  A simple formula for coordinates of carbon atoms in a unit cell of a
single-walled nanotube (SWNT) is presented and the potential of neon (Ne)
inside an infinitely long SWNT is analytically derived under the assumption of
pair-wise Lennard-Jones potential between Ne and carbon atoms. Specific heats
of dilute Ne inside infinitely long (5, 5), (10, 10), (15, 15) and (20, 20)
SWNT's are calculated at different temperatures. It is found that Ne inside
four kinds of nanotubes exhibits 3-dimensional (3D) gas behavior at high
temperature but different behaviors at low temperature: Ne inside (5, 5)
nanotube behaves as 1D gas but inside (10, 10), (15, 15), and (20, 20)
nanotubes behaves as 2D gas. Furthermore, at ultra low temperature, Ne inside
(5, 5) nanotube still displays 1D behavior but inside (10, 10), (15, 15), and
(20, 20) nanotubes behaves as lattice gas.

Mesoscale and Nanoscale Physics;Statistical Mechanics