Thermal and Structural Characterizations
of Individual Carbon Nanotubes
Michael Thompson Pettes and Li Shi
Department of Mechanical Engineering and the Center for Nano and Molecular Science and
Technology, Texas Materials Institute, University of Texas at Austin, Austin, Texas 78712, USA
Background
Conclusions
Several thermal conductance measurements have been made on individual carbon nanotubes (CNTs) since
2001. A major deficiency in these measurements is that the chiral angle, defect concentration, and thermal
contact resistance of the individual nanotubes were not characterized in detail. Additionally, thermal transport in
CNTs with high electrical bias have been shown to have large non-equilibrium phonon populations, exhibiting
different thermal transport characteristics than in CNTs with thermalized phonons.
• Defect concentration appears to increase with number of walls
• Thermal contact resistance per unit length obtained for three
as-grown multi-walled carbon nanotubes (MWCNTs) is in the
range of 78 – 585 mKW-1 at room temperature
Objectives
• Intrinsic thermal conductivity for three MWCNTs is in the range
of 42 – 343 Wm-1K-1; the calculated phonon mean free path
correlates well with the TEM observed defect concentration
• Establish the structure-thermal property relationship by conducting thermal conductance and transmission
electron microscopy (TEM) on the same individual single-walled (SW), double-walled (DW), and multi-walled
(MW) CNTs grown by thermal chemical vapor deposition (CVD) between two suspended microthermometers
• Large thermal contact resistance limits effective  for asgrown SW and DW CNTs to ~ 600 Wm-1K-1 at room
temperature
• Quantify the thermal contact resistance to CNTs by conducting thermal measurements before and after
deposition of platinum-carbon (Pt-C) composites at the contacts.
CNT Growth Method
Suspended
Microthermometer Device
•
Methods
Updated design of Shi, L., et al., ASME J. Heat Transfer 125, 881 (2003)
Thermal Resistance Circuit
•
1 nm Fe, 0.5 nm Ru thin-film evaporated / sputtered onto
electrodes
•
Growth at 900 oC with 200 cm3min-1 flowing methane.
Qh=Idc2Rh = Joule heating generated on heating
membrane
Ql=Idc2Rl = Joule heating generated in each of
the two DC current-carrying leads
 dR

Th  Th  T0   Relectrical ,h Th    electrical ,h 
dT


 dRelectrical , s 
Ts  Ts  T0   Relectrical , s Ts   

dT


Fe-Ru Catalyst
1
1
Q  Ts / RB   Th  Ts  / Rs
Th  Ts
RB 
Qh  Ql
Methane
Hinged Furnace
 T - Ts 
Rs   Rc ,l  Rc ,r  RNT   RB  h


T
s


1" Quartz
Tube
 T + Ts  Th - Ts 
 Rs   h


Q
+Q

T
L 
s
 h

900 °C
Dimensions
SWCNT Sample S1 SWCNT Sample S2
MWCNT Sample M1
Sample # Walls di / do [nm] L [µm] Lc,l [µm] Lc,r [µm]
S1
1
2.34
4.31
N/A
2.10
S2
1
1.5
2.03
0.72
N/A
D1
Samples
Frontispiece for M.T. Pettes, L. Shi, Adv. Funct. Mater.; DOI: 10.1002/adfm.200900932 to appear in issue 24/2009
Presented at the 2009 Fall Meeting of The Materials Research Society, 2009 Nov 30 – Dec 4, Boston, MA; Session K – Nanotubes and Related Structures, K18.31.
2
2.1 / 2.7
4.02
0.40
0.64
A
5
7.0 / 10.3 3.02
0.92
2.53
M1 B
5
7.0 / 10.5 2.83
2.44
2.53
C
5
6.9 / 9.9
3.06
0.80
1.63
M2
5
6.8 / 9.9
1.95
2.14
0.40
M3
7
6.7 / 11.4
1.97
3.28
0.57
Before Pt-C
Grain size, La ~ 29 nm
After Pt-C
DWCNT Sample D1
Grain size, La ~ 33 nm
MWCNT Sample M3
11
6.6 / 14.0 3.31
2.29
MWCNT Sample M4
Before Pt-C
Grain size, La ~ 20 nm
Before Pt-C
M4
MWCNT Sample M2
5.63
After Pt-C
di and do are the inner and outer CNT
diameters, respectively. L is the as-grown
CNT suspended length. Lc,l and Lc,r are left
and right CNT-membrane contact lengths.
MWCNT sample M1 consists of three
individual CNTs in parallel, labeled A, B, and
C. N/A = not available.
After Pt-C
After Pt-C
Grain size, La ~ 13 nm
Chirality determined from electron diffraction per
Gao et al., Appl. Phys. Lett. 82, 2703 (2003)
Effective Thermal Conductivity
Thermal Contact Resistance and Intrinsic Thermal Conductivity
We express the thermal contact resistance using the fin
heat transfer model:
1
Rc , j
  A

L
c, j
NT


tanh

R
'

c
  NT AR' c




Results
To estimate the per unit length thermal contact
resistance value after Pt-C deposition, R'c,a, we analyze
the work of Chang et al., Phys. Rev. Lett. 101, 075903
(2008) to obtain
We use the obtained intrinsic thermal
conductivity, and the specific heat, C, and
basal plane debye velocity, n, for graphite
to obtain the phonon mean free path, l,
using the expression from kinetic theory:
  12 Cn l
• R'c,a = 10 – 41 mKW-1
We use the measured thermal resistance before and
after Pt-C deposition along with the R'c,a value to
calculate the R'c,b value before Pt-C deposition and the
intrinsic axial thermal conductivity, NT:
As-measured effective thermal conductivity () versus temperature (T) for the
two SWCNT, one DWCNT, and four MWCNT samples in this work. Filled
symbols and unfilled symbols are results measured before and after Pt-C
deposited at the contacts, respectively.
Acknowledgements
Measured thermal resistance (Rs) versus temperature (T) for
three MWCNT samples before (filled symbols) and after
(unfilled symbols) Pt-C was deposited at the contacts.
U.S. Department of Energy award DE-FG02-07ER46377
Sample
R'c,b [mKW-1]
NT [Wm-1K-1]
M1
201 – 258
269 – 343
M3
78 – 125
178 – 336
M4
439 – 585
42 – 48
Phonon mean free path (l) determined from the
obtained intrinsic thermal conductivity versus
the effective grain size (La) obtained by TEM
for three MWCNTs.
E-mail: [email protected]
National Science Foundation Graduate Research FellowshipWeb:
Program
http://www.me.utexas.edu/~lishi
National Science Foundation Thermal
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