Andrew O. Parry

Asymptotic Decay of Liquid Structure: Oscillatory Liquid-Vapour Density Profiles and the Fisher-Widom Line

Recent work has highlighted the existence of a unified theory for the asymptotic decay of the density profile ρ(r) of an inhomogeneous fluid and of the bulk radial distribution function g(r). For a given short-ranged interatomic potential ρ(r) decays into bulk in the same fashion as g(r), i.e. with the same exponential decay length (α0/-1) and, for sufficiently high bulk density (ρb) and/or temperature (T), oscillatory wavelength (2π/α1). The quantities α0 and α1 are determined by a linear stability analysis of the bulk fluid; they depend on only the bulk direct correlation function. In this paper we reintroduce the concept of the Fisher-Widom (FW) line. This line was originally introduced, in say the (ρb, T plane, as that which separates pure exponential from exponentially damped oscillatory decay of g(r). We explore the relevance of the FW line for the form of the density profile at a liquid-vapour interface. Using a weighted density approximation (WDA) density functional theory we locate the FW line fo...

Geometry-dominated fluid adsorption on sculpted solid substrates

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.

Morphological phase transitions of thin fluid films on chemically structured substrates

Using an interface displacement model derived from a microscopic density functional theory we investigate thin liquid-like 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.

Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: I. Double-parabola approximation

We derive a non-local effective interfacial Hamiltonian model for short-ranged wetting phenomena using a Greens function method. The Hamiltonian is characterized by a binding potential functional and is accurate to exponentially small order in the radii of curvature of the interface and the bounding wall. The functional has an elegant diagrammatic representation in terms of planar graphs which represent different classes of tube-like fluctuations connecting the interface and wall. For the particular cases of planar, spherical and cylindrical interfacial (and wall) configurations, the binding potential functional can be evaluated exactly. More generally, the non-local functional naturally explains the origin of the effective position-dependent stiffness coefficient in the small-gradient limit.

Covariance for cone and wedge complete filling.

Interfacial phenomena associated with fluid adsorption in two dimensional systems have recently been shown to exhibit hidden symmetries, or covariances, which precisely relate local adsorption properties in different confining geometries. We show that covariance also occurs in three-dimensional systems and is likely to be verifiable experimentally and in Ising model simulations studies. Specifically, we study complete wetting in wedge (W) and cone (C) geometries as bulk coexistence is approached and show that the equilibrium midpoint heights satisfy l(c)(h,alpha)=l(w)(h / 2,alpha), where h measures the partial pressure and alpha is the tilt angle. This covariance is valid for both short-ranged and long-ranged intermolecular forces and identifies both leading and next-to-leading-order critical exponents and amplitudes in the confining geometries.

Wetting at nonplanar substrates: Unbending and unbinding

We consider fluid wetting on a corrugated substrate using effective interfacial Hamiltonian theory and show that breaking the translational invariance along the wall can induce an unbending phase transition in addition to unbinding. Both first-order and second-order unbending transitions can occur at and out of coexistence. Results for systems with short-ranged and long-ranged forces establish that the unbending critical point is characterized by hyperuniversal scaling behavior. We show that, at bulk coexistence, the adsorption at the unbending critical point is a universal multiple of the adsorption for the correspondent planar system.

Critical point wedge filling.

We present results of a microscopic density functional theory study of wedge filling transitions, at a right-angle wedge, in the presence of dispersionlike wall-fluid forces. Far from the corner the walls of the wedge show a first-order wetting transition at a temperature T(w) which is progressively closer to the bulk critical temperature T(c) as the strength of the wall forces is reduced. In addition, the meniscus formed near the corner undergoes a filling transition at a temperature T(f)<T(w), the value of which is found to be in excellent agreement with macroscopic predictions. We show that the filling transition is first order if it occurs far from the critical point but is continuous if T(f) is close to T(c) even though the walls still show first-order wetting behavior. For this continuous transition the distance of the meniscus from the apex grows as ℓ(w)≈(T(f)-T)(-β(w)) with the critical exponent β(w)≈0.46±0.05 in good agreement with the phenomenological effective Hamiltonian prediction. Our results suggest that critical filling transitions, with accompanying large scale universal interfacial fluctuation effects, are more generic than thought previously, and are experimentally accessible.

Fluctuation theory for the wavevector expansion of the excess grand potential of a liquid-vapour interface and the theory of interfacial fluctuations

We develop a theory for the wavevector expansion of the excess grand potential of a liquid-vapour interface emphasizing the need to minimize the grand potential density functional for a given collective coordinate l(y) denoting the position of a surface of fixed density rho X (magnetization mX). We rederive the Triezenberg-Zwanzig formula for the surface tension gamma which has a unique value independent of rho X. Our analysis yields a new expression for a rigidity kappa ( rho X) which is strongly dependent on the particular value of rho X used to define l(y). We show that the expressions derived for K( rho X) (and y) are precisely those that need to be adopted when using the recently developed Fisher-Jin method of deriving an effective interfacial Hamiltonian appropriate to an asymptotically free interface. From the set of effective Hamiltonians describing the fluctuations of surfaces of all possible fixed density/magnetization we derive the correct analytic mean-field expression for the position dependence of the spin-spin correlation function for a free interface modelled by a Landau-Ginzburg-Wilson Hamiltonian. We emphasize that allowing for the mx-dependence of the rigidity is essential in this study of interfacial correlations to achieve true thermodynamic consistency.

Drying in a capped capillary

We use a model Density Functional, based on the White-Bear version of Fundamental Measure theory, to test recent predictions, due to Evans and co-workers, that capillary condensation in a capped capillary-slit is a continuous interfacial critical phenomenon related to the complete wetting transition. Using a model with a square-well intermolecular fluid–fluid attraction we first determine accurately the location of the first-order capillary evaporation transition in an infinite (open) hard-wall capillary slit. Extending the density functional model to allow for a two-dimensional order-parameter profile, we then study the adsorption as the chemical potential is reduced to capillary evaporation but now in a capillary-slit that is capped at one end. The equilibrium density profiles obtained show that, sufficiently close to the phase boundary, a meniscus separating liquid-like and vapour-like phases forms near the capped end, and that as capillary evaporation is approached, continuously unbinds from the capped end. Our numerical results indicate that the divergence of the adsorption due to the unbinding of the meniscus is logarithmic and is the same as for the complete wetting transition in systems with short-ranged forces.

Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: II. General diagrammatic structure

In our first paper, we showed how a non-local effective Hamiltonian for short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson model. Here, we combine the Greens function method with standard perturbation theory to determine the general diagrammatic form of the binding potential functional beyond the double-parabola approximation for the Landau-Ginzburg-Wilson bulk potential. The main influence of cubic and quartic interactions is simply to alter the coefficients of the double parabola-like zigzag diagrams and also to introduce curvature and tube-interaction corrections (also represented diagrammatically), which are of minor importance. Non-locality generates effective long-ranged many-body interfacial interactions due to the reflection of tube-like fluctuations from the wall. Alternative wall boundary conditions (with a surface field and enhancement) and the diagrammatic description of tricritical wetting are also discussed.