DOI: 10.1021/nl9041966. Thermal Transport in Suspended and Supported Monolayer Graphene Grown by Chemical Vapor Deposition

Thermal Transport in Suspended and Supported Monolayer Graphene Grown by Chemical Vapor Deposition

10.1021/nl9041966

Crossref journal-article

American Chemical Society (ACS)

Nano Letters (316)

Bibliography

Cai, W., Moore, A. L., Zhu, Y., Li, X., Chen, S., Shi, L., & Ruoff, R. S. (2010). Thermal Transport in Suspended and Supported Monolayer Graphene Grown by Chemical Vapor Deposition. Nano Letters, 10(5), 1645â1651.

Authors 7

Weiwei Cai (first)
Arden L. Moore (additional)
Yanwu Zhu (additional)
Xuesong Li (additional)
Shanshan Chen (additional)
Li Shi (additional)
Rodney S. Ruoff (additional)

References 38 Referenced 1,104

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If a flat top laser beam with radiusr0is incident on the Au surface, the conduction thermal resistance of the gold support isRAu≈ 1/(4κAur0), whereκAuis the thermal conductivity of the gold support. The temperature rise of the Au layer is ΔT=QRAuwhereQis the heat absorbed by the Au. For the 100× objective lens, the maximum incident power used to obtain Fig2with 3% absorptivity of the Au layer andκAuassumed to be reduced to 100 W/m K for the evaporated Au film from the bulk value of 317 W/m K,(37)the maximum temperature rise in the Au was found to be 4 K, which is much smaller than the 114 K value measured on the supported graphene at the same incident laser power.
{'key': 'ref22/cit22', 'volume-title': 'Advanced Engineering Mathematics', 'author': 'Greenberg M.', 'year': '1998', 'edition': '2'} / Advanced Engineering Mathematics by Greenberg M. (1998)
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The maximum radiation transfer coefficient is obtained asgrad= σT3where σ is the Stefan-Boltzmann constant. The obtainedgradreaches the maximum value of 15 Wm−2K−1at the upper limit of the measured graphene temperature of 650 K. Assuming that the energy accommodation coefficient of air molecules is 1 and ignoring the diffusive thermal resistance in the air, we calculate the maximum heat transfer coefficient to the surrounding air as the air interface thermal conductance per unit area, that is,gair= (nv/4)C, wheren = P/kBTairis the number density of air molecules,v= (3kBTair/m)1/2is the root mean square velocity of air molecules,C= 5kB/2 is the specific heat of diatomic molecules such as O2and N2,kBis the Boltzmann constant,PandTairare the pressure and temperature of air molecules, andmis the mass of air molecules. The obtainedgairincreases with decreasingTairand approaches a maximum value of 1.08 × 105Wm−2K−1for the lower limit of 300 K for this measurement and is orders of magnitude larger thangrad. Thus,gradis negligible in comparison. The maximumgairvalue is used to calculate the heat loss to the airqair= ∫0R2πrgair(T(r) −Ta)dr. Neglecting the contact resistance so thatT1=Ta, we calculateqairas a function ofTmusing the measuredr0values for the two objectives. ForTm= 400 K, the obtainedqairis 0.026 and 0.033 mW, or 5 and 6 times lower than the measured absorbed laser powerQatTm400 K for the 100× and 50× objectives, respectively. In addition, usingg=gair= 1.08 x 105W m−2K−1in eq. 8, we obtain thermal conductivity values that are within 6% of the values in Figure5.
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10.1021/nn9016229

Dates

Type	When
Created	15 years, 4 months ago (April 20, 2010, 1:35 p.m.)
Deposited	2 years, 5 months ago (March 8, 2023, 10:38 a.m.)
Indexed	2 days, 4 hours ago (Aug. 21, 2025, 1:06 p.m.)
Issued	15 years, 4 months ago (April 20, 2010)
Published	15 years, 4 months ago (April 20, 2010)
Published Online	15 years, 4 months ago (April 20, 2010)
Published Print	15 years, 3 months ago (May 12, 2010)

Funders 0

None

BibTeX

@article{Cai_2010, title={Thermal Transport in Suspended and Supported Monolayer Graphene Grown by Chemical Vapor Deposition}, volume={10}, ISSN={1530-6992}, url={http://dx.doi.org/10.1021/nl9041966}, DOI={10.1021/nl9041966}, number={5}, journal={Nano Letters}, publisher={American Chemical Society (ACS)}, author={Cai, Weiwei and Moore, Arden L. and Zhu, Yanwu and Li, Xuesong and Chen, Shanshan and Shi, Li and Ruoff, Rodney S.}, year={2010}, month=apr, pages={1645–1651} }

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      "unstructured": "The maximum radiation transfer coefficient is obtained asgrad= \u03c3T3where \u03c3 is the Stefan-Boltzmann constant. The obtainedgradreaches the maximum value of 15 Wm\u22122K\u22121at the upper limit of the measured graphene temperature of 650 K. Assuming that the energy accommodation coefficient of air molecules is 1 and ignoring the diffusive thermal resistance in the air, we calculate the maximum heat transfer coefficient to the surrounding air as the air interface thermal conductance per unit area, that is,gair= (nv/4)C, wheren = P/kBTairis the number density of air molecules,v= (3kBTair/m)1/2is the root mean square velocity of air molecules,C= 5kB/2 is the specific heat of diatomic molecules such as O2and N2,kBis the Boltzmann constant,PandTairare the pressure and temperature of air molecules, andmis the mass of air molecules. The obtainedgairincreases with decreasingTairand approaches a maximum value of 1.08 \u00d7 105Wm\u22122K\u22121for the lower limit of 300 K for this measurement and is orders of magnitude larger thangrad. Thus,gradis negligible in comparison. The maximumgairvalue is used to calculate the heat loss to the airqair= \u222b0R2\u03c0rgair(T(r) \u2212Ta)dr. Neglecting the contact resistance so thatT1=Ta, we calculateqairas a function ofTmusing the measuredr0values for the two objectives. ForTm= 400 K, the obtainedqairis 0.026 and 0.033 mW, or 5 and 6 times lower than the measured absorbed laser powerQatTm400 K for the 100\u00d7 and 50\u00d7 objectives, respectively. In addition, usingg=gair= 1.08 x 105W m\u22122K\u22121in eq. 8, we obtain thermal conductivity values that are within 6% of the values in Figure5."
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  "alternative-id": [
    "10.1021/nl9041966"
  ],
  "URL": "http://dx.doi.org/10.1021/nl9041966",
  "relation": {},
  "ISSN": [
    "1530-6984",
    "1530-6992"
  ],
  "subject": [],
  "container-title-short": "Nano Lett.",
  "published": {
    "date-parts": [
      [
        2010,
        4,
        20
      ]
    ]
  }
}