Molecular dynamics of hard spheres. II. Hard spheres in a spherical cavity

Abstract

The equation of state for hard spheres in a spherical cavity is calculated and compared with the results previously found when the containing boundary was a channel. It was found that the spherical surface provides a focusing effect on both the pressure and the compressibility factor. An examination of the results suggested that the density and compressibility factors could be expanded in a series of Maxwellian functions. It was found that a six-term series which was modified in the immediate vicinity of the wall was sufficient. This has an advantage over the usual Fourier series expansion in that less terms are required. In addition, an argument can be made that such a series has a foundation in the physics of the problem.

Fluids inside a pore—an integral-equation approach

“…Numerical methods for solving these integral equations for a hardsphere fluid are described in w 4. Quantitative results are discussed and compared with simulation results [4,5] in w 5. For simplicity, we focus in this paper on a one-species hard-sphere system of particles inside hard spherical and slit pores.…”

“…Recently, the structure and thermodynamics of fluids inside micropores have attracted wide attention [1][2][3][4][5][6][7][8][9][10][11]. This is because such systems are not only related to various separation processes such as adsorption, exclusion chromatography and membrane transport, but they also exhibit a richer variety of thermodynamic [1] and structural behaviour than bulk fluid systems.…”

“…McQuarrie et al I-3] have considered the virial expansion of the grand potential for the particles inside spherical and slit pores. Computer simulations of a spherical [4], slit-like [5,6] and cylindrical pore [1][2][3][4][5][6][7]8] have been carried out for hard-sphere [4, Y. Zhou and G. Stell 5,7] and Lennard-Jones fluids [6,8]. Integral-equation theories for fluids inside a slit pore have been investigated by means of a BBGKY hierarchy with a kind of superposition approximation [5] (using a method in which both bulk and average densities have to be inputted), as well as a shielding approximation [9], in which the resulting density profile is a product of the density profile of a single-wall and an exponential factor.…”

The effect of nanopore shape on the structure and isotherms of adsorbed fluids

“…Simulations have been used to study fluids adsorbed in slit pores (Sarman, 1990;Somers and Davis, 1992;Murad et al, 1993;Han et al, 1993;Tan and Gubbins, 1992;Somers et al, 1993;Schoen et al, 1989;Jiang et al, 1993), cylindrical pores Suh, 1987, 1989;Groot et al, 1987;Antonchenko et al, 1988;Bratko et al, 1989;Heinbuch and Fischer, 1987;Glandt, 1980;Derouane and Lucas, 1988;Peterson et al, 1986;Peterson and Gubbins, 1987;Walton and Quirke, 1989;Saito and Foley, 1990;Demi, 1991), and spherical pores (Macpherson et al, 1987;Carignan et al, 1988;Dunne and Myers, 1994).…”

Fluids in Model Pores or Cavities: The Influence of Confinement on Structure and Phase Behaviour

“…Despite its appealing simplicity, there have been relatively few studies of fluids in spherical cavities [3][4][5][6], most investigators preferring slit and cylindrical capillaries [7]. Earlier work for small cavities includes virial expansions of the grand potential [3,4], integral equation theories [5], and computer simulation [6]. Direct calculation of the partition functions can be made for cavities containing up to about six atoms [4].…”