Date of Award

Summer 8-20-2021

Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Master of Science (MS)

Department

Mechanical Engineering

Advisor

Sheila Edalatpour

Second Committee Member

Yingchao Yang

Third Committee Member

Olivier Putzeys

Abstract

Every object above zero kelvin emits electromagnetic radiation with the dominant wavelength determined using the Wien’s law (10 microns at room temperature). These waves can transfer energy and hence are the foundation of radiative heat transfer (RHT). RHT consists of two regimes: far-field and near-field. If the distance between the heat exchanging media is more than the dominant wavelength, the regime is far-field and is limited to the ideal Planck’s blackbody, and only propagating waves contribute to heat transfer. On the other hand, when the distance is less than the dominant wavelength, the regime is called the near-field. In near-field radiative heat transfer (NFRHT), the contribution of evanescent waves becomes more significant than the propagating ones, and this causes a spike in the spectral RHT that exceeds Planck’s blackbody limit by several orders of magnitude. If the thermal emitter supports surface modes, NFRHT can become monochromatic.

These surface modes can be surface phonon polaritons (SPhP) and surface plasmon polaritons (SPP). Materials such as silicon carbide support SPhP and graphene is an example of a material that support SPPs. These surface modes cause the quasi-monochromatic behavior that can be exploited for applications such as thermophotovoltaic devices and thermal rectifiers. Graphene is one of the few materials that support surface modes in the infrared where these modes can be thermally excited. Another characteristic of graphene SPPs is their tunability using gate voltage or chemical doping which has transformed graphene into a revolutionary material for NFRHT applications in mid-to far-infrared regions.

Graphene has been studied both theoretically and experimentally. However, in most NFRHT studies, graphene has been investigated theoretically for its application in NFRHT. NFRHT for graphene is calculated using its electrical conductivity. The studies in NFRHT have utilized a local method for graphene’s electrical conductivity called the Kubo formula. However, graphene is a non-local material that has non-local conductivity and dielectric response, hence it is not clear whether a local model such as the Kubo formula can capture the non-local behavior of graphene. In this thesis, a non-local model called the Lindhard formula is used to calculate graphene’s conductivity, and the radiative conductance between two graphene sheets. The Lindhard predictions are compared with the results obtained from the Kubo formula. It is found that at low chemical potential both methods agree, while by increasing the chemical potential of graphene, the Kubo formula overestimates the radiative conductance between two graphene sheets by several orders of magnitude. Increasing the gap size and reducing temperature would increase the difference. It is concluded that the observed differences are due to the simplification involved when deriving the Kubo formula, and therefore it is recommended to use the Lindhard formula in NFRHT studies.

Comments

Every object above zero kelvin emits electromagnetic radiation with the dominant wavelength determined using the Wien’s law (10 microns at room temperature). These waves can transfer energy and hence are the foundation of radiative heat transfer (RHT). RHT consists of two regimes: far-field and near-field. If the distance between the heat exchanging media is more than the dominant wavelength, the regime is far-field and is limited to the ideal Planck’s blackbody, and only propagating waves contribute to heat transfer. On the other hand, when the distance is less than the dominant wavelength, the regime is called the near-field. In near-field radiative heat transfer (NFRHT), the contribution of evanescent waves becomes more significant than the propagating ones, and this causes a spike in the spectral RHT that exceeds Planck’s blackbody limit by several orders of magnitude. If the thermal emitter supports surface modes, NFRHT can become monochromatic. These surface modes can be surface phonon polaritons (SPhP) and surface plasmon polaritons (SPP). Materials such as silicon carbide support SPhP and graphene is an example of a material that support SPPs. These surface modes cause the quasi-monochromatic behavior that can be exploited for applications such as thermophotovoltaic devices and thermal rectifiers. Graphene is one of the few materials that support surface modes in the infrared where these modes can be thermally excited. Another characteristic of graphene SPPs is their tunability using gate voltage or chemical doping which has transformed graphene into a revolutionary material for NFRHT applications in mid-to far-infrared regions. Graphene has been studied both theoretically and experimentally. However, in most NFRHT studies, graphene has been investigated theoretically for its application in NFRHT. NFRHT for graphene is calculated using its electrical conductivity. The studies in NFRHT have utilized a local method for graphene’s electrical conductivity called the Kubo formula. However, graphene is a non-local material that has non-local conductivity and dielectric response, hence it is not clear whether a local model such as the Kubo formula can capture the non-local behavior of graphene. In this thesis, a non-local model called the Lindhard formula is used to calculate graphene’s conductivity, and the radiative conductance between two graphene sheets. The Lindhard predictions are compared with the results obtained from the Kubo formula. It is found that at low chemical potential both methods agree, while by increasing the chemical potential of graphene, the Kubo formula overestimates the radiative conductance between two graphene sheets by several orders of magnitude. Increasing the gap size and reducing temperature would increase the difference. It is concluded that the observed differences are due to the simplification involved when deriving the Kubo formula, and therefore it is recommended to use the Lindhard formula in NFRHT studies.

Download

Share