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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 above $T_w$ both phase transitions are continuous and their critical singularities are determined. In addition we show that for the evaporation transition above $T_w$ 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.

The phase boundaries for corner wetting (filling) in square and diagonal lattice Ising models are exactly determined and show a universal shift relative to wetting near the bulk criticality. More generally, scaling theory predicts that the filling phase boundary shift for wedges and cones is determined by a universal scaling function $R_d(\psi)$ depending only on the opening angle $2\psi$. $R_d(\psi)$ is determined exactly in $d=2$ and approximately in higher dimensions using non-classical local functional and mean-field theory. Detailed numerical transfer matrix studies of the the magnetisation profile in finite-size Ising squares support the conjectured connection between filling and the strong-fluctuation regime of wetting., Comment: 3 Figures, accepted for publication in PRL

We propose a simplified description of fluid adsorption on heterogenenous micropatterned substrates. Using this approach, we are able to rederive results obtained earlier using effective interfacial Hamiltonian methods and predict a number of new examples of surface phase behaviour for both singly and periodically striped substrates. In particular, we show that, for a singly striped system, the manner in which the locus of surface unbending phase transitions approaches the pre-wetting line of the infinite pure system, in the limit of large stripe widths, is non-trivial and sensitive to several characteristic lengthscales and competing free-energies. For periodic substrates, we investigate finite-size deviations from Cassie's law for the wetting temperature of the heterogeneous system when the domain sizes are mesoscopic., 12 pages, 13 figures

Predicting the existence and nature of phase transitions is the most important, and difficult, problem in equilibrium statistical mechanics. But the results of two of the most important methods used to study phase transitions, the renormalisation group and computer simulation, occasionally disagree. The nature of the second-order wetting transition in three-dimensional systems with short-range forces is a classic example of this problem and has troubled condensed matter theorists for almost a decade.

Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free-energy and scaling of one-point functions in critical thin films. This approach is extended to predict the two-point correlation function G in critical thin-films with symmetric surface fields in arbitrary dimension d. In d=2 we show there is exact agreement with the predictions of conformal invariance for the complete spectrum of correlation lengths as well as the detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we present new numerical predictions for the universal finite-size correlation length and scaling functions determining the structure of G across the thin-film. Highly accurate analytical closed form expressions for these universal properties are derived in arbitrary dimension., 4 pages, 1 postscript figure. Submitted to Phys Rev Lett

Using an interface displacement model derived from a microscopic density functional theory we investigate thin liquidlike wetting layers adsorbed on flat substrates with an embedded chemical heterogeneity forming a stripe. For a wide range of effective interface potentials we find first-order phase transitions as well as continuous changes between lateral interfacial configurations bound to and repelled from the stripe area. We determine phase diagrams and discuss the conditions under which these morphological changes arise., 10 pages, RevTeX, 4 Figures

We show that continuous filling or wedge-wetting transitions are possible in 3D wedge-geometries made from (angled) substrates exhibiting first-order wetting transitions and develop a comprehensive fluctuation theory yielding a complete classification of the critical behaviour. Our fluctuation theory is based on the derivation of a Ginzburg criterion for filling and also an exact transfer-matrix analysis of a novel effective Hamiltonian which we propose as a model for wedge fluctuation effects. The influence of interfacial fluctuations is shown to be very strong and, in particular, leads to a remarkable universal divergence of the interfacial roughness $\xi_{\perp}\sim (T_F-T)^{-1/4}$ on approaching the filling temperature $T_F$, valid for all possible types of intermolecular forces., Comment: 4 pages, 2 figures

We consider an effective Hamiltonian description of critical wetting transitions in systems with short-range forces at a corrugated (periodic) wall. We are able to recover the results obtained previously from a `microscopic' density-functional approach in which the system wets in a discontinuous manner when the amplitude of the corrugations reaches a critical size A*. Using the functional renormalization group, we find that A* becomes dependent on the wetting parameter \omega in such a way as to decrease the extent of the first-order regime. Nevertheless, we still expect wetting in the Ising model to proceed in a discontinuous manner for small deviations of the wall from the plane., Comment: 9 pages RevTex with 2 EPS figures. To appear in Eur. Phys. J. B

We consider phase coexistence and criticality in a thin-film Ising magnet with opposing surface fields and non-planar (corrugated) walls. We show that the loss of translational invariance has a strong and unexpected non-linear influence on the interface structure and phase diagram. We identify 4 non-thermodynamic singularities where there is a qualitative change in the interface shape. In addition, we establish that at the finite-size critical point, the singularity in the interface shape is characterized by two distint critical exponents in contrast to the planar case (which is characterised by one). Similar effects should be observed for prewetting at a corrugated substrate. Analogy is made with the behaviour of a non-linear forced oscillator showing chaotic dynamics., Comment: 13 pages, 3 figures

We consider variational (density functional) models of fluids confined in parallel-plate geometries (with walls situated in the planes z=0 and z=L respectively) and focus on the structure of the pair correlation function G(r_1,r_2). We show that for local variational models there exist two non-trivial identities relating both the transverse Fourier transform G(z_\mu, z_\nu;q) and the zeroth moment G_0(z_\mu,z_\nu) at different positions z_1, z_2 and z_3. These relations form an algebra which severely restricts the possible form of the function G_0(z_\mu,z_\nu). For the common situations in which the equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an odd or even reflection symmetry in the z=L/2 plane the algebra simplifies considerably and is used to relate the correlation function to the finite-size excess free-energy \gamma(L). We rederive non-trivial scaling expressions for the finite-size contribution to the free-energy at bulk criticality and for systems where large scale interfacial fluctuations are present. Extensions to non-planar geometries are also considered., Comment: 15 pages, RevTex, 4 eps figures. To appear in J.Phys.Condens.Matter

An exact solution of a two dimensional RSOS model of wetting at a corrugated (periodic) wall is found using transfer matrix techniques. In contrast to mean-field analysis of the same problem the wetting transition remains second-order and occurs at a lower temperature than that of the planar system. Comparison with numerical studies and other analytical approaches is made., Comment: 11 pages LaTex with 1 eps figure. To appear in J.Phys.A

We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate \ell representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions of non-universality at the upper critical dimension d=3 at critical and complete wetting respectively which are not borne out by Ising model simulation studies. (P3) relates to mean-field correlation function structure in the underlying continuum Landau model. We investigate the hypothesis that these concerns arise due to the coupling of order parameter fluctuations near the unbinding interface and wall. For quite general choices of collective coordinates X_i we show that arbitrary two-field models H[X_1,X_2] can recover the required anomalous structure of mean-field correlation functions (P3). To go beyond mean-field theory we introduce a set of Hamiltonians based on proper collective coordinates s near the wall which have both interfacial and spin-like components. We argue that an optimum model H[s,\ell] in which the degree of coupling is controlled by an angle-like variable, best describes the non-universality of the Ising model and investigate its critical behaviour. For critical wetting the appropriate Ginzburg criterion shows that the true asymptotic critical regime for the local susceptibility \chi_1 is dramatically reduced consistent with observations of mean-field behaviour in simulations (P1). For complete wetting the model yields a precise expression for the temperature dependence of the renormalized critical amplitude \theta in good agreement with simulations (P2). We highlight the importance of a new wetting parameter which describes the physics that emerges due to the coupling effects., Comment: 34 pages, RevTex, 8 eps figures. To appear in Physica A

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) = 2 sigma cos theta/L, where theta is the contact angle at the side walls and sigma is the surface tension. The order of the transition is determined by the contact angle of the capped end theta(cap); 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 Delta p(L) = 2 sigma sin theta(cap)/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 theta(cap) = 0 and the influence of corner menisci on adsorption isotherms are presented.

Recent work on the complete wetting transition has emphasized the role played by the coupling of fluctuations of the order parameter at the wall and at the depinning fluid interface. Extending this approach to the wetting transition itself we predict a novel crossover effect associated with the decoupling of fluctuations as the temperature is lowered towards the transition temperature T_W. Using this we are able to reanalyse recent Monte-Carlo simulation studies and extract a value \omega(T_W)=0.8 at T_W=0.9T_C in very good agreement with long standing theoretical predictions., Comment: 4 pages, LaTex, 1 postscript figure

We propose a fully quantitative theory for the finite-size scaling of the filling transition in a three-dimensional double wedge geometry, based on the exact transfer-matrix solution of a phenomenological interfacial model. Antisymmetric fields act at the top and bottom wedges; so each one favours a different bulk phase under coexistence conditions, i.e. gas and liquid phases in fluid models such as the lattice gas, or equivalently ferromagnetic domains of opposed magnetization in the Ising model. From this formalism we obtain an analytical form for the magnetization probability distribution function at critical filling which is valid for any aspect ratio. To test our predictions we revisit and perform new simulation studies of filling in the Ising model double-wedge geometry and use our finite-size scaling theory to locate accurately the critical filling transition.

The order of the liquid–solid phase transition of a fluid confined by a capillary of two parallel walls can be changed from first to second order if the capillary is capped at one end by a third wall. This change of order of the phase transition was predicted using an effective interfacial Hamiltonian model and was recently confirmed by a microscopic density functional theory study. In this study some geometrical aspects of the continous transition in a capped capillary are considered within the framework of density functional theory.

Recent studies have shown that there exist precise connections (or covariance relations) between adsorption properties for substrates with different shapes. This occurs, for example, when a fluid is adsorbed in a linear wedge. In this case, the influence of the geometry is to shift effectively the contact angle from theta to theta-alpha, where alpha is the tilt angle. Despite the fact that these relations are obeyed both at mean-field level and also exactly in two dimensions (when fluctuation effects dominate), their fundamental origin has been unclear. Here, we show that they can be traced to a symmetry present in interfacial Hamiltonian models, and further relate this to surface thermodynamics and the nonlocal nature of interfacial interactions in systems with short-ranged forces.

When a fluid or Ising-like magnet is confined between two parallel walls that are each completely wet by different bulk phases, the interface separating the phases is subject to large-scale fluctuations determined by the slit width. It was noted some time ago that, in two dimensions, the scaling expression for the probability distribution function describing the interfacial height across the slit shows remarkable similarities with predictions of conformal invariance. However, this local scale invariance appears to contradict the strongly anisotropic nature of (1 + 1)-dimensional interfacial fluctuations along and perpendicular to the interface, characterized by the wandering exponent. In this paper, we show that similarity with conformal invariance is not coincidental and can be understood explicitly as the projection of a local scale invariance for a wandering line in 2 + 1 dimensions.

We show that the length scale ${\mathrm{\ensuremath{\alpha}}}^{\mathrm{\ensuremath{-}}1}$, which appears in the interfacial binding potential of the effective Hamiltonian description of wetting transitions, should be identified with the ``true'' or exponential range of the pair-correlation function of the bulk (wetting) phase, rather than the Ornstein-Zernike (second-moment) bulk correlation length ${\ensuremath{\xi}}_{\mathit{b}}$. Since ${\mathrm{\ensuremath{\alpha}}}^{\mathrm{\ensuremath{-}}1}$g${\ensuremath{\xi}}_{\mathit{b}}$, this implies that the parameter \ensuremath{\omega}=${\mathit{k}}_{\mathit{B}}$T${\mathrm{\ensuremath{\alpha}}}^{2}$/4\ensuremath{\pi}\ensuremath{\Sigma}\ifmmode \tilde{}\else \~{}\fi{}, which determines the values of critical exponents for critical wetting in three dimensions, is significantly smaller than initial estimates of this quantity. For the simple-cubic Ising model (\ensuremath{\alpha}${\ensuremath{\xi}}_{\mathit{b}}$${)}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\approxeq}1.46 for T\ensuremath{\gtrsim}${\mathit{T}}_{\mathit{R}}$, the roughening temperature, and depending on the magnitude of the interfacial stiffness \ensuremath{\Sigma}\ifmmode \tilde{}\else \~{}\fi{}, we conclude \ensuremath{\omega}\ensuremath{\lesssim}0.5 is appropriate for such temperatures. We discuss the implications for recent Monte Carlo studies of critical wetting.

A long-standing problem in condensed matter physics concerns the nature of the critical wetting phase transition in the Ising model or, more generally, in 3D systems with short-ranged forces. This is of fundamental interest because 3D corresponds to the upper critical dimension of the transition and it is not clear a priori whether the behaviour of the system will be mean-field-like or fluctuation-dominated. Renormalization group studies of the standard coarse-grained effective interfacial Hamiltonian model famously predict strong non-universal critical exponents which depend on the value of the so-called wetting parameter ω. However, these predictions are at odds with extensive Monte Carlo simulations of wetting in the Ising model, due to Binder, Landau and coworkers, which appear to be more mean-field-like. Further amendments to the interfacial Hamiltonian, which included the presence of a position-dependent stiffness, worsened the problem by paradoxically predicting fluctuation-induced first-order wetting behaviour. Here we show from re-analysis of a microscopic Landau–Ginzburg–Wilson model of 3D short-ranged wetting that correlation functions are characterized by two diverging parallel length scales, not one, as previously thought. This has a simple diagrammatic explanation using a non-local interfacial Hamiltonian and yields a thermodynamically consistent theory of wetting in keeping with exact sum rules. The non-local model crucially contains long-ranged two-body interfacial interactions, characterized by the new length scale, which were missing in earlier treatments. For critical wetting the second length cuts off the spectrum of interfacial fluctuations determining the repulsion from the wall. We show how this corrects previous renormalization group predictions for fluctuation effects, based on local interfacial Hamiltonians. In particular, lowering the cut-off leads to a substantial reduction in the effective value of the wetting parameter controlling the non-universality and also prevents the transition being driven first-order. Quantitative comparison with the Ising model simulation studies is also made.

We use a non-local interfacial Hamiltonian to revisit a number of problems associated with the fluctuation theory of critical wetting transitions in three-dimensional systems with short-ranged forces. These centre around previous renormalization group predictions of strongly non-universal critical singularities and also possible fluctuation-induced first-order (stiffness-instability) behaviour, based on local interfacial models, which are not supported by extensive Monte Carlo simulations of wetting in the three-dimensional Ising model. Non-locality gives rise to long-ranged two-body interfacial interactions controlling the repulsion from the wall not modelled correctly in previous interfacial descriptions. In particular, correlation functions are characterized by two diverging parallel correlation lengths, and , not one as previously thought. Mean-field, Ginzburg criterion and linear renormalization group analyses all show that some interfacial fluctuation effects are strongly damped for wavenumbers q>1/ξNL. This prevents a stiffness-instability and reduces the size of the asymptotic critical regime where non-universality can be observed. Non-universal critical singularities along the critical wetting isotherm are determined by a smaller, effective value of the wetting parameter which slowly approaches its asymptotic limit as the wetting film grows. This is confirmed by numerical simulation of a discretized version of the non-local model.

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.

By introducing finite-size-scaling corrections into the Kelvin equation for the location of the shifted first-order phase boundary (condensation line) for a fluid confined between two parallel plates, the critical exponent \ensuremath{\mu}\ifmmode \tilde{}\else \~{}\fi{} for the liquid-gas surface tension is shown to satisfy the Widom exponent relation \ensuremath{\mu}\ifmmode \tilde{}\else \~{}\fi{}=2-\ensuremath{\alpha}-\ensuremath{\nu}. In contrast to most previous arguments, no assumptions of bulk and surface hyperscaling are required in the present derivation.

The nature of the pairwise correlation function G for a fluid undergoing critical and complete wetting transitions at an adsorbing substrate (wall) is examined using various and statistical-mechanical treatments. Sum-rule and scaling arguments predict that, in critical wetting at bulk coexistence, capillary-wave fluctuations manifest themselves throughout the wetting film, up to the wall, so that the (divergent) transverse correlation length xi /sub /// is the same for all pairs of particles. By contrast, in the case of complete wetting from off-bulk coexistence, a divergent correlation length is appropriate only for particles located in the liquid-gas edge of the wetting film. These predictions are confirmed by explicit formulae for the transverse moments of G derived from a mean-field, density-functional theory of a Yukawa fluid in the presence of a short-ranged (exponential) wall-fluid potential. The sumrule analysis also provides a surface analogue of the Cp-CV thermodynamic relation, which is used to determine a rigorous relationship between the exponents that characterise critical wetting. The same thermodynamic relation predicts corrections to scaling in bulk dimension d=3 that are similar to those found in renormalisation-group (RG) studies of effective interfacial Hamiltonians. By unfreezing capillary-wave fluctuations on a mean-field density profile and making use of a sum rule that relates a derivative of the surface tension to the profile near the wall, relationships between xi /sub /// and the thickness t of the wetting film derived for critical wetting with finite-ranged forces. For d

Pairwise correlations in fluids adsorbed at structureless substrates (walls) are investigated by means of a simple density functional theory. In the approach to complete wetting or drying from off bulk coexistence capillary-wave-like fluctuations lead to singularities in the total correlation function h when one or both of the particles are located in the edge of the growing film far from the wall. However these singular contributions are damped out when both particles lie close to the wall. For a hard-wall the theory yields explicit results for the zeroth and second transverse moments of h which are consistent with the predictions of exact statistical mechanical sum rules. In particular h 2(0, 0), the second moment evaluated with both particles at the wall, is proportional to the wall-fluid surface tension σ. The implications of this result for the case of complete drying at a wall-liquid-interface, where σ acquires a gas-liquid contribution from the detaching edge of the gas film, are discussed in some ...

The shape and chemical composition of solid surfaces can be controlled at a mesoscopic scale. Exposing such structured substrates to a gas that is close to coexistence with its liquid phase can produce quite distinct adsorption characteristics compared to those of planar systems, which may be important for technologies such as super-repellent surfaces or micro-fluidics. Recent studies have concentrated on the adsorption of liquids on rough and heterogeneous substrates, and the characterization of nanoscopic liquid films. But the fundamental effect of geometry on the adsorption of a fluid from the gas phase has hardly been addressed. Here we present a simple theoretical model which shows that varying the shape of the substrate can exert a profound influence on the adsorption isotherms of liquids. The model smoothly connects wetting and capillary condensation through a number of examples of fluid interfacial phenomena, and opens the possibility of tailoring the adsorption properties of solid substrates by sculpting their surface shape.

We consider the complete wetting transition at nonplanar wall–fluid interfaces, where the height of the substrate varies as a power-law ∝|x|γ (with exponents 0⩽γ⩽1) in one direction (x). From a general scaling analysis, supported by numerical and analytical effective interfacial model calculations, we argue that such power-law wedges can alter the growth law describing the divergence of the interfacial height l0 (measured from the wedge bottom) and other length scales as the bulk saturation chemical potential is approached. For realistic experimental systems with dispersion forces, we predict that the complete wetting critical exponents are determined by γ for wedge shape with γ>1/2. For γ

We study 2D wedge wetting using a continuum interfacial Hamiltonian model which is solved by transfer-matrix methods. For arbitrary binding potentials, we are able to exactly calculate the wedge free-energy and interface height distribution function and, thus, can completely classify all types of critical behaviour. We show that critical filling is characterized by strongly universal fluctuation dominated critical exponents, whilst complete filling is determined by the geometry rather than fluctuation effects. Related phenomena for interface depinning from defect lines in the bulk are also considered., Comment: 4 pages, 1 figure

When a fluid, or magnet, is confined between parallel walls that exert opposing surface fields ${\mathit{h}}_{2}$=-${\mathit{h}}_{1}$ the order-parameter (magnetization) profile near one wall can be modified severely by the presence of the other. For sufficiently low dimensions (d3) the surface-layer perturbation and the force between the walls decay algebraically with wall separation L for all temperatures ${\mathit{T}}_{\mathit{c},}$b\ensuremath{\ge}T\ensuremath{\ge}${\mathit{T}}_{\mathit{w}}$. Near ${\mathit{T}}_{\mathit{w}}$, the temperature of a critical wetting transition, the perturbation can be longer ranged than at the bulk critical temperature ${\mathit{T}}_{\mathit{c},}$b. The predictions of a scaling theory are supported, for d=2, by results obtained from interfacial Hamiltonians and from Monte Carlo simulations of the Ising strip.