DEPLETION FORCE IN COLLOIDAL SYSTEMS

The entropic depletion force, in colloids, arises when large particles are placed in a solution of smaller ones, and sterically constrained to avoid them. We calculate the interaction between large spheres (of radius R) in a dilute solution of mutually avoiding small spheres (of diameter sigma much less than R and volume fraction phi), to third ord er in phi. In addition to the well-known attractive force for 0 < h < sigma, we find a repulsive barrier at larger separations, and beyond t hat a secondary minimum. Except for unusually large size ratios (perha ps abetted by relatively high density phi), these features of the inte raction potential are too small, compared to k(B)T, for kinetic stabil ization (arising from the barrier) or flocculation into the secondary minimum, to be widespread, although such effects are possible in princ iple. For feasible size ratios, the same features should have observab le consequences for the radial distribution function of the large sphe res. Such effects can be viewed as precursors, at low density, of liqu idlike structuring (solvation forces) expected at higher phi. Our thir d order calculation gives satisfactory agreement with a recent compute r simulation at moderate density and size ratio (2R/sigma = 10; phi = pi/15).