Thermal conductivity of high performance carbon nanotube yarn-like fibersEric Mayhew and Vikas Prakash
Citation: Journal of Applied Physics 115, 174306 (2014); doi: 10.1063/1.4874737 View online: http://dx.doi.org/10.1063/1.4874737 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Synergistic effect of self-assembled carboxylic acid-functionalized carbon nanotubes and carbon fiber forimproved electro-activated polymeric shape-memory nanocomposite Appl. Phys. Lett. 102, 231910 (2013); 10.1063/1.4811134 Filler geometry and interface resistance of carbon nanofibres: Key parameters in thermally conductive polymercomposites Appl. Phys. Lett. 102, 213103 (2013); 10.1063/1.4807420 Branched carbon nanotube reinforcements for improved strength of polyethylene nanocomposites Appl. Phys. Lett. 101, 161907 (2012); 10.1063/1.4761936 Effective multifunctionality of poly(p-phenylene sulfide) nanocomposites filled with different amounts of carbonnanotubes, graphite and short carbon fibers AIP Conf. Proc. 1459, 142 (2012); 10.1063/1.4738424 Enhanced thermal conductivity of carbon fiber/phenolic resin composites by the introduction of carbon nanotubes Appl. Phys. Lett. 90, 093125 (2007); 10.1063/1.2710778
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
129.22.124.12 On: Tue, 05 Aug 2014 14:33:37
Thermal conductivity of high performance carbon nanotube yarn-like fibers
Eric Mayhew and Vikas Prakasha)
Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland,Ohio 44106-7222, USA
(Received 23 March 2014; accepted 19 April 2014; published online 5 May 2014)
In the present paper, we present results of thermal conductivity measurements in free standing carbon
nanotube (CNT) yarn-like fibers. The measurements are made using a T-type experimental
configuration utilizing a Wollaston-wire hot probe inside a scanning electron microscope. In this
technique, a suspended platinum wire is used both as a heater and a thermal sensor. A low frequency
alternating current source is used to heat the probe wire while the third harmonic voltage across the
wire is measured by a lock-in amplifier. The conductivity is deduced from an analytical model that
relates the drop in the spatially averaged temperature of the wire to that of the sample. The average
thermal conductivity of the neat CNT fibers and the CNT –polymer composite fibers is found to be
448 W/m-K and 225 W/m-K, respectively. These values for conductivity are amongst the highest
measured for CNT yarn-like fibers fabricated using a dry spinning process from vertically aligned
CNT arrays. The enhancement in thermal conductivity is understood to be due to an increase in the
CNT fiber elastic stiffness during the draw and twist operations, lower CNT thermal contact
resistance due to increase in CNT contact area, and better alignment of the CNT fibrils along the
length of the fiber. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4874737]
I. INTRODUCTION
In recent years, nanotube assemblies in high-packing
density and aligned configurations have been developed,
which offer a promising route to achieve higher strength and
transport properties in macroscopic materials. While the pri-
mary focus has been on production of these materials and on
their mechanical and electrical properties,1–9 other properties
including thermal conductivity are of both fundamental in-
terest and importance for applications such as heat dissipa-
tion in composite structures and thermal interface materials.
With a focus on experimental results, this paper addresses
thermal conductivity in carbon nanotube (CNT) yarn-like
fibers.
In the recent past, two distinct synthesis routes have
been utilized in the fabrication of neat CNT yarn-like fibers10
– the first route employs a solid-state process wherein CNTs
are either directly spun into a fiber from the synthesis reac-
tion zone11 or from a CNT forest array grown on a solid sub-
strate.6 The approach, however, does not lend itself to easy
scale up since it combines multiple steps, limiting options
for process and material optimization. Fibers fabricated
using this approach have been shown to have low packing
density and poor orientation and include impurities within
their structure.12 Despite these shortcomings, solid-state
CNT fibers have delivered the best mechanical properties
thus far.11,13,14 The reason for this success is understood to
be the length of CNTs that constitute these fibers.10 Longer
CNTs reduce the number of CNT ends (junctions) in a typi-
cal fiber, yielding greater strength,15 and may also increase
electrical and thermal conductivity.16 The alternate fiber pro-
duction route is wet spinning.1 In this process, the CNTs are
dissolved or dispersed in a fluid, extruded out of a spinneret,
and then coagulated into a solid fiber by extracting the dis-
persant. The process can easily be scaled to industrial levels
and is the route by which traditional high performance fibers,
such as Kevlar, are manufactured.17 Decoupling synthesis of
CNTs from spinning of the fibers also allows independent
optimization of the two steps and enables CNT purification.
Recently, using this approach, Behabtu et al.18 have shown
that exciting properties can be achieved by wet-spinning
CNTs into high-performance, multifunctional fibers.
As mentioned earlier, even though numerous studies
have been conducted to characterize mechanical and electri-
cal properties of the CNT yarn-like fibers, only a few thermal
conductivity measurements have been made to date. Ericson
et al.19 reported a measured thermal conductivity of
21 W/m-K for a CNT fiber manufactured using a wet-
spinning process. Aliev et al.13 measured thermal conductiv-
ity and thermal diffusivity of a CNT web to be 50 W/m-K
and 45 mm2/s, respectively, in a direction parallel to the web
and 26 W/m-K and 62 mm2/s for the yarn. These relatively
low thermal conductivity values were attributed to the
non-homogeneity of the fiber web structure, existence of
nanotube defects, and the extremely high surface area that
was responsible for excessive radial heat radiation. In an
another study, thermal conductivity of 26 W/(m-K) was
reported for yarn drawn from a 300 lm tall CNT array,19
which was only slightly higher than the 20 W/(m-K) reported
for single wall CNT fibers extruded from the super-acid sus-
pension of much shorter CNT.20 Recently, Jakubinek et al.21
synthesized CNT yarns of diameter ca. 15 nm by spinning
from vertically aligned CNT arrays approximately 500 lm
tall. The spun yarns had a density of about 0.9 g/cc and a
twist angle of about 1� 104/m, and showed much improved
electrical and thermal conductivities due in part to their
higher density.22 For example, for a multi-wall carbon
a)Author to whom correspondence should be addressed. Electronic mail:
[email protected]. Tel.: (216) 368-6440.
0021-8979/2014/115(17)/174306/9/$30.00 VC 2014 AIP Publishing LLC115, 174306-1
JOURNAL OF APPLIED PHYSICS 115, 174306 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
129.22.124.12 On: Tue, 05 Aug 2014 14:33:37
nanotubes (MWCNT) yarn of 10 lm diameter the room tem-
perature thermal conductivity was measured to be ca.
60 6 20 W/(m-K), which was the highest reported for a CNT
yarn to date.
More recently, Behabtu et al.18 have fabricated solid
CNT fibers by utilizing a high-throughput wet spinning
process, the same as that used to produce high-
performance industrial fibers. To understand the relative
importance of CNT alignment, packing density, and doping
on the mechanisms of electrical and thermal conduction
in these fibers, they studied the temperature-dependent
conductivity of annealed CNT fibers and isotropic films
as well as acid-doped and iodine-doped CNT fibers.
They reported an average thermal conductivity of
380 6 15 W/(m-K) in ca. 1.5-mm-long CNT fiber samples.
Iodine doping was observed to double the thermal conduc-
tivity to 635 W/m K. These reported thermal conductivity
values are about 20% of individual CNT values, possibly
due to quenching of the phonon modes by the inter-CNT
coupling, but 10 to 100 times that of other macroscopic
CNT samples usually limited by weak inter-CNT transport
due to misalignment.
In the present study, we focus on thermal conductivity
measurements in CNT yarn-like fibers fabricated by using a
solid-state sequential “draw and twist” of CNT strips out of
vertically aligned CNT forests.21,23 Besides thermal conduc-
tivity measurements in CNT fibers, we also characterize ther-
mal conductivity in higher strength CNT yarn-like
composite fibers fabricated by infiltration of PVA resin into
the neat CNT fibers. The resulting volume fraction of PVA
in the CNT fibers is �20%. In order to make the thermal
conductivity measurements in the CNT fibers, we utilize the
3x Wollaston wire T-type probe method.24,25 In this tech-
nique, a suspended wire of known electrical resistivity and
temperature coefficient of resistance is Joule heated by a cur-
rent source until it reaches steady-state. After attaching the
CNT fiber to the hot wire probe, the sample thermal conduc-
tivity is determined from the average temperature drop and
the sample geometry. The method has been successfully
used by the authors in the past to obtain the thermal proper-
ties of carbon nanofibers and CNT.25,26
II. EXPERIMENTAL METHODS
A. Carbon nanotube fiber samples
The samples studied in this work were fabricated using
a dry-spinning process comprising sequential pulling and
twisting of individual CNTs from a vertically aligned CNT
forest by Prof Qingwen Li and co-workers at the Suzhou
Institute of NanoTech and Nano Bionics, China. The fiber
specimens were provided for thermal characterization to
Case Western Reserve University (CWRU) by Prof. Tsu-
Wei Chou of the University of Delaware.
A schematic of the CNT fiber spinning is shown in
Figure 1. The vertically aligned CNT arrays were grown at
atmospheric pressure on SiO2/Si wafers. The wafer was
coated directly with a thin Fe film by electron beam evapora-
tion and C2H2 gas was used as the carbon source. The sub-
strate was then placed inside a semi-opened boat and heated
in flowing Ar gas to a growth temperature of 660–750 �C for
5–10 min. The resulting multi-wall carbon nanotubes had a
diameter of 8–10 nm with �6 walls. The array height was
�320 lm and Raman spectroscopy confirmed an IG/ID ratio
of �0.99. The mechanical strength and modulus of the indi-
vidual tubes were determined21 to be 866 MPa and 16 GPa,
respectively. The higher strength CNT yarn-like composite
fibers were fabricated by infiltration of Polyvinyi alcohol
(PVA) resin into the neat CNT fibers. The resulting volume
fraction of PVA in the CNT fibers was �20%. Because of
the strong interfacial bonding between CNT and PVA,27
these composite fibers have been shown to possess consider-
ably improved mechanical properties.21
Figures 2 and 3 show high magnification SEM images
of the CNT fiber and CNT-polymer composite fibers, respec-
tively. The images of the CNT fibers show clear evidence
that the fibers are derived from CNTs and are twisted during
the manufacturing process. Further details of the fiber fabri-
cation process and their mechanical properties can be found
in the several research articles.28–34
Raman spectroscopy is used to examine the degree of
graphitization and the composition of the CNT fibers and the
CNT-polymer composite fibers. The excitation wavelength
employed for this assessment is 785 nm. The analysis of the
sample quality is made by observing the ratio of the D band
peak intensity (occurring at �1308 cm�1) and the G-band
FIG. 1. Schematic of the dry-spinning of CNT fibers by pulling CNTs from
a vertically aligned CNT array.
FIG. 2. SEM micrographs of the CNT fiber at nominal magnifications of (A)
4000�, (B) 20 000�, (C) 50 000�, and (D) 100 000�.
174306-2 E. Mayhew and V. Prakash J. Appl. Phys. 115, 174306 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
129.22.124.12 On: Tue, 05 Aug 2014 14:33:37
peak intensity (occurring at �1596 cm�1). The D band is
associated with the loss of symmetry of atoms at the gra-
phene sheet boundaries, which appears in the form of defects
and carbonaceous impurities. The G band is associated with
sp2 bonding in the carbon systems, and it indicates the
amount of graphitization in the sample. A lower D/G ratio of
band intensity indicates that the sample batch has fewer
defects and a higher degree of graphitic crystallinity.
However, the technique provides only a qualitative compara-
tive study of defects in the neat and polymer-reinforced CNT
composite fibers.
Figures 4(a) and 4(b) compare the Raman intensities in
CNT fiber and the CNT-polymer composite fibers, respec-
tively. The D/G ratios for each sample are nearly identical
�1.15 for the pure CNT fiber and 1.16 for the CNT-polymer
composite fiber. This indicates that the carbon structures of
the two fibers are nearly the same, and the primary difference
between the two is the presence of the polymer for the CNT
composite fiber. The peak labeled as the polymer peak in
Figure 6(b) occurs around 1190 cm�1. This peak has also
been shown to be present in other studies of CNT-polymer
composites.35
B. Thermal conductivity measurements using a T-typeprobe
A T-type probe composed of a Wollaston wire is
employed to obtain the thermal characteristics of free
standing CNT fiber samples.24 The Wollaston wire has the
advantage of being extremely cost effective when com-
pared to conventional microfabrication methods,36 and
allows for a large volume of samples to be characterized in
a short span of time. To date, the T-type method has also
been used to measure thermal conductivity of a variety of
microscale samples.37–40 The details regarding the tech-
nique, including configuration and analysis for extracting
thermal conductivity in one dimensional nanostructures are
provided in Bifano et al.,25 and are discussed briefly here.
In view of the relatively long length of the CNT yarn-like
fibers, the analysis reported in Bifano et al.25 has been
extended to include radiation heat losses in the CNT fiber
samples.
Figure 5 shows a schematic of the T-type hot-wire
(henceforth referred to as the probe wire) thermal conductiv-
ity measuring system, the physical model, and the coordinate
system used in the analysis. The probe wire is supported
with lead wires (heat sink at ambient temperature) at each
end and supplied with a known low frequency alternating
current to generate a uniform heat flux in the hot wire. The
CNT fiber sample is attached to the center position of the
probe wire at one end while the other end is connected to the
manipulator probe tip which also acts as a heat sink. Both
ends of the probe wire as well as the end of the sample fiber
attached to the heat sink are maintained at the ambient tem-
perature during the experiment.
The temperature at the junction between probe wire
and the sample CNT fiber depends on the thermal conduc-
tivity of the probe wire and the sample fiber, the heat gener-
ation rate in the probe wire, and the heat transfer
coefficients (radiation losses) around the probe wire and
sample fiber. In this way, if we know exactly the relation-
ship between these quantities through the solution of one-
dimensional steady-state heat conduction along the probe
wire and the sample fiber we can obtain the thermal con-
ductivity of the sample fiber by measuring the heat
FIG. 4. Raman intensity versus wavenumber (785-nm excitation wave-
length) of (a) CNT fiber samples and (b) CNT-polymer composite fiber sam-
ples. The Raman intensity is normalized by the D-peak.
FIG. 3. SEM micrographs of the CNT-polymer composite fiber at nominal
magnifications of (A) 4000�, (B) 20 000�, (C) 50 000�, and (D) 100 000�.
174306-3 E. Mayhew and V. Prakash J. Appl. Phys. 115, 174306 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
129.22.124.12 On: Tue, 05 Aug 2014 14:33:37
generation rate and the corresponding average temperature
change in the probe wire.
1. Basic equations and boundary conditions
As described above, both ends of the probe wire and one
end of the sample fiber are supported with the lead wires that
have a high thermal conductivity and a large heat capacity
compared to those of the probe wire and the sample fiber.
Therefore, the temperature at the two ends of the probe wire
and one end of the sample fiber can be assumed to maintain
the initial (ambient) temperature during the experiment.
Assuming a uniform temperature in the radial direction for
both the probe wire and the sample fiber due to their small
Biot number (Bi ¼ hD=2k, where h is the heat transfer coef-
ficient, D is the diameter, and k is the thermal conductivity
of the probe wire or the sample fiber), the steady state ther-
mal response of the probe wire and the sample fiber can be
modeled using relevant one-dimensional heat conduction
equations as follows:
For �LP=2 < x < 0 and y¼ 0
d2h� xð Þdx2
¼ � QRMS
kPApLP: (1)
For 0 < x < LP=2 and y¼ 0
d2hþ xð Þdx2
¼ � QRMS
kPApLP: (2)
For x¼ 0 and 0 < y < LF=2
d2hF yð Þdy2
� m2hF ¼ 0 ; where m2 ¼ 4hF
kFDFand hf � 4eFrh3
o:
(3)
In Eqs. (1)–(3), h(x) is the spatial temperature rise in the
probe wire with h�ðxÞ and hþðxÞ representing the tempera-
ture distributions in the probe wire in the range �LP=2
< x < 0 and 0 < x < LP=2, respectively; hFðyÞ represents
the temperature distribution in the sample fiber along the y-
axis; QRMS is root mean sqaure heat generated due to Joule
heating of the probe wire; kP; AP; LP are the thermal conduc-
tivity, cross-sectional area, and the length of the probe wire,
respectively; kF; DF; hF are the thermal conductivity, diame-
ter, and the heat transfer coefficient of the sample fiber,
respectively; ho is the average of the ambient and the sample
fiber temperatures and is taken to be ho� 298 K; eF is the
emissivity of the sample fiber and is taken to be unity corre-
sponding to a perfect black body; and r ¼ 5:670373 �10�8Wm�2K�4 is the Stefan-Boltzman constant.
In our present analysis, heat loss due to convection and
radiation in the hot-wire probe is assumed to be negligible
since all the thermal characterization experiments are con-
ducted in vacuum inside a high resolution SEM and are made
using very small heating amplitudes and with probe wires with
relatively small lengths.41 However, because of the relatively
long length of the sample fibers, the radiation heat loss from
the fiber is expected to be significant, and is thus included in
the thermal analysis of the sample fiber (Eq. (3)).
Equations (1)–(3), are solved along with the following
boundary conditions:
At x¼ 0 and y¼ 0
h� x ¼ 0ð Þ ¼ hþ x ¼ 0ð Þ ¼ hF y ¼ 0ð Þ; (4)
and
q1 x ¼ 0; y ¼ 0ð Þ þ q2ðx ¼ 0; y ¼ 0Þ ¼ q3ðx ¼ 0; y ¼ 0Þ;(5)
where
FIG. 6. Image of the device for measuring CNT fibers and CNT-polymer
composite fibers mounted inside of the SEM chamber. The heater/sensor de-
vice has two etched Wollaston wire probes, labeled (a). The device is
secured to the SEM stage, labeled (b), used for maneuvering the device into
position for imaging.
FIG. 5. Schematic of Pt probe wire (red line), and attached sample (horizon-tal black line). The thermal resistance of the sample is incorporated into the
analytical model using a flux boundary condition at x¼ 0. The parabolic
dashed line, h1(x), represents the increase in temperature of the probe prior
to coming into contact with the sample. The solid line, h2(x), represents the
increase in temperature of the probe wire following the contact with the
sample. The manipulator tip and each end of the probe wire are assumed to
remain at ambient temperature conditions, h¼ 0.
174306-4 E. Mayhew and V. Prakash J. Appl. Phys. 115, 174306 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
129.22.124.12 On: Tue, 05 Aug 2014 14:33:37
q1ðx ¼ 0�; y ¼ 0Þ ¼ �kPAP@h�
@x;
q2ðx ¼ 0þ; y ¼ 0Þ ¼ kPAP@hþ
@x;
q3ðx ¼ 0; y ¼ 0Þ ¼ �kFAF@hF
@y:
In this way, the thermal characteristics of the sample fiber are
incorporated into the model by a flux boundary condition at the
point of sample attachment (x¼ 0, y¼ 0), to the probe wire.
At x ¼ 6LP=2 and y¼ 0
h� x ¼ �LP=2; y ¼ 0ð Þ ¼ 0 and
hþ x ¼ LP=2; y ¼ 0ð Þ ¼ 0:(6)
At x ¼ 0 and y ¼ Lf
hF x ¼ 0; y ¼ LFð Þ ¼ 0: (7)
The piecewise parabolic solution for the temperature distri-
bution in the probe wire can be expressed as
hðx; g0Þ ¼ QRMSLP
8kPAP1� x
LP=2
� �2 !
þ g0
1þ g0
� �"
����� x
LP=2
����� 1
!#; (8)
where the parameter g0 is the ratio of the thermal resistance
of the probe wire Rth,P, to the apparent thermal resistance of
the sample fiber R0th;F, and is defined as g0 ¼ Rth;P=4R0th;F.
The thermal resistance of the probe wire and the apparent
thermal resistance of the sample are given by
Rth,P¼ LP/kPAP, and R0th;F ¼ Rth;c1 þ Rth;F tanh mLFð Þ= mLFð ÞþRth;c2, respectively, where Rth;c1 is the thermal contact re-
sistance at the probe wire and sample CNT fiber junction,
Rth;c2 is the thermal contact resistance at the sample fiber and
the manipulator tip (heat sink) junction, and Rth,F¼ LF/kFAF,
is the true thermal resistance of the sample fiber under inves-
tigation. Note that if we neglect the radiation heat loss in the
sample fiber (i.e., m! 0), R0th;F ¼ Rth;c1 þ Rth;F þ Rth;c2.
Also, in the absence of the sample, i.e., R0th;F ¼ 1, g¼ 0,and the well-known inverted parabolic temperature solution
for a Joule heated suspended wire is recovered.
In our present work, the apparent thermal resistance of
the fiber sample can be simplified to R0th;F � Rth;F tanh
mLFð Þ= mLFð Þ, since both Rth;c1 and Rth;c2 are expected to be
negligibly small, as shown in a previous study on CNT by
the authors.25 In that work, at 293 K, CNT and heat sink
junctions created with Pt electron beam induced deposition
(EBID) and the amorphous carbon EBID were determined to
have thermal contact resistance of 5.79 � 10�9 Km2/W and
5.18 � 10�9 Km2/W, which are consistent with theoretical
estimates42 and experimental data for interfaces.43 The
reduction in contact resistance that occurs when using EBID
results from the increased contact area at the sample
fiber-probe junction and the sample fiber-manipulator tip.
One of the challenges in using EBID with the CNT yarn-like
fibers is the relatively large diameter of the fibers (�12 lm
to 15 lm) when compared to the diameter of individual
CNTs (10 nm to 50 nm) used by the authors in Bifano et al.25
The larger diameter makes it practically very difficult, due to
the slow deposition rate of EBID, to build up the required
thickness (i.e., larger than the diameter of the fibers) of car-
bon/platinum deposition so as to reliably clamp the relatively
large diameter CNT fibers to the substrate. Consequently, in
the present study, silver epoxy was used instead of carbon/-
platinum EBID for bonding the CNT fiber samples to sub-
strate. Because of the higher thermal conductivity of the
silver epoxy when compared to platinum/amorphous carbon
deposits, with the use of the silver epoxy the thermal contact
resistance is expected to be smaller when compared to sam-
ple CNT fiber junctions formed by using EBID. The pres-
ence of additional mass of epoxy at these interfaces is not
expected to affect the steady state temperature profile as long
as the diameter of the platinum probe wire is not altered to
interfere with the 1D thermal transport assumption. For simi-
lar reasons, the use of silver epoxy at the junctions is likely
to help enforce the constant temperature boundary conditions
at the manipulator-sample attachment point.
Integrating Eq. (8) over the length of the probe wire, the
spatially averaged temperature rise �h over the length of the
sample can be written as
�h ¼ 1
12QRMSRth;P 1� 3
4
g0
1þ g0
� �� �: (9)
2. Experimental procedure
In order to conduct the three omega measurements, the
platinum probe wire is heated using a low-frequency current,
IðtÞ ¼ I1xcosxt ¼ I1x;RMS
ffiffiffi2p
cosxt, where I1x is the current
amplitude and I1x;RMS is the RMS current. The current used
to Joule heat the Pt probe is driven at a sufficiently low fre-
quency to prevent a phase shift in the heating frequency and
the temperature rise.25 This is achieved by choosing a heat-
ing frequency whose period is much greater than the thermal
diffusion time s¼L2/a, of a suspended wire.
For sufficiently low heating currents I(t), the Joule heat-
ing in the wire is given by
QðtÞ ¼ I2ðtÞReo ¼ I21x;RMSReoðcos 2xtþ 1Þ=2; (10)
where Reo is the electrical resistance of the probe wire at
zero current. For low frequency current and under quasi-
steady state, the spatially averaged temperature of the probe
wire, �hðtÞ, can be taken to be directly proportional to Joule
heating by the thermal transfer function Zo such that�h tð Þ ¼ ZoQ tð Þ.
When the wire is Joule heated, the third harmonic volt-
age across the wire is given by
V3x;RMS ¼1
2aZoI1x;RMSQRMSReo; (11)
where QRMS � I21x;RMSReo is the RMS Joule heating.
Defining the third harmonic RMS electrical resistance as
174306-5 E. Mayhew and V. Prakash J. Appl. Phys. 115, 174306 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
129.22.124.12 On: Tue, 05 Aug 2014 14:33:37
Re3x;RMS � V3x;RMS=I1x;RMS, the third harmonic resistance is
found to be directly proportional to the RMS Joule heating
by
Re3x;RMS ¼1
2aReoZoQRMS: (12)
Using Eq. (12), the thermal transfer function Zo can be
experimentally determined by obtaining the slope of the
Re3x;RMS versus QRMS plot.
In view of Eqs. (9) and (12) the theoretical thermal
transfer function can be written as
Zo ¼1
12Rth;P 1� 3
4
g0
1þ g0
� �� �: (13)
When no sample is attached, g0 ¼ 0; using Eq. (12), the ther-
mal resistance of the probe wire is deduced to be
Rth;P ¼24
aReo
DRe3x;RMS
DQRMS
� �: (14)
The ratio of the slopes is then defined as
/ �ðDRe3x;RMS=DQRMSÞWith Sample
ðDRe3x;RMS=DQRMSÞNo Sample
; (15)
and the apparent sample thermal resistance can be found via
Eqs. (14) and (15), to be
R0th;F ¼1
4Rth;P
1
4ð1� /Þ � 1
� �: (16)
The thermal conductivity of the sample can then be
determined by iteratively solving for kF from
R0th;F � Rth;F tanh mLFð Þ= mLFð Þ. Note: in the calculation of
thermal conductivity the samples are taken to have solid
cross-sections.
3. Heater/sensor for three omega CNT fiber andCNT-polymer composite fiber experiments
The probe wires used for the measurement of the sample
CNT fibers and CNT-polymer composite fibers are con-
structed from commercially available Wollaston wire
obtained from the Goodfellow Corporation. The wires are
composed of a 99.9% platinum core with a nominal diameter
of 5 lm, surrounded by a silver sheath approximately 40 lm
in diameter. A total of two Wollaston wire probes can be
mounted on the device as shown in Figure 6. The probes are
soldered to copper pads using low temperature solder
(Cerrolow-117 alloy). Each probe wire is etched using 10%
aqueous nitric acid such that a nominal length of 4 mm of the
platinum core is exposed.
An important consideration in the design of the test ap-
paratus is ensuring that the thermal resistance of the probe
wire is properly matched to the thermal resistance of the
sample.25 Thermal resistance matching ensures that the sen-
sitivity of the temperature response of the probe wire to the
sample is high so that small changes in sample thermal
resistance result in relatively large changes in the spatially
averaged temperature rise in the probe wire. Following
Bifano et al.,25 it can be shown that g0 must be between
0.077 and 12.923 to keep the uncertainty in measured sample
resistance within ten percent of the true value.
The heating/sensing device used in the thermal conduc-
tivity measurements of the CNT fibers and CNT-polymer
composite fibers is first verified by measuring thermal con-
ductivity in 99.99% purity Au wire with a nominal diameter
of 20 lm; the Au wire is chosen as a benchmark sample
because of its uniformity in diameter. The 3x thermal con-
ductivity measurements yielded measurements of
312 6 7 W/m-K and 290 6 7 W/m-K in the Au wire. These
values are 2.0% and 8.8% less than the literature value of
318 W/m-K for 99.99% purity Au wire. Thus, the experi-
mental setup and methods employed for characterizing ther-
mal conductivity in CNT fiber and CNT-polymer composite
fiber were considered to be valid.
III. RESULTS AND DISCUSSION
A. Thermal conductivity of CNT fibers andCNT-polymer composite fibers
Thermal conductivity measurements were made in both
the neat CNT fibers as well as the CNT-polymer composite
fibers. Images of an example experiment conducted on a
CNT-polymer composite fiber are shown in Figure 7.
The length, diameter, and the measured apparent and
true (radiation heat loss corrected) thermal conductivities for
FIG. 7. Image (A) of experimental setup with CNT-polymer composite sam-
ple attached. The platinum core of the Wollaston wire is labeled (a). The
CNT-polymer composite fiber, labeled (b), is attached to the probe wire and
low-temperature solder (ambient temperature heat sink) by thermally con-
ductive silver epoxy. The low-temperature solder with thermally conductive
silver epoxy is labeled (c). The setup with the shown sample is representa-
tive of all experiments conducted on the CNT fibers and CNT-polymer com-
posite fibers. Images (B) and (C) show the sample-probe wire contact and
sample-heat sink contacts in greater detail.
174306-6 E. Mayhew and V. Prakash J. Appl. Phys. 115, 174306 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
129.22.124.12 On: Tue, 05 Aug 2014 14:33:37
the CNT fiber samples and CNT-polymer composite fiber
samples are listed in Table I and Table II, respectively. The
standard deviation associated with length is due to the uncer-
tainty in measurement of the length, while the standard devi-
ations associated with the diameter are dominated by
diameter variation along the length of the sample rather than
uncertainty in the measurement of the diameter. Thus, meas-
urements made on samples with significant diameter varia-
tion along the length of the sample result in large error bars
for the thermal conductivity.
Figure 8 shows the thermal conductivity for the two sets
of samples. The average true thermal conductivity for the
CNT fibers was 448 6 61 W/m-K and 225 6 15 W/m-K for
the CNT-polymer composite fibers. The standard deviation
associated with the average value reflects the variation in
individual sample thermal conductivity measurements rather
than uncertainty in the measurements themselves.
The measurements reported in this study are by far the
highest measured thermal conductivities reported for CNT
fibers.10,13,18,21,44,45 fabricated using solid state draw and
twist processing of CNT films directly from vertically
aligned multi walled carbon nanotube arrays. The previous
maximum thermal conductivity was reported by Jakubinek
et al.21 to be 60 W/m-K. While the mechanism for thermal
transport in CNT fibers is not well understood,30 there are a
few noteworthy factors that are understood to contribute to
the much larger thermal conductivity.
Before discussing the aforementioned results on CNT
fibers, it is instructive to look at results of thermal conductiv-
ity measurements obtained on aligned CNT bundles. In gen-
eral, experimental results have shown the thermal
conductivity of CNT bundles to be lower than those obtained
for individual CNTs25,46,47 even when the low apparent den-
sity of bundles is taken into account. Simulations indicate that
thermal conductivity decreases by roughly a factor of three for
close-packed bundles in comparison to individual SWCNTs.48
The effect of bundle size was explored by Aliev et al.,44 who
measured thermal conductivity in individual CNTs and CNT
bundles of increasing size and found that the thermal conduc-
tivity decreased by approximately four times as the bundle
size increased to 100 CNTs. The decrease in thermal conduc-
tivity in CNT bundles is understood to be attributed to
coupling between CNTs in bundles, where bundles restrict
out-of-plane phonon vibrations and therefore suppress low
lying optical modes that are known to contribute significantly
to thermal conductivity at room temperatures. When heat
transfer between CNTs is involved, the interface thermal re-
sistance between the nanotubes further reduces thermal con-
duction. In this case, heat transfer is inhibited by small contact
area and high thermal interfacial resistance at the CNT-CNT
contacts, estimated from simulations to be >10�8 m2-K/W
even for short CNT-CNT separations.49 Such resistances can
lead to CNT assemblies with thermal insulating properties.
For packed beds composed of 10–20 vol. % CNT produced by
compressing random mats of CNT, thermal conductivity
<0.02 W/m-K has been reported due to the dominant effect of
CNT-CNT thermal contact resistance.50
In the case of CNT fibers, however, the CNT bundles
are drawn and twisted from a CNT array. The drawing is
expected to improve the fiber alignment along its length
while twisting has been shown to decrease the CNT fiber di-
ameter as well as increase its mechanical stiffness. This
decrease in the CNT fiber diameter during twisting can be
attributed to the collapse of the CNTs in the radial direction
due to increased radial compressive stresses and conse-
quently enhanced inter-CNT interactions. The decrease in
overall CNT fiber diameter is also expected to reduce the
inter-tube spacing between the CNTs. Zhong et al.,49 using
molecular dynamics have shown that the decrease in spacing
between the CNTs result in a decrease in the interfacial
boundary resistance thus increasing the thermal conductivity
of the CNT fiber.9 Moreover, Badaire et al.51 have shown
that alignment of SWCNT within an SWCNT-polyvinyl
alcohol composite fiber play a major role in the fiber’s
TABLE I. CNT fiber sample dimensions and the measured apparent and
true (radiation heat loss corrected) thermal conductivities.
Length (mm)
Diameter
(lm)
Apparent thermal
conductivity of CNT
fibers (W/m-K)
True thermal
conductivity of CNT
fibers (W/m-K)
8.84 6 0.04 12.9 6 0.7 504 6 57 456 6 41
7.19 6 0.30 12.2 6 1.0 489 6 80 431 6 67
11.56 6 0.08 13.9 6 1.1 584 6 94 457 6 71
TABLE II. CNT-polymer composite fiber sample dimensions and the meas-
ured apparent and true (radiation heat loss corrected) thermal conductivities.
Length (mm)
Diameter
(lm)
Apparent thermal
conductivity of CNT
composite fibers
(W/m-K)
True thermal
conductivity of CNT
composite fibers
(W/m-K)
8.00 6 0.01 14.6 6 0.5 322 6 22 287 6 12
8.34 6 0.06 14.1 6 1.0 358 6 52 256 6 25
9.42 6 0.02 12.8 6 0.5 216 6 16 131 6 10
FIG. 8. Plot of thermal conductivity versus diameter for the CNT fibers and
CNT-polymer composite fibers.
174306-7 E. Mayhew and V. Prakash J. Appl. Phys. 115, 174306 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
129.22.124.12 On: Tue, 05 Aug 2014 14:33:37
overall thermal conductivity. In their case, the alignment of
the SWCNT in the SWCNT fibers was achieved by axial
stretching, and the room temperature thermal conductivity
was observed to improve from 4 W/m-K for 21.5% stretch to
10 W/m-K for a 58.4% stretch.
IV. SUMMARY
In the present paper, we present results of thermal con-
ductivity measurements in free standing carbon nanotube
strands, CNT yarn-like fibers, and CNT yarn-like polymer
composite fibers. Thermal conductivity measurements were
made using a T-type experimental configuration utilizing a
Wollaston wire hot-probe inside a SEM. In this technique, a
suspended platinum wire is used both as a heater and a ther-
mal sensor. A CNT fiber specimens are attached to the mid-
point of the suspended platinum wire using conductive silver
epoxy, reducing the thermal contact resistance at the sample-
platinum wire junction. During the experiment, the platinum
wire is heated using a low frequency alternating current
source while the third harmonic voltage across the suspended
wire is measured by a lock-in amplifier. The thermal conduc-
tivity is deduced from an analytical model that relates the
drop in the spatially averaged temperature of the wire to the
thermal resistance and thermal conductivity of the sample.
The average measured thermal conductivity of the CNT fiber
samples was 448 6 61 W/m-K and 225 6 15 W/m-K for the
CNT-polymer composite fibers. These values of thermal
conductivity for the CNT fibers are much higher than previ-
ously measured for any CNT fibers. The higher thermal con-
ductivity are understood to be due to the increased stiffness,
lower CNT-CNT boundary resistance, and better CNT align-
ment along the length of the fiber brought on by the twisting
and pulling of the fiber during the manufacturing process.
ACKNOWLEDGMENTS
The authors would like to thank Professor Qingwen Li
at the Suzhou Institute of NanoTech and Nano Bionics,
China, and Professor Tsu-Wei Chou at the University of
Delaware, for providing the CNT fiber samples for thermal
characterization reported in this work. The authors would
like to acknowledge the support of the Air Force Office of
Scientific Research (AFOSR) MURI Grant No. FA9550-12-
1-0037 (Program Manager: Dr. Joycelyn Harrison) for con-
ducting this research.
1B. Vigolo, B. Vigolo, A. Penicaud, C. Coulon, C. Sauder, R. Pailler, C.
Journet, P. Bernier, and P. Poulin, Science 290, 1331–1334 (2000).2K. Jiang, Q. Li, and S. Fan, Nature 419, 801 (2002).3H. W. Zhu, C. L. Xu, D. H. Wu, B. Q. Wei, R. Vajtai, and P. M. Ajayan,
Science 296, 884–886 (2002).4A. B. Dalton, S. Collins, E. Mu~noz, J. M. Razal, V. H. Ebron, J. P.
Ferraris, J. N. Coleman, B. G. Kim, and R. H. Baughman, Nature 423, 703
(2003).5Y. L. Li, I. A. Kinloch, and A. H. Windle, Science 304, 276–278 (2004).6M. Zhang, K. R. Atkinson, and R. H. Baughman, Science 306, 1358–1361
(2004).7Q. W. Li, X. F. Zhang, R. F. DePaula, L. X. Zheng, Y. H. Zhao, L. Stan,
T. G. Holesinger, P. N. Arendt, D. E. Peterson, and Y. T. Zhu, Adv. Mater.
18, 3160–3163 (2006).
8X. Zhang, Q. Li, T. G. Holesinger, P. N. Arendt, J. Huang, P. D. Kirven,
T. G. Clapp, R. F. DePaula, X. Liao, Y. Zhao, L. Zheng, D. E. Peterson,
and Y. Zhu, Adv. Mater. 19, 4198–4201 (2007).9X. Zhang, Q. Li, Y. Tu, Y. Li, J. Y. Coulter, L. Zheng, Y. Zhao, Q. Jia, D.
E. Peterson, and Y. Zhu, Small 3, 244–248 (2007).10N. Behabtu, M. J. Greena, and M. Pasqualia, Nanotoday 3, 24–34 (2008).11K. Koziol, J. Vilatela, A. Moisala, M. Motta, P. Cunniff, M. Sennett, and
A. Windle, Science 318, 1892–1895 (2007).12R. J. Davies, C. Riekel, K. K. Koziol, J. J. Vilatela, and A. H. Windle,
J. Appl. Crystallogr. 42, 1122–1128 (2009).13A. E. Aliev, C. Guthy, M. Zhang, S. Fang, A. A. Zakhidov, J. E. Fischer,
and R. H. Baughman, Carbon 45, 2880–2888 (2007).14K. Liu, Y. Sun, R. Zhou, H. Zhu, J. Wang, L. Liu, S. Fan, and K. Jiang,
Nanotechnology 21, 045708 (2010).15B. I. Yakobsona, G. Samsonidzea, and G. G. Samsonidzeb, Carbon 38,
1675–1680 (2000).16A. Nieuwoudt and Y. Massoud, IEEE Trans. Electron Devices 55,
2097–2110 (2008).17H. H. Yang, Aromatic High-Strength Fibers (Wiley, New York, 1989).18N. Behabtu, C. C. Young, D. E. Tsentalovich, O. Kleinerman, X. Wang,
A. W. Ma, E. A. Bengio, R. F. ter Waarbeek, J. J. de Jong, R. E.
Hoogerwerf, S. B. Fairchild, J. B. Ferguson, B. Maruyama, J. Kono, Y.
Talmon, Y. Cohen, M. J. Otto, and M. Pasquali, Science 339, 182–186
(2013).19L. M. Ericson, H. Fan, H. Peng, V. A. Davis, W. Zhou, J. Sulpizio, Y.
Wang, R. Booker, J. Vavro, C. Guthy, A. N. Parra-Vasquez, M. J. Kim, S.
Ramesh, R. K. Saini, C. Kittrell, G. Lavin, H. Schmidt, W. W. Adams, W.
E. Billups, M. Pasquali, W. F. Hwang, R. H. Hauge, J. E. Fischer, and R.
E. Smalley, Science 305, 1447–1450 (2004).20W. Zhou, J. Vavro, C. Guthy, K. I. Winey, J. E. Fischer, L. M. Ericson, S.
Ramesh, R. Saini, V. A. Davis, C. Kittrell, M. Pasquali, R. H. Hauge, and
R. E. Smalley, J. Appl. Phys. 95, 649–655 (2004).21M. B. Jakubinek, M. B. Johnson, M. A. White, C. Jayasinghe, G. Li, W.
Cho, M. J. Schulz, and V. Shanov, Carbon 50, 244–248 (2012).22Y. Yun, V. Shanov, Y. Tu, S. Subramaniam, and M. J. Schulz, J. Phys.
Chem. B. 110, 23920–23925 (2006).23J. Zhao, X. Zhang, J. Di, G. Xu, X. Yang, X. Liu, Z. Yong, M. Chen, and
Q. Li, Small 6, 2612–2617 (2010).24C. Dames, S. Chen, C. T. Harris, J. Y. Huang, Z. F. Ren, M. S.
Dresselhaus, and G. Chen, Rev. Sci. Instrum. 78, 104903 (2007).25M. F. P. Bifano, J. Park, P. B. Kaul, A. K. Roy, and V. Prakash, J. Appl.
Phys. 111, 054321 (2012).26E. Mayhew and V. Prakash, Carbon 62, 493–500 (2013).27M. Cadek, J. N. Coleman, V. Barron, K. Hedicke, and W. J. Blau, Appl.
Phys. Lett. 81, 5123 (2002).28J. Jia, J. Zhao, G. Xu, J. Di, Z. Yong, Y. Tao, C. Fang, Z. Zhang, X.
Zhang, L. Zheng, and Q. Li, Carbon 49, 1333–1339 (2011).29F. Deng, W. Lu, H. Zhao, Y. Zhu, B.-S. Kim, and T.-W. Chou, Carbon 49,
1752–1757 (2011).30W. Lu, M. Zu, J. H. Byun, B. S. Kim, and T. W. Chou, Adv. Mater. 24,
1805–1833 (2012).31A. S. Wu and T.-W. Chou, Mater. Today 15, 302–310 (2012).32T.-W. Chou, L. Gao, E. T. Thostenson, Z. Zhang, and J.-H. Byun,
Compos. Sci. Technol. 70, 1–19 (2010).33A. S. Wu, X. Nie, M. C. Hudspeth, W. W. Chen, T.-W. Chou, D. S.
Lashmore, M. W. Schauer, E. Tolle, and J. Rioux, Carbon 50, 3876–3881
(2012).34M. Zu, Q. Li, Y. Zhu, M. Dey, G. Wang, W. Lu, J. M. Deitzel, J. W.
Gillespie, J.-H. Byun, and T.-W. Chou, Carbon 50, 1271–1279 (2012).35T. McNally, P. P€otschke, P. Halley, M. Murphy, D. Martin, S. E. J. Bell,
G. P. Brennan, D. Bein, P. Lemoine, and J. P. Quinn, Polymer 46,
8222–8232 (2005).36L. Shi, D. Y. Li, C. H. Yu, W. Y. Jang, D. Kim, Z. Yao, P. Kim, and A.
Majumdar, J. Heat Transfer 125, 881–888 (2003).37X. Zhang, S. Fujiwara, and M. Fujii, Int. J. Thermophys. 21, 965–980
(2000).38J. L. Wang, M. Gu, X. Zhang, and Y. Song, J. Phys. D: Appl. Phys. 42,
105502 (2009).39W. Jian-li, G. Ming, M. Wei-gang, Z. Xing, and S. Yan, New Carbon
Mater. 23, 259–263 (2008).40X. Zhang, S. Fujiwara, and M. Fujii, High Temp.-High Pressures 32,
493–500 (2000).41Using an analytic 1D steady state model to represent a 1 mm Pt probe wire
having a 750 nm diameter, omission of a radiation term in Eq. (7) is found
174306-8 E. Mayhew and V. Prakash J. Appl. Phys. 115, 174306 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
129.22.124.12 On: Tue, 05 Aug 2014 14:33:37
to contribute approximately 0.5% error in the measured electrical resist-
ance of the probe wire.42P. Reddy, K. Castelino, and A. Majumdar, Appl. Phys. Lett. 87, 211908
(2005).43R. Costescu, M. Wall, and D. Cahill, Phys. Rev. B 67, 054302 (2003).44A. E. Aliev, M. H. Lima, E. M. Silverman, and R. H. Baughman,
Nanotechnology 21, 035709 (2010).45M. H. Miao, Particuology 11, 378–393 (2013).46J. Park, M. F. Bifano, and V. Prakash, J. Appl. Phys. 113, 034312 (2013).
47P. B. Kaul, M. F. P. Bifano, and V. Prakash, J. Compos. Mater. 47, 77–95
(2013).48J. W. Che, T. Cagin, and W. A. Goddard, Nanotechnology 11, 65–69
(2000).49H. Zhong and J. Lukes, Phys. Rev. B 74, 125403 (2006).50R. S. Prasher, X. J. Hu, Y. Chalopin, N. Mingo, K. Lofgreen, S. Volz, F.
Cleri, and P. Keblinski, Phys. Rev. Lett. 102, 105901 (2009).51S. p. Badaire, V. Pichot, C. c. Zakri, P. Poulin, P. Launois, J. Vavro, C.
Guthy, M. Chen, and J. E. Fischer, J. Appl. Phys. 96, 7509 (2004).
174306-9 E. Mayhew and V. Prakash J. Appl. Phys. 115, 174306 (2014)
[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
129.22.124.12 On: Tue, 05 Aug 2014 14:33:37