J. R. Henderson

On the interface between a fluid and a planar wall

The statistical mechanics of inhomogeneous systems is usefully discussed from at least two complementary approaches: (i) the virial route, in which calculations of the structure and the thermodynamic properties are based on knowledge of the intermolecular forces in conjunction with the distribution function hierarchy, and (ii) the fluctuation theory route, based on formal results linking the equilibrium structure and properties of a system to its response to a change in external field. This paper makes use of both of these approaches to discuss the properties of a fluid in the presence of a strong localized external field. Particular attention is paid to the limiting case when the external field acts as a hard wall. Fluctuation theory yields a unified approach to interfaces stabilized by one body external fields of arbitrary strength, the strength determining the stability of the interfacial boundary with respect to wave-like fluctuations; with the weak field limit identified as a free fluid-fluid interfa...

Asymptotic decay of correlations in liquids and their mixtures

We consider the asymptotic decay of structural correlations in pure fluids, fluid mixtures, and fluids subject to various types of inhomogeneity. For short ranged potentials, both the form and the amplitude of the longest range decay are determined by leading order poles in the complex Fourier transform of the bulk structure factor. Generically, for such potentials, asymptotic decay falls into two classes: (i) controlled by a single simple pole on the imaginary axis (monotonic exponential decay) and (ii) controlled by a conjugate pair of simple poles (exponentially damped oscillatory decay). General expressions are given for the decay length, the amplitude, and [in class (ii)] the wavelength and phase involved. In the case of fluid mixtures, we find that there is only one decay length and (if applicable) one oscillatory wavelength required to specify the asymptotic decay of all the component density profiles and all the partial radial distribution functions gij(r). Moreover, simple amplitude relations lin...

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...

Vapour sensing using surface functionalized gold nanoparticles

The electrical and optical response of thin films of surface functionalized nanoparticles upon exposure to various chemical vapours has been studied. It was found that the electrical response to chemical vapours adsorbed on the various nanoparticle films varied markedly and was determined by the surface functional groups. Ellipsometric studies revealed that the film thickness increased during exposure to the chemical vapours. These thickness changes of the films correlate with the changes in electrical conductivity. Two physical effects are believed to play a role in determining these conductivity changes. Under high partial pressure, the change in nanoparticle core-core separation is the main contribution to the change in conductivity and generally leads to a reduction in the conductivity. However, for relatively low partial pressures the adsorption of vapour molecules leads to permittivity changes that tend to increase the conductivity.

Liquid‐state integral equations at high density: On the mathematical origin of infinite‐range oscillatory solutions

Analytic asymptotic analysis and finite element numerical procedures are used to elucidate the mathematical reasons for the appearance of infinite‐range oscillatory solutions to certain integral equation theories of wall–fluid interfacial structure and liquid state radial distribution functions. The results contribute to two issues of recent debate: (i) what physical significance (if any) can be attributed to the apparent ‘‘solidlike’’ structure that is often (but not always) seen in high density solutions to liquid state integral equation theories and (ii) is the same mathematical structure present in density functional theories (i.e., in the presence of a variational condition arising from a free energy functional)?

Molecular dynamics simulations of wetting and drying in LJ models of solid-fluid interfaces in the presence of liquid-vapour coexistence

The structure and phase behaviour of adsorbed films is modelled by cut and shifted LJ fluid in the presence of cut and shifted 9-3 walls. At fixed N, it is straightforward to use molecular dynamics simulation procedures to study planar adsorbed films in the presence of ‘bulk’ liquid-vapour coexistence. A series of five isotherms are investigated in detail, ranging from temperatures close to the bulk triple point to a little over half way to the critical point. As a by-product, accurate data are obtained for liquid-vapour coexistence properties and surface tensions of cut and shifted LJ fluid. Wall-fluid excess grand potentials are calculated and compared with the predictions of weighted density functional theory. Isotherms of contact angle against wall-fluid attractive interaction strength are given, each covering the entire region from complete drying to complete wetting. The dynamics of wetting transitions is not accessible in our geometry. In contrast, the presence of a suitable collective mode enables...

Simulation study of the disjoining pressure profile through a three-phase contact line.

Computer simulations are performed to measure the disjoining pressure profile Pi(y) across the three-phase contact line formed by a liquid-vapor interface intersecting a planar substrate wall lying in the xy plane. The method makes use of an exact expression for the disjoining pressure in terms of the density profile and the wall-fluid interaction. Pi(y) is reported for three distinct values of the wall-fluid attractive potential, representing differing levels of partial wetting by macroscopic adsorbed drops. Mechanical force-balance normal to the substrate is confirmed by direct evaluation of the required analog to Youngs equation. For the model system under study, the disjoining pressure profiles are well-fitted by inverted Gaussians. The fitted results are used with an extension (to large values of Youngs contact angle theta) of the interface Hamiltonian theory of Indekeu, thereby enabling us to report the line tension tau(theta).

Surface energy of ethylene-co-1-butene copolymers determined by contact angle methods.

Wilhelmy plate measurements of contact angles with a series of test liquids are used to calculate the surface energies of two poly(ethylene-co-1-butene) random copolymers. Results from five methods of calculation are reported: one-liquid (Good-Girifalco and Neumann), two-liquid (harmonic mean and geometric mean), and three-liquid (Lifshitz-van der Waals acid-base) methods. We find that all five methods are sensitive to the choice of test liquids used for contact angle measurements, as previously reported, but consistent results are obtained if recommended combinations of liquids are used. The mean results of the three-liquid acid-base method are judged to be the most reliable and informative, leading to surface energies of 30.8 mJ/m2 for poly(ethylene-co-1-butene) copolymer composed of 92 mol% ethylene and 30.2 mJ/m2 for copolymer composed of 88 mol% ethylene.

Wetting at a fluid–wall interface. Computer simulation and exact statistical sum rules

We report on a search by computer simulation to locate an example of a wetting transition at a fluid–wall interface, namely, the transition between partial wetting and complete ‘wetting’ by vapour at a weakly attractive wall in the presence of bulk liquid–vapour coexistence, for a system with strictly finite-range interactions. In addition, general statistical-mechanical theory with direct application to wetting phenomena is described and used to interpret simulation results. Our data clearly show the presence of a first-order wetting transition at a moderately attractive wall, particularly when analysed with the help of statistical-mechanical sum rules. Both theory and simulation indicate that our type of wetting transition is qualitatively influenced by the local fluid structure at the wall. We also find that simple fluctuation theory yields a semi-quantitative description of our results. In the partial wetting region, the surface tension data are consistent with a first-order wetting transition at the point indicated by the adsorption results and with the prediction of an exact statistical sum rule for the variation of the contact angle with wall strength.

Interfacial statistical geometry: Fluids adsorbed in wedges and at edges

An exact sum rule is derived that links the structure of fluids adsorbed in wedges and at edges to the interfacial free energy far from the wedge apex. By focusing on hard-wall models, one observes a correspondence between interfacial statistical mechanics and geometry. The physical necessity of this correspondence can be argued from the presence of complete drying at a hard wall. Invoking the potential distribution theorem generates yet another class of geometric results, this time concerning the excluded volume generated by a sphere rolling along the surface of the wedge. Direct proof of these latter geometric theorems is straightforward in two-dimensions. Acute wedges and the right-angled wedge, provide examples of models for which comparison with simulation data and density functional theory are available.