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RESEARCH PAPERS: Micro/Nanoscale Heat Transfer

# Thermal Contact Resistance and Thermal Conductivity of a Carbon Nanofiber

[+] Author and Article Information
Choongho Yu1

Department of Mechanical Engineering and Center for Nano and Molecular Science and Technology, Texas Materials Institute,  The University of Texas at Austin, Austin, Texas 78712

Sanjoy Saha, Jianhua Zhou

Department of Mechanical Engineering and Center for Nano and Molecular Science and Technology, Texas Materials Institute,  The University of Texas at Austin, Austin, Texas 78712

Li Shi2

Department of Mechanical Engineering and Center for Nano and Molecular Science and Technology, Texas Materials Institute,  The University of Texas at Austin, Austin, Texas 78712

Alan M. Cassell, Brett A. Cruden, Quoc Ngo, Jun Li

Center for Nanotechnology,  NASA Ames Research Center, Moffett Field, CA 94035

1

Current address: Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720.

2

Author to whom correspondence should be addressed; e-mail: lishi@mail.utexas.edu

J. Heat Transfer 128(3), 234-239 (Sep 18, 2005) (6 pages) doi:10.1115/1.2150833 History: Received December 20, 2004; Revised September 18, 2005

## Abstract

We have measured the thermal resistance of a $152‐nm$-diameter carbon nanofiber before and after a platinum layer was deposited on the contacts between the nanofiber and the measurement device. The contact resistance was reduced by the platinum coating for about 9–13% of the total thermal resistance of the nanofiber sample before the platinum coating. At a temperature of $300K$, the axial thermal conductivity of the carbon nanofiber is about three times smaller than that of graphite fibers grown by pyrolysis of natural gas prior to high-temperature heat treatment, and increases with temperature in the temperature range between $150K$ and $310K$. The phonon mean free path was found to be about $1.5nm$ and approximately temperature-independent. This feature and the absence of a peak in the thermal conductivity curve indicate that phonon-boundary and phonon-defect scattering dominate over phonon-phonon Umklapp scattering for the temperature range.

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## Figures

Figure 1

Cross-sectional transmission electron micrographs of the as grown carbon nanofibers obtained from PECVD. Panel (a) shows a low magnification image depicting the vertical orientation and alignment of the carbon nanofibers. Panel (b) shows a higher magnification image which reveals the microstructural arrangement of the graphitic sheets in the fibers and panel (c) details the disordered crystalline morphology that reveals nanofiber cone angles around 10deg. Scale bars are 2μm, 50nm, and 20nm, respectively, for (a), (b), and (c).

Figure 2

(a) A scanning electron microscopy (SEM) image of the microdevice before the nanofiber was deposited. (b) A SEM image of a rectangular portion in (a) showing a carbon nanofiber bridging two membranes. The scale bars correspond to 20μm and 2μm, respectively, in (a) and (b).

Figure 3

Calculated temperature distribution in the measurement device. Each membrane is 25μm long, 14μm wide, and 0.5μm thick. Each of the ten supporting beams of the actual device was 210μm long and 2μm wide. In the calculation, the beam length was scaled down to 10μm with the thermal resistance of the beams kept the same by rescaling the thermal conductivity of the beams. The edges of the RTs and the nanowire are highlighted in white. The contact resistance per unit length between the nanofiber and the membrane was taken to be 0.03Km∕W.

Figure 4

(a) Measurement results of Qh+QL plotted as a function of ΔTh+ΔTs; (b) Measurement results of ΔTs plotted as a function of ΔTh−ΔTs. Also shown in each figure are the equation and the square of the Pearson product moment correlation coefficient (R2) of the linear curve fitting.

Figure 5

SEM images of the two contacts between the nanofiber and the two membranes after a thin Pt layer was deposited on the contacts. The scale bars in the two images are 500nm.

Figure 6

Measured thermal resistance of the nanofiber sample before a Pt layer was deposited (solid black circles) and after a Pt layer was deposited with the use of the electron beam (open circles). The inset shows the reduction in contact resistance, ΔRc, after the Pt coating.

Figure 7

Calculation results of thermal contact resistance (Rc) at 150K and 300K as a function of the cross-plane thermal conductivity (k⊥ or kcross‐plane) of the nanofiber. The five lines in each figure correspond to a contact width of 2b=0.1nm (long dashed line), 2b=1nm (dotted line), 2b=10nm (short dashed line), 2b=50nm (double dotted line), and 2b=100nm (solid line).

Figure 8

Thermal conductivity of the nanofiber (solid circles) calculated from the measured thermal resistance of the sample after the Pt coating. The uncertainty error bars do not include the residual contact resistance after the Pt coatings. The thermal conductivity of a graphite fiber (open circles) from Ref. 3 is shown for comparison.

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