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

TL;DR

This paper derives an analytical potential for neon inside a single-walled carbon nanotube and studies its specific heats, revealing a transition from 3D to 2D gas behavior at different temperatures, with implications for low-temperature physics.

Contribution

It provides an analytical formula for neon potential inside nanotubes and analyzes the temperature-dependent specific heats, highlighting dimensional behavior transitions.

Findings

Ne exhibits 3D gas behavior at high temperatures.

Ne behaves as 2D gas at low temperatures.

At ultra low temperatures, Ne acts as a lattice gas.

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 $\mathcal{T}_c$ for low density gas in a potential is put forward. If $\mathcal{T}\gg \mathcal{T}_c$, we just need to use the classical statistical mechanics without solving the Shr\"{o}dinger equation to consider the thermal behavior of gas in the potential. But if $\mathcal{T}\sim \mathcal{T}_c$, we must solve the Shr\"{o}dinger equation. For Ne in (20,20) nanotube, we obtain $\mathcal{T}_c\approx 60$ K.