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Scientists in the US have used a novel photonic microscope to make the first real-time observations of thermal vibrations in carbon nanotubes (CNTs). Their results reveal a rich dynamical regime that has not yet been explored in these miniature resonators, including weakly chaotic behaviour and quasi-periodic modulations that yield a long-range coherence about three orders of magnitude higher than previously reported.
Scientists have long been interested in the mechanical vibrations of CNTs for use in applications such as nanoscale biosensors, but probing these dynamics has proved challenging. Standard electrical techniques tend to produce noise, while electron microscopes can cause unwanted material deposition on CNTs at room temperature. Even optical detection presents a problem as the tiny optical cross-section of CNTs causes most light to pass straight through them without any significant interaction.
The research team, led by Paul McEuen at Cornell University in the US, found a way around the limitations of optical detection by fabricating an optical resonator from a silicon nitride micro-disk. Coupling the nanotube to such an optical cavity boosts the effective cross-section of the nanotube to allow its mechanical motion to be detected in real time.
In the experiment, a nanotube was suspended next to the optical cavity using electrically-connected gold microtweezers. This strengthens the light–CNT interaction by orders of magnitude, allowing the nanotube to absorb as much as 50% of light from the cavity. As the nanotube vibrates in the evanescent field from the optical cavity, its movements can be measured by a fast photodiode that monitors the light transmitted through the cavity. Since the CNT was much longer than the size optical mode, the scientists could be sure that the tweezers would not affect the measurement.
The researchers found that the CNT oscillates with a period of 1.5 µs. However, they also observed that the frequency and amplitude show pseudo-periodic behaviour over much longer timescales, typically 10 ms. This shows that the nanotube vibrations exhibit nonlinear behaviour that is driven only by weak thermal fluctuations
McEuen and colleagues believe that the CNT oscillator behaves in a similar way to the dynamics that is described by the so-called Fermi-Pasta-Ulam-Tsingou (FPUT) problem. The FPUT observation shows how introducing nonlinearity to an oscillator causes recurrences over long time periods, rather than rapidly dissipating mechanical energy to reach equilibrium.
Their analysis reveals that some of the energy in this system dissipates rapidly, over millisecond timescales, but then quasi-periodic modulations decay over a much longer time period. As a result, the quality-factor for the nanotube oscillator is calculated to be 4000 for the initial decay, rising to 20,000 when computed over the full decay time. This overall system value is between two and three orders of magnitude larger than the known quality-factor of CNTs, which was previously estimated with time-averaging methods.
According to the researchers, the pseudo-periodicity they observe bears the hallmarks of a weakly chaotic mechanical “breather” – in which energy concentrates in low-frequency modes, disperses into higher-frequency modes, and then returns.
This long-period energy dissipation is reminiscent of macroscopic mechanical systems, while the strong thermal coupling observed in CNT dynamics is also similar to the behaviour of semi-flexible polymers. This new insight into the dynamics of nanomechanical systems could, the researchers hope, lead to a better understanding of the mechanisms that govern fast molecular processes.
The full results are published in Nature.