Frank van Swol

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...

Lennard‐Jones fluids in cylindrical pores: Nonlocal theory and computer simulation

We present adsorption isotherms, phase diagrams, and density profiles for a Lennard‐Jones fluid confined to a cylindrical pore. In particular, we concentrate on the gas–liquid transition in the pore (capillary condensation). We compare simulations for a series of radii and different temperatures with mean field density functional theory (MFT). Two forms of MFT are considered, the simple local density approximation (LDA) and Tarazona’s nonlocal or smoothed density approximation (SDA). We find that the SDA provides a quite accurate description of fluid structure in the pore and that it produces phase diagrams in good agreement with the simulation data. For larger radii and temperatures T/Tc≳0.6 the SDA shows steep rises in adsorption close to the transition. This strongly affects the shape of the coexistence curve in the T, ρ plane. Here ρ is defined as the average density inside the pore. This behavior is confirmed by the simulation. In contrast, LDA gives a poor representation of the fluid structure and...

Liquid-vapour coexistence in a cylindrical pore

We report molecular dynamics calculations of a Lennard-Jones fluid in a cylindrical pore. Following a temperature quench the fluid spontaneously phase-separates into a liquid-like region and a gas-like region. The two regions are separated by a hemispherical meniscus. The capillary condensation is located for two temperatures via a calculation of the chemical potential of the two-phase system. Coexistence disappears when the temperature is raised to kTϵ = 1·0, indicating the existence of a capillary critical point.

Adsorption hysteresis in narrow pores

We present molecular dynamics computer simulation results for adsorption hysteresis in a cylindrical pore. The adsorption is examined by inducing pore filling and emptying by changing the pore length at constant number of particles. By calculating the full density profile of the fluid in the pore, one can observe both processes. Hysteresis, overshooting the thermodynamic transition, is observed for both pore filling and emptying. That is, we observe metastable one‐phase states on either side of the transition. The end of the gas branch (pore filling) is signaled by the growth of an unduloid, resulting in the formation of a biconcave lens of liquid, while the end of the liquid branch (pore emptying) occurs by the formation of a bubble. However, the latter appears to be an artifact of the lack of pore ends in the model. In the presence of pore ends, the bubble formation is expected to be preempted by the receding of the meniscus.

Hard-sphere Mixtures Near A Hard-wall

We report a study of hard‐sphere mixtures of different sizes near a hard wall using both the Monte Carlo method and density functional theory. The theory is based on a semiempirical free‐energy functional for an inhomogeneous hard‐sphere mixture and is similar to that developed by Tarazona for pure hard‐sphere fluids. Comparison between the theoretical results and the simulations for the density profiles of both species and the mole fraction profile shows that the present theory is capable of describing the structure of hard‐sphere mixtures against a hard wall up to a size ratio, R≡σ2/σ1, of about 3. For R values greater than 3 the theory gives some discrepancies for densities very close to the wall.

On the approach to complete wetting by gas at a liquid-wall interface

We study the approach to complete wetting by gas at the interface between a repulsive wall and dense liquid, paying particular attention to the basic model consisting of a hard-wall system approaching bulk liquid-vapour coexistence. This class of wetting phenomena is of special interest from the point of view of the compressibility route to interfacial statistical mechanics and for its suitability to direct observation by computer simulation. On the theoretical side, there exists a battery of exact sum rules that are of direct relevance to the problem and it is possible to make use of capillary wave fluctuation theory in almost the same form as has been developed for the study of liquid-vapour interfaces. The main conclusion of our study is that in the approach to complete wetting the capillary wave fluctuations of the developing liquid-vapour interface continue to manifest themselves at the wall, even when the liquid is separated from the wall by a macroscopic layer of gas. This implies a diverging trans...

Lennard-Jones Mixtures In A Cylindrical Pore. A Comparison of Simulation and Density Functional Theory

Abstract We report simulation results for binary Lennard-Jones mixtures in narrow cylindrical pores. The parameters are chosen to model an Ar-Kr mixture in a carbon dioxide pore. We focus on capillary condensation and locate this transition directly via a molecular dynamics simulation of two-phase coexistence. The chemical potentials in the pore are obtained via the particle insertion method. The latter results are used in a subsequent grand canonical Monte Carlo simulation in order to determine the bulk pressure, density and composition. We report density profiles and phase diagrams and compare the results with the local version of mean field density functional theory predictions for the same model. The simulation results for a mixture in which we neglect the size difference between Ar and Kr are compared with the non-local theory.

Lennard-Jones mixtures in cylindrical pores

We report mean field density functional theory results for Lennard-Jones mixtures in straight cylindrical pores. The interaction parameters were chosen to model argon-krypton. We present density profiles, adsorption isotherms and phase diagrams and discuss the effects of temperature and pore size on capillary condensation.

Perturbation theory of a model hcp solid

Spherically averaged radial distribution functions of hard-sphere hexagonal close-packed (hcp) structures have been estimated by Monte Carlo simulations for a wide range of solid densities. By fitting the Monte Carlo data, an accurate analytical expression for that function was obtained for use in thermodynamic perturbation theory of the solid state. We present results of perturbation theory for hcp structures over a range of temperatures and densities in the solid region. The method of Kang et al. employed in these calculations is a generalization of the Weeks, Chandler and Andersen theory, which accurately describes high density fluids and solids. Following a calculation of the relative stability of model hcp and fcc solids, the phase boundary between these two structures was determined. For the familiar cut and shifted Lennard-Jones potential, the fcc lattice is more stable along the gas-solid line for temperatures above T* = 0·3. There is a transition to the hcp structure at lower temperatures. The di...

Grand potential densities of wall–liquid interfaces approaching complete drying

We present molecular dynamics computer simulation data for the pressure tensor components of planar wall–liquid interfaces, along two ‘‘orthogonal’’ approaches to complete drying states. The interfacial structure varies from incipient solid‐like packing, at positive adsorption, to smooth behavior, close to complete drying. We pay particular attention to the accompanying changes in the grand potential density, or to be more precise, in the transverse component of the pressure tensor of Irving and Kirkwood.