Deriving the thermal conductivity of graphene

In summary, the thermal conductivity of graphene is an important physical property that measures how well graphene can transfer heat. It is typically measured in watts per meter kelvin (W/mK) and can be derived using various experimental and theoretical methods. The size and quality of the graphene sample, temperature, impurities, defects, orientation, and surrounding materials can all affect the thermal conductivity. Phonons, which are quantized lattice vibrations, play a crucial role in carrying heat energy through the graphene lattice. The thermal conductivity of graphene is extremely high, surpassing even traditional heat conductors such as copper and diamond.
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How do I go about deriving the thermal conductivity of graphene (specifically, in the low temperature limit) when I'm given the phonon dispersion relation?

I haven't been able to find anything explaining how the dispersion relation relates to the thermal conductivity in materials. (this is for a solid state physics course)
 
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What is the thermal conductivity of graphene?

The thermal conductivity of graphene is an important physical property that measures how well graphene can transfer heat. It is typically measured in watts per meter kelvin (W/mK) and can vary depending on the size and quality of the graphene sample.

How is the thermal conductivity of graphene derived?

The thermal conductivity of graphene can be derived using a variety of experimental and theoretical methods. One common method is to measure the temperature change across a graphene sample when a known amount of heat is applied, and then use this data to calculate the thermal conductivity using Fourier's Law.

What factors affect the thermal conductivity of graphene?

The thermal conductivity of graphene can be affected by a number of factors, including the size and quality of the graphene sample, the temperature, and any impurities or defects in the graphene structure. Additionally, the thermal conductivity of graphene can also be influenced by its orientation and the presence of other materials in its surroundings.

What is the role of phonons in the thermal conductivity of graphene?

Phonons, which are quantized lattice vibrations, play a crucial role in the thermal conductivity of graphene. They are responsible for carrying heat energy through the graphene lattice and can be affected by factors such as temperature, defects, and interactions with other materials.

How does the thermal conductivity of graphene compare to other materials?

The thermal conductivity of graphene is extremely high, with values reaching up to 5000 W/mK at room temperature. This makes it one of the most thermally conductive materials known, surpassing even traditional heat conductors such as copper and diamond.

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