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Recently the double layer forces and interaction free energies between spherical colloidal particles, according to the Poisson-Boltzmann equation, have been accurately calculated by us and others. In this paper we conclude our investigations in this area by extending the calculation of double layer interactions to unequal spherical particles. We also consider the case of a sphere and a plate, a geometry relevant to atomic force microscope measurements when a colloidal particle is attached to the cantilever tip. We compare the results against those of the linearized Poisson-Boltzmann equation and the Deryaguin approximation over a wide range of conditions. The Deryaguin approximation is found to be highly accurate for the force in sphere/plate geometry and acceptably so for dissimilar spheres under typical colloidal conditions. We conclude with comments on the double layer forces acting on a bare atomic force microscope tip.

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