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 (3d), 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 2d 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 2d and 3d.
This paper is devoted to the thermally activated dynamics of the capillary condensation. We present a simple model which enables us to identify the critical nucleus involved in the transition mechanism. This simple model is then applied to calculate the nucleation barrier from which we can obtain informations on the nucleation time. These results are compared to the numerical simulation of a Landau-Ginzburg model for the liquid-vapor interface combined with a Langevin dynamics.
We study the influence of wetting on the capillary condensation for a simple fluid in a pore-like geometry, where the reference system is an infinitely long slit. The Corner Transfer Matrix Renormalization Group method has been extended to study a two-dimensional Ising model confined in an L x L geometry with equal surface fields. Our results have confirmed that in both geometries the coexistence line shift is governed by the same scaling powers, but their prefactors are different.
We investigate with Monte Carlo computer simulations the capillary phase behaviour of model colloid-polymer mixtures confined between a flat wall and a corrugated wall. The corrugation is modelled via a sine wave as a function of one of the in-plane coordinates leading to a depletion attraction between colloids and the corrugated wall that is curvature dependent. We find that for increased amplitude of corrugation the region of the phase diagram where capillary condensation occurs becomes larger. We derive a Kelvin equation for this system and compare its predictions to the simulation results.…
Using molecular simulation, we analyze the capillary condensation and evaporation processes for Argon confined in a cylindrical nanopore. For this purpose, we define the entropy of the adsorbed fluid as a reaction coordinate and determine the free energy associated with both processes along entropic pathways. For capillary condensation, we identify a complex free energy profile resulting from the multi-stage nature of this phenomenon. We find capillary condensation to proceed through the nucleation of a liquid bridge across the nanopore, followed by its expansion throughout the pore to give ri…
Within self-consistent field theory we study the phase behaviour of a symmetric binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding semi-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surface fields to the interface localisation/delocalisation transition for antisymmetric surface fields. In the former case the phase diagram has a…
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 i…
We investigate the critical behavior of a near-critical fluid confined between two parallel plates in contact with a reservoir by calculating the order parameter profile and the Casimir amplitudes (for the force density and for the grand potential). Our results are applicable to one-component fluids and binary mixtures. We assume that the walls absorb one of the fluid components selectively for binary mixtures. We propose a renormalized local functional theory accounting for the fluctuation effects. Analysis is performed in the plane of the temperature T and the order parameter in the reservoi…
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 $T_w$ condensation is first-order and evaporation is continuous with the metastability of the condensation being well described by the complementary Kelvin equation. In contrast abo…
We argue that in a fluid, or magnet, confined by adsorbing walls which favour liquid, or (+) phase, the solvation (Casimir) force in the vicinity of the critical point is strongly influenced by capillary condensation which occurs below the bulk critical temperature T_c. At T slightly below and above T_c, a small bulk field h<0, which favours gas, or (-) phase, leads to residual condensation and a solvation force which is much more attractive (at the same large wall separation) than that found exactly at the critical point. Our predictions are supported by results obtained from density-matrix r…
We propose a comprehensive theoretical description of hysteresis in capillary condensation of gases in mesoporous disordered materials. Applying mean-field density functional theory to a coarse-grained lattice-gas model, we show that the morphology of the hysteresis loops is influenced by out-of-equilibrium transitions that are different on filling and on draining. In particular, desorption may be associated to a depinning process and be percolation-like without explicit pore-blocking effects.
We study the low temperature phase equilibria of a fluid confined in an open capillary slit formed by two parallel walls separated by a distance $L$ which are in contact with a reservoir of gas. The top wall of the capillary is of finite length $H$ while the bottom wall is considered of macroscopic extent. 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 $a=L/H$ and divides into three regimes: For long capillaries, with $a<2/π$,…
A lattice-gas model with heterogeneity is developed for the description of fluid condensation in finite sized one-dimensional pores of arbitrary shape. An exact solution of the model is presented for zero-temperature that reproduces the experimentally observed dependence of the amount of fluid adsorbed in the pore on external pressure. Finite-temperature Metropolis dynamics simulations support analytical findings in the limit of low temperatures. The proposed framework is viewed as a fundamental building block of the theory of capillary condensation necessary for reliable structural analysis o…
The excess adsorption $Γ$ in two-dimensional Ising strips $(\infty \times L)$ subject to identical boundary fields, at both one-dimensional surfaces decaying in the orthogonal direction $j$ as $-h_1j^{-p}$, is studied for various values of $p$ and along various thermodynamic paths below the 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, are strongly influenced by confinement effects. Along isotherms $T=const$ the asymptotic power law dependences …
We present a theoretical study of capillary condensation of fluids adsorbed in mesoporous disordered media. Combining mean-field density functional theory with a coarse-grained description in terms of a lattice-gas model allows us to investigate both the out-of-equilibrium (hysteresis) and the equilibrium behavior. We show that the main features of capillary condensation in disordered solids result from the appearance of a complex free-energy landscape with a large number of metastable states. We detail the numerical procedures for finding these states, and the presence or absence of transitio…
Beyond capillary condensation: Shear-induced bridging transitions in patterned slits
The Czech Academy of Sciences, Institute of Chemical Process Fundamentals（捷克科学院化学过程基础研究所）；University of Chemistry and Technology Prague（布拉格化工大学）；Imperial College London（伦敦帝国理工学院）
We study the interplay between hysteresis and equilibrium behavior in capillary condensation of fluids in mesoporous disordered materials via a mean-field density functional theory of a disordered lattice-gas model. The approach reproduces all major features observed experimentally. We show that the simple van der Waals picture of metastability fails due to the appearance of a complex free-energy landscape with a large number of metastable states. In particular, hysteresis can occur both with and without an underlying equilibrium transition, thermodynamic consistency is not satisfied along the…
We present a quantitative comparison between extensive Monte Carlo simulations and self-consistent field calculations on the phase diagram and wetting behavior of a symmetric, binary (AB) polymer blend confined into a film. The flat walls attract one component via a short range interaction. The critical point of the confined blend is shifted to lower temperatures and higher concentrations of the component with the lower surface free energy. The binodals close the the critical point are flattened compared to the bulk and exhibit a convex curvature at intermediate temperatures -- a signature of …
We apply local mean-field (i.e. density functional) theory to a lattice model of a fluid in contact with a dilute, disordered gel network. The gel structure is described by a diffusion-limited cluster aggregation model. We focus on the influence of porosity on both the hysteretic and the equilibrium behavior of the fluid as one varies the chemical potential at low temperature. We show that the shape of the hysteresis loop changes from smooth to rectangular as the porosity increases and that this change is associated to disorder-induced out-of-equilibrium phase transitions that differ on adsorp…
Extending the Swendsen-Wang cluster algorithm to include both bulk (H) and surface fields (H_1) in L x L x D Ising films of thickness D and two free L x L surfaces, a Monte Carlo study of the capillary condensation critical point of the model is presented. Applying a finite-size scaling analysis where the lateral linear dimension L is varied over a wide range, the critical temperature T_c(D) and the associated critical field H_c(D) are estimated for 4 <= D <= 32 lattice spacings, for a choice of the surface field H_1 small enough that the dependence of H_c(D) on H_1 is still linear. It is show…
We report a numerical study of equilibrium phase-diagrams and interfacial properties of bulk and confined colloid-polymer mixtures using grand canonical Monte Carlo simulations. Colloidal particles are treated as hard spheres, while the polymer chains are described as soft repulsive spheres. The polymer-polymer, colloid-polymer, and wall-polymer interactions are described by density-dependent potentials derived by Bolhuis and Louis [Macromolecules, 35 (2002), p.1860]. We compared our results with those of the Asakura-Oosawa-Vrij model, that treats the polymers as ideal particles. We find that …
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 which 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…
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 $\ell$ of a meniscus formed at the liquid-gas interface. For macroscopically deep grooves ($D\to\infty$), and in the presence of long-range (dispersion) forces, the condensation corresponds to a second order phase transition, such that $\ell\sim (μ_{cc}-μ)^{-1/4}$ as $μ\toμ_{cc}^-$ where $μ…
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 int…
When a fluid that undergoes a vapor to liquid transition in the bulk is confined to a long cylindrical pore, the phase transition is shifted (mostly due to surface effects at the walls of the pore) and rounded (due to finite size effects). The nature of the phase coexistence at the transition depends on the length of the pore: For very long pores the system is axially homogeneous at low temperatures. At the chemical potential where the transition takes place fluctuations occur between vapor-like and liquid-like states of the cylinder as a whole. At somewhat higher temperatures (but still far b…
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 $θ^{\rm cap}(L)$ 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^{\rm cap}>…
The Derjaguin - Broekhoff - de Boer theory of capillary condensation is employed to describe deformation of mesoporous solids in the course of adsorption-desorption hysteretic cycles. We suggest a thermodynamic model, which relates the mechanical stress induced by adsorbed phase to the adsorption isotherm. Analytical expressions are derived for the dependence of the solvation pressure on the vapor pressure. The proposed method provides a description of non-monotonic hysteretic deformation during capillary condensation without invoking any adjustable parameters. The method is showcased drawing …
We study the competition between local (bridging) and global condensation of fluid in a chemically heterogeneous capillary slit made from two parallel adjacent walls each patterned with a single stripe. Using a mesoscopic modified Kelvin equation, which determines the shape of the menisci pinned at the stripe edges in the bridge phase, we determine the conditions under which the local bridging transition precedes capillary condensation as the pressure (or chemical potential) is increased. Provided the contact angle of the stripe is less than that of the outer wall we show that triple points, w…
Density-functional theory is used to investigate the phase behavior of colloidal binary hard-platelet and hard-rod fluids near a single hard wall or confined in a slit pore. The Zwanzig model, in which the orientations of the particles of rectangular shape are restricted to three orthogonal orientations, is analyzed by numerical minimization of the grand potential functional. The density and orientational profiles as well as the surface contributions to the grand potential are determined. The calculations exhibit a wall-induced continuous surface transition from uniaxial to biaxial symmetry fo…
Utilizing a 3D mean-field lattice-gas model, we analyze the effect of confinement on the nature of capillary phase transition in granular aggregates with varying disorder and their inverse porous structures obtained by interchanging particles and pores. Surprisingly, the confinement effects are found to be much less pronounced in granular aggregates as opposed to porous structures. We show that this discrepancy can be understood in terms of the surface-surface correlation length with a connected path through the fluid domain, suggesting that this length captures the true degree of confinement.…
We study the dynamics of condensation for a stochastic continuous mass transport process defined on a one-dimensional lattice. Specifically we introduce three different variations of the truncated random average process. We generalize hereby the regular truncated process by introducing a new parameter $γ$ and derive a rich phase diagram in the $ρ-γ$ plane where several new phases next to the condensate or fluid phase can be observed. Lastly we use an extreme value approach in order to describe the conditions of a condensation transition in the thermodynamic limit. This leads us to a possible e…
We have employed the Density Functional Theory formalism to investigate the nematic-isotropic capillary transitions of a nematogen confined by walls that favor antagonist orientations to the liquid crystal molecules (hybrid cell). We analyse the behavior of the capillary transition as a function of the fluid-substrate interactions and the pore width. In addition to the usual capillary transition between isotropic-like to nematic-like states, we find that this transition can be suppressed when one substrate is wet by the isotropic phase and the other by the nematic phase. Under this condition t…
Multicanonical ensemble simulations for the simulation of first-order phase transitions suffer from exponential slowing down. Monte Carlo autocorrelation times diverge exponentially with free energy barriers $ΔF$, which in $L^d$ boxes grow as $L^{d-1}$. We exemplify the situation in a study of the 2D Ising-model at temperature $T/T_c=0.63$ for two different lattice manifolds, toroidal lattices and surfaces of cubes. For both geometries the effect is caused by discontinuous droplet shape transitions between various classical crystal shapes obeying geometrical constraints. We use classical dropl…
Using general scaling arguments combined with mean-field theory we investigate the critical ($T \simeq T_c$) and off-critical ($T\ne T_c$) behavior of the Casimir forces in fluid films of thickness $L$ governed by dispersion forces and exposed to long-ranged substrate potentials which are taken to be equal on both sides of the film. We study the resulting effective force acting on the confining substrates as a function of $T$ and of the chemical potential $μ$. We find that the total force is attractive both below and above $T_c$. If, however, the direct substrate-substrate contribution is subt…
We study the condensation transition of counterions on a charged cylinder via Monte Carlo simulations. Varying the cylinder radius systematically in relation to the system size, we find that all counterions are bound to the cylinder and the heat capacity shows a drop at a finite Manning parameter. A finite-size scaling analysis is carried out to confirm the criticality of the complete condensation transition, yielding the same critical exponents with the Manning transition. We show that the existence of the complete condensation is essential to explain how the condensation nature alters from c…
Exploiting the mapping between a binary mixture and the Ising model we have analyzed the critical fluctuations by means of the density-matrix renormalization group technique. The calculations have been carried out for a two-dimensional Ising strip subject to equal strong surface fields. It was found that the critical Casimir force displays significantly different behavior on opposite sides of the capillary condensation line, especially below the critical temperature. It can be concluded that in a real binary mixtures the most attractive force appears at temperatures near T_C and at reservoir c…
We study phase behaviour of a model fluid confined between two unlike parallel walls in the presence of long range (dispersion) forces. Predictions obtained from macroscopic (geometric) and mesoscopic arguments are compared with numerical solutions of a non-local density functional theory. Two capillary models are considered. For a capillary comprising of two (differently) adsorbing walls we show that simple geometric arguments lead to the generalized Kelvin equation locating capillary condensation very accurately, provided both walls are only partially wet. If at least one of the walls is in …
Using a specially tuned mean-field Bose gas as a reference system, we establish a positive lower bound on the condensate density for continuous Bose systems with superstable two-body interactions and a finite gap in the one-particle excitations spectrum, i.e. we prove for the first time standard homogeneous Bose-Einstein condensation for such interacting systems.
Bose-Einstein condensation and the $λ$-transition are described in molecular detail for bosons interacting with a pair potential. New phenomena are identified that are absent in the usual ideal gas treatment. Monte Carlo simulations of Lennard-Jones helium-4 neglecting ground momentum state bosons give a diverging heat capacity approaching the transition. Pure permutation loops give continuous growth in the occupancy of the ground momentum state. Mixed ground and excited momentum state permutation loops give a discontinuous transition to the condensed phase. The consequent latent heat for the …
