Specific heats of dilute neon inside long single-walled carbon nanotube

An elegant 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 out under the condition of the LennardJones potential between Ne and carbon atoms. Specific heats of dilute Ne inside long (20, 20) SWNT are calculated at different temperatures. It is found that Ne exhibits 3-dimensional (3D) gas behavior at high temperature but behaves as 2D gas at low temperature. Especially, at ultra low temperature, Ne inside (20, 20) nanotubes behaves as lattice gas. A coarse method to determine the characteristic temperature Tc for low density gas in a potential is put forward. If T ≫ Tc, we just need to use the classical statistical mechanics without solving the Shrödinger equation to consider the thermal behavior of gas in the potential. But if T ∼ Tc, we must solve the Shrödinger equation. For Ne in (20,20) nanotube, we obtain Tc ≈ 60 K. Submitted to: J. Phys.: Condens. Matter PACS numbers: 61.46.+w, 82.60.Fa ∗ To whom correspondence should be addressed ([email protected]) Specific heats of Ne inside single-walled carbon nanotube 2