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Heat transfer and friction between two closely spaced objects due to phonon transfer across a vacuum gap

Periodic Reporting for period 1 - PhononGap (Heat transfer and friction between two closely spaced objects due to phonon transfer across a vacuum gap)

Reporting period: 2016-04-01 to 2018-03-31

The problem being addressed is the possibility of phonons - which is one of the primary carriers of heat in solids - being able to transmit across a vacuum gap from one surface to another due to the presence of van der Waals force between the two surfaces, and the subsequent quantification of heat transfer and friction due to this phonon transmission.

This quantification is important to the nano and microelectromechanical industry especially for the design of miniature devices where distance between components is of the order of a few nanometers – the nanometer spacing between writing head and the storage disk in hard drives is a case in point.

The main objectives of my work were to develop an analytical model to quantify phonon transmission across a vacuum gap due to the presence of van der Waals forces, and use this analytical model to estimate the heat transfer and friction between surfaces.
During the fellowship, I along with my principal supervisor Sir John Pendry and collaborator Prof. Richard Craster, were successful in the objective of developing a model to quantify phonon transmission by using the theory of elastic wave propagation. Interestingly, we were able to show that low frequency phonons can transmit across vacuum gap with a transmission coefficient of near unity. Using this model we were also able to estimate the heat transfer across vacuum gap due to the transmission of phonons.

In order for this result to be relevant to the industry, we quantified the heat transfer values for different materials commonly used in the nano and micro-mechanical industry such as silicon, germanium, quartz and polyethylene. We showed that for nanometer spacings the heat transfer from this mode of phonon transmission can exceed the heat conduction in the presence of air gap at room temperature and atmospheric pressure.

This result is highly important to the nano and microelectromechanical industry especially for the design of miniature devices where distance between components is of the order of a few nanometers. These results were discussed with the research staff of Seagate Hard drives during a Heat Transfer conference in Bad Honneff, Germany.

While developing the model we discovered that a simple coupled harmonic oscillator description can be used for such an analysis. A collaboration with Professor Girish Agarwal from Texas A&M university was established to extend this model to optical phonons. We successfully showed that such a coupled harmonic oscillator model can be used in place of the complication fluctuational electrodynamics theory that is currently employed by researchers to analyse near-field heat transfer.
At the time when the project was started there were three publications which attempted to quantify the phenomenon of phonon transmission due to van der Waals force between surfaces. These were listed in the 'state of the art' section in the project proposal. However, none of these publications took into account the effect of surface distortions due to the the presence of phonons on the van der Waals forces. Taking these surface distortions into account we were able to develop a new model which accurately quantifies the phonon transmission across vacuum gap and the resulting heat transfer from this. We showed that the other authors have overestimated the heat transfer that can occur due to this van der Waals force.

With advancement in nanotechnology the distance between components in several miniature devices in daily use - such as that between writing head and magnetic storage disk in a hard drive - is of the order of a few nanometers. During this fellowship we showed that for nanometer spacings the heat transfer from this mode of phonon transmission can exceed the heat conduction in the presence of air gap at room temperature and atmospheric pressure. Such an analysis becomes important in the design of miniature devices where the components are separated by a few nanometers as this heat transfer, if unaccounted for, can lead to failure of devices. Indeed, we had communication with hard disk drive manufacturers (Seagate Industries) to confirm these findings.
phonon reflection and trasmission due to van der Waals force