Theory and calculation of colloidal depletion interaction

Abstract

Colloidal dispersion is composed of particles with size ranging from 1 nm to [Formula: see text]m dispersed in solvents. There are the volume exclusion interaction and other interactions between colloidal particles, of which the former interaction causes the depletion effect. When a big sphere is immersed in the colloidal system of small spheres, there is a depletion layer around the big sphere where the center of small sphere cannot enter. The depletion layers of two big spheres overlap if they are close to each other, increasing the free volume accessed by small spheres and thereby enlarging the entropy of the system. As a result, an effective interaction between the two big spheres is resulted from the change of entropy as a function of their distance, which is referred to as the depletion interaction. This paper first introduces the concept and scenario of the depletion interaction in colloidal systems. Then we briefly introduce various numerical or simulations methods of the depletion interaction of hard sphere systems, such as the acceptance ratio method, Wang–Landau method, and the density functional theory method. Taking the Asakura–Oosawa model as an example, we introduce a useful approximation method, Derjaguin approximation as well as the derivation of some approximate formula for the depletion interaction of different hardcore colloidal systems, such as between a pair of spheres in mono-disperse small spheres, between a hard sphere and a hard wall in a liquid of small spheres, and between a pair of hard spheres in a liquid of thin rods and thin disks.