Theory of the depletion force due to rodlike polymers

The entropic depletion force, in colloids, arises when large particles are placed in a solution of smaller ones, and sterically constrained to avoid them. In this paper, we consider a system of two parallel plates suspended in a semidilute solution of long thin rods of length L and diameter D. By numerically solving an integral equation, which is exact in the “Onsager limit” (D≪L), we obtain the depletion force between the plates. The second integral of this determines (via the Derjaguin approximation) the depletion potential between two large hard spheres of radius R, immersed in a solution of hard rods (satisfying D≪L≪R). The results for this potential are compared with our previous second order perturbation treatment [Y. Mao, M. E. Cates, and H. N. W. Lekkerkerker, Phys. Rev. Lett. 75, 4548 (1995)], as well as with newly computed third order perturbation results. There is good agreement at low and intermediate densities (which validates our numerical procedures for the integral equation) but the gradua...

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