  We study the Casimir force between a nanoparticle and a substrate. We
consider the interaction of metal nanoparticles with different substrates
within the dipolar approximation. We study the force as a function of the
distance for gold and potassium spheres, which are over a substrate of titanium
dioxide, sapphire and a perfect conductor. We show that Casimir force is
important in systems at the nanometer scale. We study the force as a function
of the material properties, radii of the spheres, and the distance between the
sphere and the substrate.
