MOLECULAR PHYSICS, 2003, VOL. 101, NO. 6, 805–815 Computer simulation of cavity pair distribution functions of hard spheres in a hard slit pore WILLIAM R. SMITH 1 and HORST L. VO ¨ RTLER 2 * 1 Department of Mathematics and Statistics, and School of Engineering, College of Physical and Engineering Science, University of Guelph, Guelph, Ontario, Canada N1G2W1 2 Department of Molecular Dynamics and Computer Simulation, Institute for Theoretical Physics, University of Leipzig, Augustusplatz 9-11, 04109 Leipzig, Germany (Received 18 July 2002; revised version accepted 16 September 2002) We describe efficient Monte Carlo computer simulation techniques to calculate conditional distribution functions for pairs of hard-sphere (HS) cavities in a hard slit pore of width L, n  ðz 1 ; z 2 ; rÞ, and use these as an efficient route to calculating the corresponding dimensionless excess chemical potentials " e ðz 1 ; z 2 ; rÞ. z i is the distance of an HS centre from a (specified) wall and r is the distance between the cavity centres. This is the first calculation of such functions, which are of interest in their own right and provide data for the testing of theories, in addition to providing data for a simple model for the infinite dilution behaviour of a polyatomic solute in a simple molecularly confined solvent. Results are presented for special cases for the cavity functions n  ðz 1 ; z 2 ; rÞ which occur when the spheres are in the same plane, when the line of sphere centres is perpendicular to the walls, and when the spheres are in contact. We compare results obtained using the Kirkwood superposition approximation in conjunction with results obtained from the computer simulation data using the first member of the BGY integral equation hierarchy. The approximation is found to be exact in certain limiting geometrical situations, but in general is quantitatively poor. 1. Introduction The behaviour of fluids in molecularly confined media is of broad interest and importance in many areas, including chromatography, oil recovery, catalysis, sep- aration technologies, and colloid behaviour. A system of pure hard spheres (HS) in a hard slit pore is one of the simplest molecular-based models of confined fluids (referred to herein as an HSSP system). The basic thermodynamic quantity of interest for an HSSP system is the adsorption isotherm, giving the HS pore density as a function of the properties of the bulk HS fluid with which it is in equilibrium. The basic struc- tural quantities are the HS density profile in the slit, &ðzÞ, where z is the distance of a particle from a wall, and the dimensionless excess chemical potential, " e ðzÞ, where  ¼ 1=kT, k is Boltzmann’s constant and T the absolute temperature. (In the following, all distances are measured in units of the sphere diameter, which is set to unity.) These quantities have been studied for the HSSP system using various methods, including com- puter simulation [1–7], integral equation [3, 4, 8], density- functional theory (DFT) [8, 9–11], and theories using geometrical arguments similar to those used in scaled- particle theory (SPT) [2, 12]. More detailed information concerning the molecular structure of an HSSP system is provided by the cavity correlation function, yðz 1 ; z 2 ; rÞ, and the corresponding dimensionless excess chemical potential, " e ðz 1 ; z 2 ; rÞ, where z i are particle distances from a specified wall and r is the inter-particle centre–centre distance. These quantities are of interest in their own right, and also provide basic data for the testing of theories. " e ðz 1 ; z 2 ; rÞ are equivalent to the infinite dilution excess chemical potentials of corresponding fused- hard-sphere (FHS) molecules in the HS solvent in the slit, and as such they provide a basic model for the corresponding situation involving a real polyatomic solute in a simple molecularly confined solvent. To our knowledge, no results for these quantities exist in the literature for HSSP systems. The purpose of this paper is to present efficient com- puter simulation techniques to calculate structural quan- tities related to pairs of HS in the HSSP system, and to present results for representative state conditions. In the Molecular Physics ISSN 0026–8976 print/ISSN 1362–3028 online # 2003 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/0026897021000044061 *Author for correspondence. e-mail: horst.voertler@ physik.uni-leipzig.de