Three-Dimensional Density Profiles of Small and Medium Spheres near a Pair of Large Spheres: Relevance to Entropic Interaction Induced between Large Spheres

In the system we consider, a pair of large hard spheres, whose surface separation is fixed at a prescribed value. is immersed in a binary mixture comprising small and medium hard spheres. The density profiles of the medium and small spheres near the large spheres are calculated using the three-dimensional integral equation theory. When the surface separation equals the medium-sphere diameter, a medium sphere is held between the large spheres in contact with both of their surfaces. This is represented by an extremely sharp, high peak in the reduced density profile of medium spheres. It is found that the profile can be reproduced by the Kirkwood superposition approximation Using the reduced density profile Of Medium spheres around a single large sphere, which is calculated Using the radial-symmetric integral equation theory. The small spheres are excluded by the medium sphere held as described above, and the thermal pressure due to the small spheres acting on each large-sphere surface becomes highly asymmetrical. This asymmetry induces a strongly attractive force between the large spheres. The exclusion of the small spheres by the medium sphere is exhibited in the reduced density profile of the small spheres.