Depletion interactions in colloidal fluids: statistical mechanics of Derjaguinʹs analysis

The statistical mechanics of hard-body models of colloidal fluids is reviewed for specific comparison with the well-known analysis of Derjaguin, predicting the nature of solvent-mediated colloidal interactions. Special attention is focussed on the so-called depletion interaction, for which Derjaguinʹs analysis predicts dramatic effects at medium to high solvent density, not supported by standard integral equation approximations, liquid state density functional theory, nor available simulation data. Nevertheless, the Derjaguin approximation/limit can be expressed in terms of an exact statistical mechanical sum rule, whose nature makes it difficult to argue for a qualitative breakdown of the Derjaguin prediction for depletion forces. I focus attention on the remarkable structural consequences implied by the Derjaguin sum rule analysis, including a possible physical interpretation in terms of the difficulty of squeezing out the final layer of solvent adsorbed between colloids or a colloid and a wall. I conclude that the statistical mechanics of colloidal depletion is extremely interesting, in that either current standard approximations in liquid state physics qualitatively fail to describe the phenomena, or our understanding of the physics of colloidal interactions is seriously defective.