A O Parry

Liquids at interfaces: what can a theorist contribute?

Reviews some recent theoretical and computer simulation studies of simple atomic fluids adsorbed at structureless substrates. Emphasis is placed on phase transitions, especially the various types of wetting transition. Criticality is associated with capillary-wave-like fluctuations in a continuously growing wetting film. This is of a subtle nature, which is best understood in terms of the pairwise correlation function of the fluid. Other surface phase transitions, such as prewetting and layering, occur out of bulk coexistence. Theory suggests that for sufficiently attractive substrates a sequence of first-order transitions, corresponding to the growth of new adsorbed liquid layers, should occur as the pressure of the bulk gas increases towards saturation at temperatures not too far above the bulk triple point. The extent to which such behaviour is found in adsorption experiments is discussed. The authors also argue that a simple fluid confined between two parallel hard-walls can exhibit surprisingly rich equilibria.

Novel phase behaviour of a confined fluid or Ising magnet

Abstract The phase behaviour of a simple fluid or Ising magnet (at temperatures above its roughening transition) confined between parallel walls that exert opposing surface fields h 2 = - h 1 is found to be markedly different from that which arises for h 2 = h 1 . Whereas critical wetting plays little role for confinement by identical walls, it is of crucial importance for opposing surface fields. Analysis of a Landau functional and other mean-field treatments show that if h 1 is such that critical wetting occurs at a single wall ( L = ∞) at a transition temperature T w , then phase coexistence, for finite wall separation L , is restricted to temperatures T T c , L , where the critical temperature T c , L lies below T w . In the temperature range T c , b > T > T w there is a single soft mode phase that is characterized, for zero bulk field and large L , by a +- interface located at the centre of the slit, a transverse correlation length ξ ∼≈ e L and a solvation force that is repulsive. For large h 1 , T w can lie arbitrarily far below the bulk critical temperature T c , b . Scaling arguments, whose validity we have confirmed in two dimensions by comparison with exact solutions for interfacial Hamiltonians, predict that such behaviour persists beyond mean-field for systems with short-ranged forces. They also predict similar phase behaviour for long-ranged forces, but with ξ ξ ∼ increasing algebraically with L in the soft mode phase. The solvation force tf s changes from repulsive to attractive (at large L ) as the temperature is reduced below T w , i.e. the sign of tf s reflects wetting characteristics.

Critical effects at 3D wedge wetting

We show that continuous filling transitions are possible in 3D wedge geometries made from substrates exhibiting first-order wetting transitions, and develop a fluctuation theory yielding a complete classification of the critical behavior. Our fluctuation theory is based on the derivation of a Ginzburg criterion for filling and also on an exact transfer-matrix analysis of a novel effective Hamiltonian that we propose as a model for wedge fluctuation effects. The influence of interfacial fluctuations is very strong and, in particular, leads to a remarkable universal divergence of the interfacial roughness xi( perpendicular) approximately (T(F)-T)(-1/4) on approaching the filling temperature T(F), valid for all possible types of intermolecular forces.

Universality for 2D Wedge Wetting

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.

Wedge filling, cone filling and the strong-fluctuation regime

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.

Three-dimensional wetting revisited

We review progress made towards resolving long-standing problems associated with the theory of wetting transitions in three-dimensional systems with short-ranged forces (corresponding to the marginal dimension). We begin by emphasizing the importance of two seemingly unrelated problems faced by the standard (capillary-wave) effective interfacial Hamiltonian model: (a) the discrepancy with the results of Monte Carlo simulation studies of the critical wetting transition in the Ising model which do not reveal any of the predicted non-universal behaviour; (b) the failure of the interfacial model to describe the structure of correlation functions (at the wall) known from mean-field studies of the complete wetting transition. Recent work suggests that these problems may be overcome by introducing new effective Hamiltonians which improve on the capillary-wave model and lead to novel fluctuation effects in d = 3. The new models follow directly from the development of much improved systematic techniques concerning their derivation and justification initiated by Fisher and Jin. These workers emphasized the importance of allowing for the position dependence of the stiffness coefficient and showed that it may drive a (bare) critical wetting transition first order. This has been further developed by Parry, Boulter and co-workers who argue that it is essential to model the coupling of order-parameter fluctuations at the wall and interface and show how this resolves problem (b). The coupled Hamiltonian also leads to new predictions for fluctuation effects in d = 3 which are in good agreement with more recent Ising model simulations by Binder and co-workers as well as providing a likely explanation for problem (a).

Nonlocality and short-range wetting phenomena.

We propose a nonlocal interfacial model for 3D short-range wetting at planar and nonplanar walls. The model is characterized by a binding-potential functional depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tubelike fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong nonperturbative influence of nonlocality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.

Wedge covariance for two-dimensional filling and wetting

A comprehensive theory of interfacial fluctuation effects occurring at two-dimensional wedge (corner) filling transitions in pure (thermal disorder) and impure (random bond disorder) systems is presented. Scaling theory and the explicit results of transfer matrix and replica trick studies of interfacial Hamiltonian models reveal that, for almost all examples of intermolecular forces, the critical behaviour at filling is fluctuation dominated, characterized by universal critical exponents and scaling functions that depend only on the wandering exponent ζ. Within this filling-fluctuation (FFL) regime, the critical behaviour of the midpoint interfacial height, probability distribution function, local compressibility and wedge free energy are identical to corresponding quantities predicted for the strong-fluctuation (SFL) regime for critical wetting transitions at planar walls. In particular the wedge free energy is related to the SFL regime point tension, which is calculated for systems with random bond disorder using the replica trick. The connection with the SFL regime for all these quantities can be expressed precisely in terms of special wedge covariance relations, which complement standard scaling theory and restrict the allowed values of the critical exponents for both FFL filling and SFL critical wetting. The predictions for the values of the exponents in the SFL regime recover earlier results based on random walk arguments. The covariance of the wedge free energy leads to a new, general relation for the SFL regime point tension, which derives the conjectured Indekeu-Robledo critical exponent relation and also explains the origin of the logarithmic singularity for pure systems known from exact Ising studies due to Abraham and co-workers. Wedge covariance is also used to predict the numerical values of critical exponents and position dependence of universal one-point functions for pure systems.

Fluid adsorption at a non-planar wall: Roughness-induced first-order wetting

We study the problem of fluid adsorption at a non-planar wall with a view to understanding the influence of surface roughness on the wetting transition. Starting from an appropriate Landau-type free-energy functional we develop a linear response theory relating the free energy of the non-planar system to the correlation functions in its planar counterpart. Using this approach we are able to generalize the well known graphical construction method used to study the planar surface phase diagram and derive analytical expressions for the shift in the phase boundary for first- and second-order wetting transitions. The results of the calculation are compared and contrasted with simple phenomenological and scaling arguments. Of particular interest is the influence of surface roughness on a second-order wetting transition which is driven first order, even for small deviations from the plane.

Fluid adsorption near an apex: covariance between complete and critical wetting.

Critical wetting is an elusive phenomenon for solid-fluid interfaces. Using interfacial models we show that the diverging length scales, which characterize complete wetting at an apex, precisely mimic critical wetting with the apex angle behaving as the contact angle. Transfer matrix, renormalization group, and mean-field analysis show that this covariance is obeyed in 2D and 3D and for long- and short-ranged forces. This connection should be experimentally accessible and provides a means of checking theoretical predictions for critical wetting.