Dimensional Crossover of Dilute Neon inside Infinitely Long Single-Walled Carbon Nanotubes Viewed from Specific Heats

TL;DR

This study analytically investigates the specific heats and dimensional crossover behavior of dilute neon gas confined inside various single-walled carbon nanotubes, revealing temperature-dependent transitions from 3D to 1D or 2D behaviors.

Contribution

It provides a simple formula for nanotube atom coordinates and derives neon potential energy, analyzing how neon's thermodynamic behavior changes with temperature and nanotube size.

Findings

Ne exhibits 3D gas behavior at high temperatures.

Ne behaves as 1D gas in small nanotubes at low temperatures.

Ne behaves as 2D gas or lattice gas in larger nanotubes at low temperatures.

Abstract

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.