  In this report, we discuss whether the optimal electric field to promote the
growth of armchair- type nanotubes (metallic character) evaluated using the
previous Huckel-Poisson method can be applied at the tip of a nanotube in a
realistic system. Setting the cross-section of a nanotube and the external
field by the sheath, we estimate an effective area at the sheath edge. Since
the electric charge distribution in a nanotube caused by the external electric
field was determined in our previous study, we obtained the electric field
distribution out of a nanotube by solving the Poisson equation and clarified
the structure of the electric field lines. By determining the effective area,
we show the optimal interval of the catalyst metal, which is necessary to
selectively grow the metallic nanotubes. When nanotubes grow thickly during the
initial stage of growth, a strong electric field cannot be applied to the tips
of the tubes. As a tube grows and the tube length increases, we found that the
optimal electric field decreased. To maintain the chemical activity at the tip,
the sheath electric field must be decreased. We estimated the decreasing rate
of the sheath field to the tube length.
