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Research Papers

Modeling the Optical and Radiative Properties of Vertically Aligned Carbon Nanotubes in the Infrared Region

[+] Author and Article Information
Richard Z. Zhang, Xianglei Liu

George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Zhuomin M. Zhang

George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: zhuomin.zhang@me.gatech.edu

1Corresponding author.

Manuscript received March 12, 2014; final manuscript received November 12, 2014; published online May 14, 2015. Assoc. Editor: L. Q. Wang.

J. Heat Transfer 137(9), 091009 (Sep 01, 2015) (9 pages) Paper No: HT-14-1129; doi: 10.1115/1.4030222 History: Received March 12, 2014; Revised November 12, 2014; Online May 14, 2015

During the past decade, research on carbon nanotubes has revealed potential advances in thermal engineering applications. The present study investigates the radiative absorption and reflection of vertically aligned carbon nanotubes (VACNTs) in the broad spectrum from the near-infrared to far-infrared regions. The optical constants of VACNT are modeled based on the dielectric function of graphite and an effective medium approach that treats the CNT film as a homogenized medium. Calculated radiative properties show characteristics of near-unity index matching and high absorptance up to around 20 μm wavelength. The packing density and degree of alignment are shown to affect the predicted radiative properties. The Brewster angle and penetration depth of VACNTs are examined in the infrared spectrum. The radiative properties for VACNT thin films are also evaluated, showing some reduction of absorptance in the near-infrared due to transmission for film thicknesses less than 50 μm. This study provides a better understanding of the infrared behavior of VACNT and may guide the design for its applications in energy harvesting, space-borne detectors, and stealth technology.

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Figures

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Fig. 1

Optical constants (n and κ) of graphite: (a) electric field perpendicular to the optical axis and (b) electric field parallel to the optical axis

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Fig. 2

(a) Illustration of a VACNT film of thickness H grown on a silicon substrate, where the inset shows a unit cell of width a containing a multiwalled CNT of diameter d for a periodic array; (b) perfectly aligned CNTs with an alignment factor x = 1.0; and (c) imperfectly aligned CNTs where x < 1. Typical VACNT coatings have alignment factor ranging from x = 0.95 to x = 0.99.

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Fig. 3

Effective optical constants of VACNT films with varying filling ratios f and alignment factors x: (a) and (b) refractive index for ordinary and extraordinary waves, respectively and (c) and (d) extinction coefficient for ordinary and extraordinary waves, respectively

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Fig. 4

Normal reflectance spectra of a semi-infinite VACNT films with varying filling ratios and alignment factors. The incidence angle upon the VACNT film is illustrated in the inset.

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Fig. 5

Contours of the reflectance versus wavelength and incidence angle for: (a) s-polarization and (b) p-polarization. The VACNT film is assumed to be semi-infinite with filling ratio f = 0.05 and alignment factor x = 0.98.

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Fig. 6

(a) Correlation of the Brewster angle θB and the principal angle θP with the wavelength. The abscissa and ordinate are interchanged in order to compare the traces with Fig. 5(b). (b) The reflectance as a function of the incidence angle for both polarizations at four distinct wavelengths.

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Fig. 7

Hemispherical absorptance spectra for s- and p-polarization, and the average of the two

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Fig. 8

Radiation penetration depths for: (a) s-polarization and (b) p-polarization at incidence angles θi = 0 deg, 30 deg, and 60 deg, with f = 0.05 and x = 0.98

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Fig. 9

Absorptance of VACNT film of different thicknesses with f = 0.05 and x = 0.98, at incidence angles of θi = 0 deg, 30 deg, and 60 deg: (a) s-polarization, H = 10 μm; (b) p-polarization, H = 10 μm; (c) s-polarization, H = 25 μm; (d) p-polarization, H = 25 μm; (e) s-polarization, H = 50 μm; and (f) p-polarization, H = 50 μm

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