Thermal transport in isotopically disordered carbon nanotubes

TL;DR

This study investigates how isotopic disorder affects phononic thermal conductivity in carbon nanotubes, revealing size-dependent divergence, significant conductance reduction, and validating Green's function results with Boltzmann approaches.

Contribution

It introduces a scalable Green's function method to analyze thermal transport in large disordered nanotubes and compares it with Boltzmann models, highlighting their agreement.

Findings

Thermal conductivity diverges with system length in nanotubes.

Isotopic disorder causes up to 80% reduction in thermal conductance.

Green's function and Boltzmann methods show good agreement for experimental sizes.

Abstract

We present a study of the phononic thermal conductivity of isotopically disordered carbon nanotubes. In particular, the behavior of the thermal conductivity as a function of the system length is investigated, using Green's function techniques to compute the transmission across the system. The method is implemented using linear scaling algorithms, which allows us to reach systems of lengths up to $L=2.5\mu$m (with up to 400,000 atoms). As for 1D systems, it is observed that the conductivity diverges with the system size $L$. We also observe a dramatic decrease of the thermal conductance for systems of experimental sizes (roughly 80% at room temperature for $L = 2.5$ $\mu$m), when a large fraction of isotopic disorder is introduced. The results obtained with Green's function techniques are compared to results obtained with a Boltzmann description of thermal transport. There is a good agreement between both approaches for systems of experimental sizes, even in presence of Anderson localization. This is particularly interesting since the computation of the transmission using Boltzmann's equation is much less computationally expensive, so that larger systems may be studied with this method.