Casimir Forces Between Nanoparticles and Substrates

We study the Casimir force between a nanoparticle and a substrate using a spectral representation formalism. We consider the interaction of metal nanoparticles with dierent substrates within the dipolar approximation. The force is calculated as a function of the distance between the particles and the substrate. The particles are made of gold or potassium spheres, and the substrate is titanium dioxide, sapphire or a perfect conductor.