J. A. White

HOW THE STRUCTURE OF A CONFINED FLUID DEPENDS ON THE ENSEMBLE : HARD SPHERES IN A SPHERICAL CAVITY

The equilibrium structure of a hard-sphere fluid confined in a small spherical cavity is investigated. In such systems the statistical mechanical ensembles are no longer equivalent and we consider both open (grand canonical) and closed (canonical) cavities in order to analyze the effects of size and packing constraints on the density profile of the confined fluid. For systems in the grand canonical ensemble the profiles are obtained from grand canonical ensemble Monte Carlo simulations and from density functional theory. The profiles of the closed (canonical) systems are obtained by means of canonical ensemble Monte Carlo simulations. A scheme is proposed which expands the canonical ensemble density profiles in terms of grand canonical averages; this is formally a series in powers of the inverse average number of particles. By comparing canonical ensemble Monte Carlo data with the results of the expansion applied to grand canonical ensemble Monte Carlo data and to the results of density functional theory ...

On the universal behavior of some thermodynamic properties along the whole liquid-vapor coexistence curve

When thermodynamic properties of a pure substance are transformed to reduced form by using both critical- and triple-point values, the corresponding experimental data along the whole liquid-vapor coexistence curve can be correlated with a very simple analytical expression that interpolates between the behavior near the triple and the critical points. The leading terms of this expression contain only two parameters: the critical exponent and the slope at the triple point. For a given thermodynamic property, the critical exponent has a universal character but the slope at the triple point can vary significantly from one substance to another. However, for certain thermodynamic properties including the difference of coexisting densities, the enthalpy of vaporization, and the surface tension of the saturated liquid, one finds that the slope at the triple point also has a nearly universal value for a wide class of fluids. These thermodynamic properties thus show a corresponding apparently universal behavior along the whole coexistence curve.

Density functional theory of fluids in nanopores: Analysis of the fundamental measures theory in extreme dimensional-crossover situations

Two density functional theories, the fundamental measures theory of Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)] and a subsequent approximation by Tarazona [Phys. Rev. Lett. 84, 694 (2000)] are applied to the study of the hard-sphere fluid in two situations: the cylindrical pore and the spherical cavity. The results are compared with those obtained with grand canonical ensemble Monte Carlo simulations. The differences between both theories are evaluated and interpreted in the terms of the dimensional crossover from three to one and zero dimensions.

Fluctuations in an equilibrium hard-disk fluid: Explicit size effects

Explicit size corrections in the calculation of the fluctuations in the number of particles in a finite subvolume of a hard-disk fluid composed of a fixed number of particles are considered. The size corrections are obtained on the basis of a Taylor series expansion of the pair distribution function of the N-particle system in powers of 1/N. Analytical density dependent expressions are obtained at low density. These expressions show that not only explicit size effects (due to consideration of a fixed number of particles) but also edge effects that result from considering a finite subvolume must be taken into account. A general density dependence study is also reported by relating the relative fluctuation in the number of particles to the equation of state. Numerical results for the Henderson equation of state are obtained. These theoretical results are compared with Monte Carlo computer simulation results.

The Ornstein-Zernike equation in the canonical ensemble

A general density-functional formalism using an extended variable space is presented for classical fluids in the canonical ensemble (CE). An exact equation that plays the role of the Ornstein-Zernike (OZ) equation in the grand canonical ensemble (GCE) is derived in the CE. When applied to the ideal gas we obtain the exact result for the total correlation function hN. In the case of the homogeneous fluid with N particles, the new equation only differs from OZ by 1/N and it allows us to obtain an approximate expression for hN in terms of its GCE counterpart that agrees with the expansion of hN in powers of 1/N.

Fluctuations in a small hard-disk system: Implicit finite size effects

The influence of implicit finite size effects on the fluctuation in the number of particles in a subvolume is studied for a small system of hard disks with a fixed number of particles. The implicit (or anomalous) finite size effects—that arise from the use of periodic boundary conditions—are taken into account by including the periodicity of the total system into a model pair correlation function. Two pair correlation functions are considered; the accurate Percus–Yevick result and an approximation proposed by Baus and Colot that yields an excellent isothermal compressibility. Although very good agreement with canonical ensemble Monte Carlo results is obtained in both cases, it appears that the theoretical expression obtained for the fluctuation in the number of particles is rather sensitive to the thermodynamic and structural information conveyed by the pair correlation function.

Fluctuations in the random sequential adsorption of disks and parallel squares: Finite size effects at low coverages

This work is focused on explicit finite size corrections in the calculation of the fluctuation in the number of hard disks and parallel (aligned) hard squares deposited on a finite flat surface through a random sequential adsorption process. Explicit size effects are made evident by using a finite-system pair correlation function for calculating the fluctuation. The method is based on the relation between this pair correlation function and its infinite-system counterpart. A diagrammatic density (coverage) expansion of the corresponding infinite-system pair correlation function is used to calculate the low-coverage behavior of the fluctuation. Results also include border effects due to consider a finite size region for evaluating the fluctuation. A comparison with Monte Carlo computer simulations shows an excellent agreement between theoretical and simulation results.

Finite-size effects in the microscopic structure of a hard-sphere fluid in a narrow cylindrical pore

We examine the microscopic structure of a hard-sphere fluid confined to a small cylindrical pore by means of Monte Carlo simulation. In order to analyze finite-size effects, the simulations are carried out in the framework of different statistical mechanics ensembles. We find that the size effects are specially relevant in the canonical ensemble where noticeable differences are found with the results in the grand canonical ensemble (GCE) and the isothermal isobaric ensemble (IIE) which, in most situations, remain very close to the infinite system results. A customary series expansion in terms of fluctuations of either the number of particles (GCE) or the inverse volume (IIE) allows us to connect with the results of the canonical ensemble.

Microcanonical single-particle distributions for an ideal gas in a gravitational field

The single-particle energy, velocity and height probability distributions for an ideal gas in a gravitational field are obtained within the microcanonical ensemble framework. The asymptotic expressions for these distributions in the thermodynamic limit are also reported.

Density profiles of a hard disk mixture inside a small circular cavity: Effect of the conservation of the total angular momentum

We investigate the finite-size effect due to the conservation of the total angular momentum L in a hard-disk mixture confined to a hard circular cavity. The study is made by means of molecular dynamics simulations in the microcanonical ensemble. Given the geometry of the cavity and the nature of interparticle interactions, L is conserved if the cavity hard wall is smooth, that is, if one considers particle–wall specular collisions. Conversely, L fluctuates about its mean value for a rough hard wall for which the (energy-conserving) collisions are not specular. The size effect due to the conservation of L becomes apparent in several situations where the two types of wall lead to density profiles that are significantly different. The rough-wall results are related to the smooth-wall ones by means of a series expansion in terms of the fluctuations in the total angular momentum.