researchers from the international centre for theoretical physics (ictp) and the international school for advanced studies (sissa), both in trieste, italy, have studied the physical mechanisms behind the movement of a single gold nanocluster on a graphene membrane from a hot region to a cold one.
a nanocluster of gold moves from a hot region to cold on a sheet of graphene. (emanuele panizon)
according to a report on the sissa website, the thermophoretic forces that push the particle away from the heat do not decrease as the length of the membrane increases and, through simulations, the researchers showed that flexural phonons, vertical thermal oscillations in the graphene, are pushing the gold nanocluster like a wave pushing a surfboard.
“using specific software, the researchers have simulated the behavior of a tiny gold nanocluster, made of a few hundred atoms, adsorbed on a graphene sheet suspended between two ends with different temperatures,” the report explained.
the researchers were not surprised to see the particle move to the colder gradient but were not expecting the force to be the same regardless of the length of the membrane. they named this particular thermophoretic force ballistic.
one of the researchers explained, “using a simple metaphor, imagine the two ends of the graphene sheet as the top and the bottom of a slide at the playground, and the temperature difference as the height gap. in the macroscopic world we experience in our everyday life, the closer the ends of the slide are, the faster the drop of the object will be. in the nanoworld, according to our simulations, this is not what happens. at this scale, force and dropping speed only depend on the temperature gradient. but not on the distance.”
the flexural phonons transfer mechanical momentum to the gold nanocluster, which induces it to move.
the research was published by proceedings of the national academy of sciences. the abstract stated:
“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 nonequilibrium molecular dynamics study of a test system—a gold nanocluster adsorbed on free-standing graphene clamped between two temperatures δtapart—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 100-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. however, 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.”
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