On the Distribution Functions of Depletion Interactions

Abstract

Molecular dynamics computer simulations were performed on model colloidal binary mixtures of two large and many small soft repulsive spheres. Depletion forces arise between the two large spheres, as a function of their distance, because of the nonadditivity of the volume they exclude to the small spheres. The probability distribution functions of both longitudinal and transverse component of the total force exerted by the small particles were calculated and generally turned out non-Gaussian. The distributions of the collective forces were analyzed in terms of the distribution of the force that a single small sphere exerts on a large sphere and of the number of the surrounding small spheres. The reconstructed function matches well the corresponding exact distribution. Residual correlation among small particles, combined with a relatively small number of neighbors, slows the approach to the Gaussian limit. In our fully repulsive model, the direct force between a large and a small sphere is a monotonic function of their distance. On these bases, we propose and successfully test an approach that relates the probability distribution function of the depletion forces to the large-sphere-small-sphere radial distribution function. This approach can be extended to experimental data of radial distribution function, thus allowing for an estimate of depletion force fluctuations in real colloidal mixtures.