Using the second virial coefficient as physical criterion to map the hard-sphere potential onto a continuous potential.

In the same sense as in the extended law of corresponding states [M. Noro and D. Frenkel, J.

Assessment of the micro-structure and depletion potentials in two-dimensional binary mixtures of additive hard-disks.

Depletion forces are a particular class of effective interactions that have been mainly investigated in binary mixtures of hard-spheres in bulk. Although there are a few contributions that point toward the effects of confinement on the depletion potential, little is known about such entropic potentials in two-dimensional colloidal systems. From theoretical point of view, the problem resides in the fact that there is no general formulation of depletion forces in arbitrary dimensions and, typically, any approach that works well in three dimensions has to be reformulated for lower dimensionality.

A Brownian dynamics algorithm for colloids in curved manifolds.

The many-particle Langevin equation, written in local coordinates, is used to derive a Brownian dynamics simulation algorithm to study the dynamics of colloids moving on curved manifolds. The predictions of the resulting algorithm for the particular case of free particles diffusing along a circle and on a sphere are tested against analytical results, as well as with simulation data obtained by means of the standard Brownian dynamics algorithm developed by Ermak and McCammon [J. Chem.

Demixing transition, structure, and depletion forces in binary mixtures of hard-spheres: the role of bridge functions.

Asymmetric binary mixtures of hard-spheres exhibit several interesting thermodynamic phenomena, such as multiple kinds of glassy states. When the degrees of freedom of the small spheres are integrated out from the description, their effects are incorporated into an effective pair interaction between large spheres known as the depletion potential. The latter has been widely used to study both the phase behavior and dynamic arrest of the big particles.