Dielectrophoresis has appeared recently as a non-destructive means to manipulate and sort carbon nanotubes. In order to compute the electrostatic forces that act on carbon nanotubes when subjected to an external field and placed in the vicinity of metallic protrusions, we develop a technique that relies on a monopole-dipole description of the nanotubes and on a dielectric-function model of the metallic elements. The technique proceeds iteratively between these two descriptions in order to determine the nanotube polarization and the resulting counter-polarization of the metallic elements. Specific differentiation schemes as well as a finite-difference formulation of Poisson's equation are given in cartesian and cylindrical coordinates. As an application, we compute the polarization and forces that act on a metallic (5, 5) and a semiconducting (10, 0) nanotube, when placed in the vicinity of a flat metallic support with either a conical or semi-elliptical protrusion. The results quantify the relevant electrostatic forces as well as the contribution of the image interaction to these forces. It is shown that the nanotubes get more polarized and attracted to the protrusion when the latter has a semi-elliptical shape. The differences in the polarization and forces that act on the metallic (5, 5) and semiconducting (10, 0) nanotubes support the idea that dielectrophoresis may be used to separate them.
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