Polymer-mediated interaction between a sphere and a plate

A recently developed method is applied to calculate the depletion interaction between a sphere and a flat plate due to nonadsorbing ideal polymers for arbitrary polymer-sphere ratios. The interaction potential is calculated from the polymer concentration profiles surrounding the sphere and plate based on the adsorption around the particles. The polymer concentration profile in the space near the two particles is the product of the polymer concentration profile due to the single plate and its profile around the single sphere. The product function profile is in good agreement with profiles calculated by computer simulations. The interaction potential derived from the adsorption using the product function agrees with analytical results for infinitely small and large spheres. It is shown that the force between a flat plate and a sphere goes to a minimum for large polymer-colloid ratios. These results show that a product function applies to the sphere-plate geometry and facilitates the calculation the depletion interaction between colloidal particles in complex cases.