Table of contents

The subject of the present Special Issue is a hybrid of two areas: `liquids and soft matter' and `surfaces and interfaces', both of which have special sections of Journal of Physics: Condensed Matter devoted to them. The topic `liquids at interfaces' is a very active area of research in physics as testified by the collection of papers included in this Special Issue. These papers contain both fresh research results and reviews of recent developments in the field of inhomogeneous liquids.

The basic challenge is to understand macroscopic properties of liquid matter at interfaces on a `microscopic' scale, on the basis of either theories or computer simulations of models incorporating the microscopic interactions between the individual particles, or on the basis of experimental studies which resolve the structural and dynamical correlation on a molecular~scale.

The range of problems discussed under this heading is fairly narrow, comprising liquid films on substrates, near walls and in confining geometries, as well as free liquid-solid and liquid-gas interfaces. Interesting questions concern the thermodynamics, structure and dynamics of the free interfaces and phase transitions near interfaces and surfaces. A particular emphasis of the present Issue is on wetting transitions near structured walls in different situations including wedges, periodically structured templates and corrugated or decorated substrates. As documented by several articles, the resulting wetting scenarios are fairly complicated, depending sensitively on the substrate structure. Furthermore, dynamical issues are discussed, both for equilibrium and for non-equilibrium situations, that are relevant to phase separation, crystal growth, conduction and drainage.

On the other hand, the present Issue demonstrates that there is a great diversification both of the systems investigated and the methods applied. The kinds of system investigated range from molecular binary mixtures to supramolecular aggregates such as polymers, colloidal suspensions, amphiphilic systems and biological systems. Furthermore, even aspects of quantum fluids and foams are touched upon.

Among the broad range of methods applied are different theoretical approaches to model systems such as density functional theory, liquid integral equations and other more phenomenological methods from statistical mechanics. Computer simulations provide another approach used to resolve the liquid structure and dynamics on a microscopic level. Last but not least, a wealth of different experimental techniques, such as neutron and x-ray reflectivity, atomic force and scanning tunnelling microscopy and the quartz crystal microbalance technique, to name just a few, have been applied to extract precise data.

As also documented by the present Issue, there has been significant progress in our microscopic understanding of inhomogeneous liquids achieved by combining and comparing these three complementary approaches of theory, computer simulation and experiment. This synergetic interplay will be exploited further in the near future, so a flourishing future can be expected for the physics of liquids at interfaces.

Interfacial fluctuation effects occurring at wedge- and cone-filling transitions are investigated and shown to exhibit very different characteristics. For both geometries we argue that the conditions for observing critical (continuous) filling are much less restrictive than for critical wetting, which is known to require the fine tuning of the Hamaker constants. Wedge filling is critical if the wetting binding potential does not exhibit a local maximum, whilst conic filling is critical if the line tension is negative. This latter scenario is particularly encouraging for future experimental studies.

Using mean-field and effective Hamiltonian approaches, which allow for breather-mode fluctuations which translate the interface up and down the sides of the confining geometry, we are able to completely classify the possible critical behaviours (for purely thermal disorder). For the three-dimensional wedge, the interfacial fluctuations are very strong and characterized by a universal roughness critical exponent ν_⊥^W = 1/4 independent of the range of the forces. For the physical dimensions d = 2 and d = 3, we show that the effect of the cone geometry on the fluctuations at critical filling is to mimic the analogous interfacial behaviour occurring at critical wetting in the strong-fluctuation regime. In particular, for d = 3 and for quite arbitrary choices of the intermolecular potential, the filling height and roughness show the same critical properties as those predicted for three-dimensional critical wetting with short-ranged forces in the large-wetting-parameter (ω>2) regime.

A surprising lowering of the surface energy of liquid surfaces was recently found in x-ray scattering experiments which enhances thermal fluctuations of fluid interfaces at microscopic scales and calls for a re-examination of small-scale interfacial processes. This reduction was predicted for microscopic undulations below a few nm by density functional theory taking into account the long-range attraction of molecular interaction potentials. Here, a self-consistent theory is proposed for the fluctuation of fluid interfaces in arbitrary potentials which can significantly alter thermodynamical and structural properties of liquid drops, thin films, or membranes near a substrate. The substrate-induced hindrance of thermally excited capillary waves increases considerably the thickness of thin liquid films, which cannot be neglected in the analysis of adsorption data. An explicit expression for adsorption isotherms is given depending on temperature, Hamaker constant A, and surface tension γ which takes into account the influence of capillary waves on the thickness of the fluid film and removes reported discrepancies with the Lifshitz theory of van der Waals forces. Also the steric repulsion potential of a membrane at distance D from a hard wall can be calculated self-consistently in excellent agreement with Monte Carlo simulations.

Here we consider how phase-separation kinetics and morphology are affected by the preferential wetting of a solid surface by one component of a binary fluid mixture. The behaviour is crucially dependent upon whether the spinodal decomposition is bicontinuous-type or droplet-type, i.e. the composition symmetry. Near a symmetric composition, wetting effects are strongly delocalized by hydrodynamic effects unique to bicontinuous phase separation. We discuss the physical mechanism of the unusually fast lateral growth of wetting domains found by Wiltzius and Cumming, the thickening dynamics of wetting layers, and pattern evolution under the influence of surface fields, focusing on the roles of hydrodynamics. We point out a novel possibility of double phase separation: that the quick hydrodynamic reduction of the interface area may spontaneously destabilize the phase-separated macroscopic domains and induce secondary phase separation. We also consider effects of the preferential wetting of immobile and mobile particles by one component of a fluid mixture on phase separation and the resulting complex pattern evolution. It is demonstrated that hydrodynamics always plays crucial roles in the pattern evolution of a phase-separating fluid mixture interacting with solid surfaces.

It is shown that a fluid near a topographically patterned wall exhibits crystallization below the bulk freezing point (so-called precrystallization). In detail, a periodic array of fixed hard spheres is considered as a wall pattern. The actual type of the pattern corresponds to a face-centred-cubic (fcc) lattice cut along the (111), (100) or (110) orientation, a hexagonal-close-packed (hcp) solid with (110) orientation as well as a rhombic lattice distorted with respect to the triangular one. The fluid is represented by mobile hard spheres of the same diameter as the fixed wall spheres. By computer simulation we find complete wetting by a crystalline sheet proceeding via a cascade of layering transitions as the bulk freezing point is approached for the fcc (111) and hcp (110) cases, provided that the wall crystal lattice exactly matches that of the coexisting bulk crystal. On the other hand, there is incomplete wetting for the fcc (100) and (110) cases. The freezing of the first layer starts at lower bulk pressures for a lattice with a larger lattice constant as compared to that of the coexisting bulk crystal. A rhombic pattern either results in incomplete wetting by a solid sheet, which is unstable as a bulk phase, or prevents wetting completely. Using a phenomenological theory we derive scaling relations for the thickness of the crystalline layer which are confirmed by the simulation data. We furthermore show that the Lindemann rule of bulk freezing can be applied also for interfacial freezing transitions.

The phase behaviour of a lattice gas confined between two identical plane-parallel substrates decorated with weakly and strongly adsorbing stripes that alternate periodically in one transverse direction is explored within mean-field theory. It is shown that in the limit of zero temperature (T = 0), the mean-field approximation becomes exact. A modular approach is used to enumerate the possible structural types of phases (morphologies) that can exist at T = 0. Analytic expressions for the grand potentials associated with the morphologies can be obtained and used to determine the exact phase diagram at T = 0. In addition to the known `gas', `liquid', and `bridge' phases, new `vesicle', `droplet', and `layered' morphologies arise, which were overlooked in previous studies of this model. These T = 0 morphologies are taken as trial starting solutions in an iterative numerical procedure for solving the mean-field equations for T>0. The complete phase diagram is thus obtained and its structure is studied as a function of the relative strength of `strong' and `weak' stripes. A key finding is that the number of possible morphologies increases rapidly with the geometrical complexity of the decoration of the substrate. The implications for the determination of phase diagrams for very complex confined systems (e.g. fluids in random porous media) are discussed.

The structure of a fluid of hard Gaussian overlap particles of elongation κ = 5, confined between two hard walls, has been calculated from density-functional theory and Monte Carlo simulations. By using the exact expression for the excluded volume kernel (Velasco E and Mederos L 1998 J. Chem. Phys.109 2361) and solving the appropriate Euler-Lagrange equation entirely numerically, we have been able to extend our theoretical predictions into the nematic phase, which had up till now remained relatively unexplored due to the high computational cost. Simulation reveals a rich adsorption behaviour with increasing bulk density, which is described semi-quantitatively by the theory without any adjustable parameters.

Wetting of periodically corrugated substrates is studied in the framework of the effective interface Hamiltonian approach applied to two non-smooth substrates with different convexity properties. We observe that first-order wetting of a planar substrate induces first-order wetting of a corrugated substrate. It is accompanied by a shift of the wetting temperature. The magnitude of this shift is discussed analytically and numerically as a function of parameters characterizing the corrugation when both the period and the amplitude of the corrugation change simultaneously leading to rescaling of the substrate. Critical wetting of the planar substrate induces critical wetting of the weakly corrugated substrate with no shift of the wetting temperature.

In this work we present and discuss new molecular dynamics simulation procedures and the application of density functional theory to the liquid-vapour interface of pure fluids and their liquid mixtures. Our aim was to further investigate the simulation set-up and parameters to obtain reliable simulation data for the phase behaviour, interfacial structure and surface tension. The influence of box geometries and summation techniques is discussed.

In the application of the density functional theory we analysed the influence of different approximations within the theory on the calculation of interfacial behaviour and optical properties. In particular, the attractive free-energy term of a local density functional approach is modified by introducing an analytical representation of the radial distribution function of the uniform reference fluid. The calculated liquid and gas densities and surface tensions are in good agreement with recent molecular dynamics simulations. But the results clearly show that capillary-wave contributions, acting on different scales of length and time, have to be taken into consideration in predicting both surface tensions and optical properties such as ellipticity and specular reflectivity.

A method for studying the structure and thermodynamic properties of interfaces between coexisting fluid phases has been developed recently. The density functional approach employs correlation functions calculated from reference hypernetted-chain integral equations. We report here results for liquid-liquid interfaces: the interface of a symmetrical binary Lennard-Jones mixture, a mixture of particles with different sizes and a polar-nonpolar liquid interface. Also model potentials for argon, CHF₃, C₆H₁₂ and H₂O are tested with respect to surface properties.

Within the Onsager theory we study the planar isotropic-nematic interface of fluids of hard rods. We present a method with which interfacial biaxiality can be dealt with efficiently and systematically, and apply it (i) to the pure hard-rod fluid and (ii) to a binary mixture of thin and thick hard rods. In the one-component system we find a surface tension that is lower by 15% than earlier estimates, and monotonic profiles of the density and the uniaxial order parameter. The biaxial order parameter profile is non-monotonic. In the two-component system we find the possibility of non-monotonic density profiles, and a maximum in the surface tension as a function of the pressure.

This article deals with the electric double-layer force between a charged colloidal sphere and a charged dielectric planar wall. To introduce the problem and to uncover the basic physics involved, we start by first reviewing the effective wall-colloid potentials that one obtains in linearized Poisson-Boltzmann theory. The important key concepts in this context are: charge renormalization, confinement effects, salty interfaces, and image-charge effects due to the dielectric discontinuity at the wall. Starting from the potentials derived in linear theory, we then come to approximate wall-colloid potentials that are valid also in the parameter regime where the non-linearity of the Poisson-Boltzmann equation becomes important. The range of validity of these potentials is systematically investigated by comparing them with potentials based on the exact numerical solution to the Poisson-Boltzmann equation. The important parameters of the calculation are the salt content of the electrolytic solution, the colloidal sphere radius, and the surface charge densities on both the wall and the colloid. We then briefly discuss what additional effect a concentrated suspension of such colloidal spheres has on the interfacial colloid, and close with a short report of an optical experiment that has recently been performed to measure the approximate wall-colloid potentials investigated here.

In the present paper we overview our recent results on intrinsic frictional properties of adsorbed monolayers, composed of mobile hard-core particles undergoing continuous exchanges with a vapour phase. Within the framework of a dynamical master equation approach, describing the time evolution of the system, we determine in the most general form the terminal velocity of some biased impure molecule - the tracer particle (TP), constrained to move inside the adsorbed monolayer, probing its frictional properties - and define the frictional forces as well as the particle-density distribution in the monolayer. Results for one-dimensional solid substrates, appropriate to adsorption on polymer chains, are compared against the Monte Carlo simulation data, which confirm our analytical predictions.

Coarse-grained models of monolayers of amphiphiles (Langmuir monolayers) have been studied theoretically and by means of computer simulations. We discuss some of the insights obtained with this approach, and present new simulation results which show that idealized models can successfully reproduce essential aspects of the generic phase behaviour of Langmuir monolayers.

The experimental results of Koehler and co-workers have indicated that vertices (nodes) can in some cases play a dominant role in the dissipative process that controls foam drainage. We present calculations of numerical constants that can express the effect of the vertices, in a first approximation. Two limiting cases are treated: Poiseuille flow, and free-boundary flow (in the sense that the stress at the surface of the Plateau borders is everywhere zero). Consequences for the relationship between average flow velocity and volume flow rate in steady drainage are indicated.

The second-order phase transition of ⁴He from a normal fluid to a superfluid is ideally suited for studies of critical behaviour. In particular, effects of confinement have been studied recently to verify theoretical predictions of correlation-length scaling and calculations of specific scaling functions. These predictions are summarized for the specific heat and the superfluid density. The method of achieving confinement is discussed, as well as the measuring technique. The specific heat and the superfluid density in planar confinement are examined. It is found that the specific heat scales well on the normal side, and just as well on the superfluid side until the region of the specific heat maximum is reached. Here deviations from scaling are seen. It is possible that this behaviour is associated with the specific crossover in two dimensions. The superfluid fraction, which has been measured for the same type of confinement in two different ways, does not scale. Results of a calculation for the superfluid density to assess the role of the inhomogeneity induced by the van der Waals attraction at the confining walls are presented.

We show that a careful analysis of the Navier-Stokes equation in the low Reynolds number limit has two distinct solutions, one valid for a deep, thin curtain of flow and the other for a thin wide flow. We derive a solution to the latter situation and use the results to develop a new way to control fluid flows in thin, wide sheet flow.

We give a phenomenological overview of recently discovered complex wetting states in simple liquid mixtures relevant to both fundamental research and industrial applications such as oil recovery. Alkanes on water show a sequence of two wetting transitions, from partial wetting to `frustrated-complete wetting', and finally to complete wetting: a first-order thin-thick transition between a microscopic and a mesoscopic adsorbed alkane film is followed by a long-range critical wetting transition to a macroscopic wetting layer. The existence of the new `frustrated-complete wetting' state follows from a competition between short-range and long-range components of the intermolecular forces, the latter opposing wetting. The effective long-range forces between interfaces consist of Debye dipolar and London dispersion contributions, which can also be in mutual competition. The London component is ultimately responsible for the frustration preventing complete wetting at ambient temperatures and pressures.

We study, in both theory and experiment, the shape of sessile, nanometre-sized droplets generated from the rupture of unstable or metastable films of a polymer melt (polystyrene) on Si wafers. We find perfect agreement of the droplet shapes determined by atomic force microscopy with simple exact scaling results obtained from an effective interface displacement model for droplets in the `macroscopic' limit. The experimentally determined line tension is of the magnitude expected from the interface model approach. Our results thus corroborate other recent findings on the qualitative and quantitative validity of the interface model approach to wetting phenomena.

Thin liquid films on non-wettable solid surfaces are not stable; rather, they are transformed by a symmetry-breaking process termed `dewetting' into their equilibrium state, a set of droplets. The morphologies observed upon dewetting contain information about the kind of symmetry-breaking process. In this study, we report on experiments on a model system, thin (2-80 nm) polystyrene films dewetting solid substrates, the wettability of which can be varied. We characterize and classify the emerging dewetting patterns. With the help of the effective interface potential, which we determined for our experimental system, we discuss the interplay of short- and long-range forces and the possibilities for influencing the stability of the liquid. Our experimental findings are also in accordance with recent three-dimensional numerical simulations of other groups.

The adsorption of 2, 5 DMP (2, 5-dimethylpyridine) at the free surface of water (1)-2, 5 DMP (2) liquid mixtures was determined from surface tension and activity measurements. Two divergences were found: the former was observed at T_c for the critical isochore and the 2, 5 DMP-rich γ-phase which, at coexistence, completely wets the surface at T_c, whereas the latter was noticed at T_w for the water-rich β-phase. These results were compared with those found under similar conditions for the same liquid system with silica as the wall; this comparison is quite fruitful because, with silica, the preferentially wetting phase is the β-phase.

Thin films of the binary liquid mixture hexane/perfluorohexane were prepared on silicon wafers. The film thicknesses were between 140 Å and 350 Å; this range was chosen in order to achieve strong confinement of the mixture. The vertical structure of these films was investigated by means of x-ray reflectivity measurements. The data show that the component with the lower surface tension (perfluorohexane) segregates in the surface region of the films in agreement with theoretical predictions. Furthermore, no complete miscibility of the two components was observed in regions of the phase diagram where a one-component bulk system is expected. Preliminary results are given for the internal hexane/perfluorohexane interface.

Over the last 20 years, neutron reflection has emerged as a powerful technique for investigating inhomogeneities across an interface, inhomogeneities either in composition (Lu and Thomas 1998 J. Chem. Soc. Faraday Trans.94 995) or magnetization (Felcher 1981 Phys. Rev. B 24 1995). By measuring the reflected over the incoming intensity of a well collimated beam striking at an interface, as a function of the incident angle and wavelength, the concentration profile giving rise to a reflectivity curve is calculated. The success of neutron reflection arises from the fact that, because of the short wavelengths available, it has a resolution of a fraction of a nanometre, so that information is gained at the molecular level. Unlike x-rays it is not destructive and can be used at buried interfaces, which are not easily accessible to other techniques, such as liquid/liquid or solid/liquid, as well as at solid/air and liquid/air interfaces. It is particularly useful for soft-matter studies since neutrons are strongly scattered by light atoms like H, C, O and N of which most organic and biological materials are formed. Moreover, the nuclei of different isotopes of the same element scatter neutrons with different amplitude and sometimes, as in the case of protons and deuterons, with opposite phase. This allows the use of the method of contrast variation, described below, and different parts of the interface may be highlighted. For biophysics studies, a major advantage of reflectivity over other scattering techniques is that the required sample quantity is very small (<10^-6 g) and it is therefore suitable for work with expensive or rare macromolecules.

While specular reflection (angle of incoming beam equal to angle of reflected beam) gives information in the direction perpendicular to the interface, the lateral structure of the interface may be probed by the nonspecular scattering measured at reflection angles different from the specular one (Sinha et al 1998 Phys. Rev. B 38 2297, Pynn 1992 Phys. Rev. B 45 602). This technique is widely used with x-rays while there are far fewer data in the neutron case due to the smaller intensity of neutron beams. An example relevant in biophysics where the neutron technique has been applied is the off-specular scattering from highly oriented multilamellar phospholipid membranes (Munster et al 1999 Europhys. Lett.46 486).

Neutron reflection is now being used for studies of surface chemistry (surfactants, polymers, lipids, proteins and mixtures adsorbed at liquid/fluid and solid/fluid interfaces), surface magnetism (ultrathin Fe films, magnetic multilayers, superconductors) and solid films (Langmuir-Blodgett films, thin solid films, multilayers, polymer films). The number of reflectometers in the neutron facilities all around the world is increasing although the use of the technique is not yet very common because the availability of beam time is restricted by cost.

Since many biological processes occur at interfaces, the possibility of using neutron reflection to study structural and kinetic aspects of model as well as real biological systems is of considerable interest. However, the number of such experiments so far performed is small. The reason for this is probably because it is well known that the most effective use of neutron reflection involves extensive deuterium substitution and this is not usually an available option in biological systems. This problem may be partially solved by deuteriating other parts of the interface as described by Fragneto et al (2000 Phys. Chem. Chem. Phys.2 5214).

In this paper we shall concentrate on the use of specular neutron reflection at the solid/liquid interface, less studied than the solid/air or liquid/air interfaces, although technologically more important.

After a brief introduction to the theory and measurement of neutron reflectivity, solid/liquid interfaces both from hydrophilic and hydrophobic solids will be described. Three examples of applications in biophysics will be given:

(1) the adsorption of two proteins, β-casein and β-lactoglobulin, on hydrophobic silicon;

(2) the interaction of the peptide p-Antp43-58 with phospholipid bilayers deposited on silicon;

(3) the fluid floating bilayer, a new model for biological membranes.

We have investigated the changes in interfacial friction of toluene on mica and Ag(111) both in the presence and in the absence of interfacial C₆₀ layers employing atomic force microscope (AFM) and quartz crystal microbalance (QCM) techniques. The lateral force measurements fail to detect C₆₀ at the toluene/mica interface, presumably because the C₆₀ is dislodged by the slow-moving probe tip. In contrast, QCM measurements of interfacial friction and slippage for toluene/Ag(111) are sensitive to the presence of interfacial C₆₀. We see the friction double when C₆₀ is present. The results are discussed in the light of the full-slip boundary condition which had been previously reported for surface forces apparatus (SFA) measurements on toluene/mica in the presence and absence of interfacial C₆₀.

A supersaturated solution of NH₄Cl cools while rotating in a horizontal drum. When crystals nucleate, they accumulate in well-defined periodic bands, normal to the axis of rotation. The mechanism responsible for this periodic pattern is not understood, but some ideas are proposed.

We present an overview on the method of analysing equilibrium step fluctuations on metal electrodes to study atomic transport processes at the solid/liquid interface. It is demonstrated that this method provides an access road to a quantitative understanding of surface mobility on metal electrodes. Likewise it is shown that the investigation of step fluctuations is a method to determine activation energies and - with the help of recently introduced temperature dependence experiments - pre-exponential factors. We will show that the dependence of surface mobility on electrode potential and on the electrolyte may be rather complex. As examples, we present STM studies on stepped Cu(111) and Ag(111) electrodes in aqueous electrolytes. For Cu(111) in HCl, we find that the time dependence of step fluctuations obeys a t^1/3-law, which entails that step fluctuations are dominated by fast attachment/detachment kinetics at steps and slow terrace diffusion. For Ag(111) in CuSO₄ and H₂SO₄, an L^1/2t^1/2-dependence (with L the step distance) near the potential of fast Ag dissolution is observed. This time dependence corresponds to an atomic transport based on terrace diffusion and transport through the liquid. We also show that the results of temperature dependent studies of step fluctuations on Ag(111) are in excellent agreement with previous investigations concerning the potential dependence.

This paper deals with the dynamics of liquids, water in particular, at hard surfaces. The stacking of the first adjacent molecules leads to a thin layer which upon shear appears phenomenologically stagnant. Electrokinetic phenomena are particularly suited to study such layers. We shall show how surface conduction studies contribute to the understanding of the dynamics of stagnant layers.