Specific heats of dilute neon inside long single-walled carbon nanotube and related problems
Abstract
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 Lennard-Jones 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 Shr\"odinger equation to consider the thermal behavior of gas in the potential. But if T Tc, we must solve the Shr\"odinger equation. For Ne in (20,20) nanotube, we obtain Tc≈ 60 K.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.