dielectric constant and nano science

First- it is good to know that permittivity is not a constant. It depends upon frequency, among other things.
Permittivity is a response of a non-conductive material (not exclusively) to electromagnetic field. It is important to define the "nano-scale" to know a reply to your question. In physical interpretation, permittivity may be expressed as a resistance to moving a charge. The elastic resistance can be interpreted as the real part of permittivity, the braking effect, to imaginary part.
Nano-scale can be a size of a grain, a size of a molecule, or, an atom. Such structures do have a charge, and should have a permittivity. It is easier to experiment with light wave that is comparable with nano-scale. Longer waves also move charges but maybe their effect upon nano-scale objects is weaker.