Depletion forces between two spheres in a rod solution

– We study the depletion interaction between spherical particles of radius R immersed in a dilute solution of rigid rods of length L. The computed interaction potential is, within numerical accuracy, exact for any value of L/R. In particular we find that for L ∼ R, the depth of the depletion well is smaller than the prediction of the Derjaguin approximation. Our results bring new light into the discussion on the lack of phase separation in colloidal mixtures of spheres and rods. Mixtures of colloids are abundant in industry as paints, glues, lubricants and other materials [1]. They are also present in the preparation of foods and drugs, and in the biological realm: many living organisms or components of living organisms are colloidal suspensions of a variety of sizes and shapes. A pervasive issue in the colloidal domain is the stability of colloidal suspensions. Stability is often necessary for practical purposes as in paint formulation for instance, but certain applications like water treatment or mineral recovery might instead require aggregation or flocculation to occur. The determination of the stability criteria or the study of the flocculation kinetics can be achieved with reasonably good accuracy once the interparticle interaction potentials are known [2]. In a system of a pure colloidal species the two main interactions are the van der Waals attraction and the hard-core repulsion. Such a system is intrinsically unstable, the van der Waals attractive component of the potential always leading to flocculation. In practice the stabilization of the suspension is enforced by using the screened electrostatic repulsion in aqueous solutions or steric polymer layers in organic solvents. To a good approximation the stabilized suspension can then be regarded as hard-core particles with no attractive potential component. One way of treating the stability issue in a colloidal mixture of two components is by considering the effective potential that the second species induces between two particles of the first species. A well-studied case [3], [4] is the attractive potential that a solution of hard-core spheres of radius r0 induce between two spheres of radius R (see fig. 1). To first order in concentra-