Ballistic thermophoresis of adsorbates on free-standing graphene

TL;DR

This study reveals a ballistic thermophoretic force acting on adsorbates on graphene, driven by flexural phonons, which persists over long distances and differs from traditional diffusive thermophoresis.

Contribution

It demonstrates a novel ballistic thermophoresis mechanism on graphene, linking flexural phonons to real momentum transfer via anharmonic coupling, extending understanding of nanoscale heat and mass transport.

Findings

Ballistic thermophoretic force persists beyond 100 nm.

Flexural phonons carry real momentum through anharmonic coupling.

Force is independent of local temperature gradient magnitude.

Abstract

The textbook thermophoretic force which acts on a body in a fluid is proportional to the local temperature gradient. The same is expected to hold for the macroscopic drift behavior of a diffusive cluster or molecule physisorbed on a solid surface. The question we explore here is whether that is still valid on a 2D membrane such as graphene at short sheet length. By means of a non-equilibrium molecular dynamics study of a test system -- a gold nanocluster adsorbed on free-standing graphene clamped between two temperatures $\Delta T$ apart -- we find a phoretic force which for submicron sheet lengths is parallel to, but basically independent of, the local gradient magnitude. This identifies a thermophoretic regime that is ballistic rather than diffusive, persisting up to and beyond a hundred nanometer sheet length. Analysis shows that the phoretic force is due to the flexural phonons, whose flow is known to be ballistic and distance-independent up to relatively long mean-free paths. Yet, ordinary harmonic phonons should only carry crystal momentum and, while impinging on the cluster, should not be able to impress real momentum. We show that graphene, and other membrane-like monolayers, support a specific anharmonic connection between the flexural corrugation and longitudinal phonons whose fast escape leaves behind a 2D-projected mass density increase endowing the flexural phonons, as they move with their group velocity, with real momentum, part of which is transmitted to the adsorbate through scattering. The resulting distance-independent ballistic thermophoretic force is not unlikely to possess practical applications.