Long nanotube dielectric properties used as sensors of large molecules: a semicontinuum approach

A semicontinuum approach on the basis of an effective polarizability tensor per length and radius units is used to describe the dielectric response of a long single wall nanotube to the adsorption of an extended molecule. Changes in the permittivity ratio of the nanotube+molecule over the nanotube alone, which are directly connected to frequency shifts of the nanotube in a resonator configuration due to the presence of the molecule, provide a test of sensitivity of the system. The behavior of this ratio is analyzed for linear and circular geometries of the molecule, as a function of the tube characteristics (length and radius) and of the molecular size and polarizability distribution. Extension to three dimensional systems with a large set of polarizable centers is discussed in terms of self-polarization of the centers and morphology of the surface of the sensed system.