Interrelation of elasticity and thermal bath in nanotube cantilevers

TL;DR

This study investigates how the stiffness of individual carbon nanotubes varies with temperature by measuring their resonance frequencies, revealing a significant reduction in Young's modulus influenced by phonon interactions.

Contribution

It presents the first experimental analysis of the thermal dependence of nanotube stiffness and compares it with theoretical models based on lattice thermal dynamics.

Findings

Young's modulus decreases with temperature at about -173 ppm/K

Resonance frequencies are affected by phonon interactions in the nanotube

Theoretical models successfully reproduce the observed thermal behavior

Abstract

We report the first study on the thermal behaviour of the stiffness of individual carbon nanotubes, which is achieved by measuring the resonance frequency of their fundamental mechanical bending modes. We observe a reduction of the Young's modulus over a large temperature range with a slope $-(173\pm 65)$ ppm/K in its relative shift. These findings are reproduced by two different theoretical models based on the thermal dynamics of the lattice. These results reveal how the measured fundamental bending modes depend on the phonons in the nanotube via the Young's modulus. An alternative description based on the coupling between the measured mechanical modes and the phonon thermal bath in the Akhiezer limit is discussed.