Depletion potential between large spheres immersed in a multicomponent mixture of small spheres

We analyze the depletion potential between large spheres in a multicomponent mixture of dense small spheres (up to seven components) using the integral equation theory (IET), in which semiempirical bridge functions are incorporated, and the insertion approach within the framework of density functional theory (DFT). The diameters of the small spheres considered are in the range of $dS–5dS$⁠. The results from the IET and DFT are in close agreement with each other. The depletion potential in the mixture is substantially different from that in a one-component system of dense small spheres with diameter $dS$⁠. In comparison with the latter, the former possesses in general a less pronounced oscillatory structure, and the free-energy barrier for large spheres to overcome before reaching the contact is significantly reduced. This tendency can be enhanced as the number of components increases. In a several-component mixture of small spheres whose diameters are suitably chosen and in which the packing fractions of the components share the same value, the depletion potential is essentially short ranged and attractive and possesses a sufficiently large, negative value at the contact.