically patterned wall and a wedge. Through density-functional computations we demonstrate that for these simply structured substrates the behaviour of the solid-gas interface is already highly complex and non-trivial.

Continuous condensation in nanogrooves

We consider condensation in a capillary groove of width L and depth D, formed by walls that are completely wet (contact angle θ=0), which is in a contact with a gas reservoir of the chemical potential μ. On a mesoscopic level, the condensation process can be described in terms of the midpoint height ℓ of a meniscus formed at the liquid-gas interface. For macroscopically deep grooves (D→∞), and in the presence of long-range (dispersion) forces, the condensation corresponds to a second-order phase transition, such that ℓ∼(μ_{cc}-μ)^{-1/4} as μ→μ_{cc}^{-} where μ_{cc} is the chemical potential pertinent to capillary condensation in a slit pore of width L. For finite values of D, the transition becomes rounded and the groove becomes filled with liquid at a chemical potential higher than μ_{cc} with a difference of the order of D^{-3}. For sufficiently deep grooves, the meniscus growth initially follows the power law ℓ∼(μ_{cc}-μ)^{-1/4}, but this behavior eventually crosses over to ℓ∼D-(μ-μ_{cc})^{-1/3} above μ_{cc}, with a gap between the two regimes shown to be δ[over ¯]μ∼D^{-3}. Right at μ=μ_{cc}, when the groove is only partially filled with liquid, the height of the meniscus scales as ℓ^{*}∼(D^{3}L)^{1/4}. Moreover, the chemical potential (or pressure) at which the groove is half-filled with liquid exhibits a nonmonotonic dependence on D with a maximum at D≈3L/2 and coincides with μ_{cc} when L≈D. Finally, we show that condensation in finite grooves can be mapped on the condensation in capillary slits formed by two asymmetric (competing) walls a distance D apart with potential strengths depending on L. All these predictions, based on mesoscopic arguments, are confirmed by fully microscopic Rosenfeld's density functional theory with a reasonable agreement down to surprisingly small values of both L and D.

Dynamical density functional theory with hydrodynamic interactions in confined geometries

We study the dynamics of colloidal fluids in both unconfined geometries and when confined by a hard wall. Under minimal assumptions, we derive a dynamical density functional theory (DDFT) which includes hydrodynamic interactions (HI; bath-mediated forces). By using an efficient numerical scheme based on pseudospectral methods for integro-differential equations, we demonstrate its excellent agreement with the full underlying Langevin equations for systems of hard disks in partial confinement. We further use the derived DDFT formalism to elucidate the crucial effects of HI in confined systems.

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.

Modified Kelvin Equations for Capillary Condensation in Narrow and Wide Grooves

We consider the location and order of capillary condensation transitions occurring in deep grooves of width L and depth D. For walls that are completely wet by liquid (contact angle θ=0) the transition is continuous and its location is not sensitive to the depth of the groove. However, for walls that are partially wet by liquid, where the transition is first order, we show that the pressure at which it occurs is determined by a modified Kelvin equation characterized by an edge contact angle θ_{E} describing the shape of the meniscus formed at the top of the groove. The dependence of θ_{E} on the groove depth D relies, in turn, on whether corner menisci are formed at the bottom of the groove in the low density gaslike phase. While for macroscopically wide grooves these are always present when θ<45° we argue that their formation is inhibited in narrow grooves. This has a number of implications including that the local pinning of the meniscus and location of the condensation transition is different depending on whether the contact angle is greater or less than a universal value θ^{*}≈31°. Our arguments are supported by detailed microscopic density functional theory calculations that show that the modified Kelvin equation remains highly accurate even when L and D are of the order of tens of molecular diameters.

Edge contact angle and modified Kelvin equation for condensation in open pores

We consider capillary condensation transitions occurring in open slits of width L and finite height H immersed in a reservoir of vapor. In this case the pressure at which condensation occurs is closer to saturation compared to that occurring in an infinite slit (H=∞) due to the presence of two menisci that are pinned near the open ends. Using macroscopic arguments, we derive a modified Kelvin equation for the pressure p_{cc}(L;H) at which condensation occurs and show that the two menisci are characterized by an edge contact angle θ_{e} that is always larger than the equilibrium contact angle θ, only equal to it in the limit of macroscopic H. For walls that are completely wet (θ=0) the edge contact angle depends only on the aspect ratio of the capillary and is well described by θ_{e}≈sqrt[πL/2H] for large H. Similar results apply for condensation in cylindrical pores of finite length. We test these predictions against numerical results obtained using a microscopic density-functional model where the presence of an edge contact angle characterizing the shape of the menisci is clearly visible from the density profiles. Below the wetting temperature T_{w} we find very good agreement for slit pores of widths of just a few tens of molecular diameters, while above T_{w} the modified Kelvin equation only becomes accurate for much larger systems.

Classical density functional study of wetting transitions on nanopatterned surfaces

Even simple fluids on simple substrates can exhibit very rich surface phase behaviour. To illustrate this, we consider fluid adsorption on a planar wall chemically patterned with a deep stripe of a different material. In this system, two phase transitions compete: unbending and pre-wetting. Using microscopic density-functional theory, we show that, for thin stripes, the lines of these two phase transitions may merge, leading to a new two-dimensional-like wetting transition occurring along the walls. The influence of intermolecular forces and interfacial fluctuations on this phase transition and at complete pre-wetting are considered in detail.

Thermostability analysis of line-tension-associated nucleation at a gas-liquid interface

The influence of line tension on the thermostability of a droplet nucleated from an oversaturated vapor at the interface of the vapor and another immiscible liquid is investigated. Along with the condition of mechanical equilibrium, the notion of extremization of the reversible work of formation is considered to obtain the critical parameters related to heterogeneous nucleation. From the energetic formulation, the critical reversible work of formation is found to be greater than that of homogeneous nucleation for high value of the positive line tension. On the other hand, for high value of the negative line tension, the critical reversible work of formation becomes negative. Therefore, these thermodynamic instabilities under certain substrate wettability situations necessitate a free-energetics-based stability of the nucleated droplet, because the system energy is not minimized under these conditions. This thermostability is analogous to the transition-based stability proposed by Widom [B. Widom, J. Phys. Chem. 99, 2803 (1995)]10.1021/j100009a041 in the case of partial wetting phenomena along with the positive line tension. The thermostability analysis limits the domain of the solution space of the present critical-value problem as the thermodynamic transformation in connection with homogeneous and workless nucleation is considered. Within the stability range of the geometry-based wetting parameters, three limiting modes of nucleation, i.e., total-dewetting-related homogeneous nucleation, and total-wetting-associated and total-submergence-associated workless nucleation scenarios, are identified. Either of the two related limiting wetting scenarios of workless nucleation, namely, total wetting and total submergence, is found to be favorable depending on the geometry-based wetting conditions. The line-tension-associated nucleation on a liquid surface can be differentiated from that on a rigid substrate, as in the former, the stability based on mechanical equilibrium and a typical case of workless nucleation with complete submergence are observed.

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.

Density functional study of condensation in capped capillaries

We study liquid adsorption in narrow rectangular capped capillaries formed by capping two parallel planar walls (a slit pore) with a third wall orthogonal to the two planar walls. The most important transition in confined fluids is arguably condensation, where the pore becomes filled with the liquid phase which is metastable in the bulk. Depending on the temperature T, the condensation in capped capillaries can be first-order (at T≤Tcw) or continuous (at T>Tcw), where Tcw is the capillary wetting temperature. At T>Tcw, the capping wall can adsorb mesoscopic amounts of metastable under-condensed liquid. The onset of condensation is then manifested by the continuous unbinding of the interface between the liquid adsorbed on the capping wall and the gas filling the rest of the capillary volume. In wide capped capillaries there may be a remnant of wedge filling transition, which is manifested by the adsorption of liquid drops in the corners. Our classical statistical mechanical treatment predicts a possibility of three-phase coexistence between gas, corner drops and liquid slabs adsorbed on the capping wall. In sufficiently wide capillaries we find that thick prewetting films of finite length may be nucleated at the capping wall below the boundary of the prewetting transition. Prewetting then proceeds in a continuous manner manifested by the unbinding interface between the thick and thin films adsorbed on the side walls. Our analysis is based on a detailed numerical investigation of the density functional theory for the fluid equilibria for a number of illustrative case studies.

Structures of simple liquids in contact with nanosculptured surfaces

We present a density functional study of Lennard-Jones liquids in contact with a nanocorrugated wall. The corresponding substrate potential is taken to exhibit a repulsive hard core and a Van der Waals attraction. The corrugation is modeled by a periodic array of square nanopits. We have used the modified Rosenfeld density functional in order to study the interfacial structure of these liquids which with respect to their thermodynamic bulk state are considered to be deep inside their liquid phase. We find that already considerably below the packing fraction of bulk freezing of these liquids, inside the nanopits a three-dimensional-like density localization sets in. If the sizes of the pits are commensurate with the packing requirements, we observe high-density spots separated from each other in all spatial directions by liquid of comparatively very low density. The number, shape, size, and density of these high-density spots depend sensitively on the depth and width of the pits. Outside the pits, only layering is observed; above the pit openings these layers are distorted with the distortion reaching up to a few molecular diameters. We discuss quantitatively how this density localization is affected by the geometrical features of the pits and how it evolves upon increasing the bulk packing fraction. Our results are transferable to colloidal systems and pit dimensions corresponding to several diameters of the colloidal particles. For such systems the predicted unfolding of these structural changes can be studied experimentally on much larger length scales and more directly (e.g., optically) than for molecular fluids which typically call for sophisticated x-ray scattering.

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.

Condensation and evaporation transitions in deep capillary grooves

We study the order of capillary condensation and evaporation transitions of a simple fluid adsorbed in a deep capillary groove using a fundamental measure density functional theory (DFT). The walls of the capillary interact with the fluid particles via long-ranged, dispersion, forces while the fluid-fluid interaction is modelled as a truncated Lennard-Jones-like potential. We find that below the wetting temperature Tw condensation is first-order and evaporation is continuous with the metastability of the condensation being well described by the complementary Kelvin equation. In contrast above Tw both phase transitions are continuous and their critical singularities are determined. In addition we show that for the evaporation transition above Tw there is an elegant mapping, or covariance, with the complete wetting transition occurring at a planar wall. Our numerical DFT studies are complemented by analytical slab model calculations which explain how the asymmetry between condensation and evaporation arises out of the combination of long-ranged forces and substrate geometry.