Research Article
www.acsami.org
Continuous Carbon Nanotube-Based Fibers and Films for
Applications Requiring Enhanced Heat Dissipation
Peng Liu,†,‡ Zeng Fan,‡ Anastasiia Mikhalchan,‡ Thang Q. Tran,‡ Daniel Jewell,§ Hai M. Duong,*,‡
and Amy M. Marconnet*,†
†
School of Mechanical Engineering and the Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United
States
‡
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, EA-07-05, Singapore 117575,
Singapore
§
Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB2 1TN, United Kingdom
S Supporting Information
*
ABSTRACT: The production of continuous carbon nanotube (CNT) fibers and films has paved the way to leverage the
superior properties of individual carbon nanotubes for novel macroscale applications such as electronic cables and multifunctional
composites. In this manuscript, we synthesize fibers and films from CNT aerogels that are continuously grown by floating catalyst
chemical vapor deposition (FCCVD) and measure thermal conductivity and natural convective heat transfer coefficient from the
fiber and film. To probe the mechanisms of heat transfer, we develop a new, robust, steady-state thermal characterization
technique that enables measurement of the intrinsic fiber thermal conductivity and the convective heat transfer coefficient from
the fiber to the surrounding air. The thermal conductivity of the as-prepared fiber ranges from 4.7 ± 0.3 to 28.0 ± 2.4 W m−1 K−1
and depends on fiber volume fraction and diameter. A simple nitric acid treatment increases the thermal conductivity by as much
as a factor of ∼3 for the fibers and ∼6.7 for the thin films. These acid-treated CNT materials demonstrate specific thermal
conductivities significantly higher than common metals with the same absolute thermal conductivity, which means they are
comparatively lightweight, thermally conductive fibers and films. Beyond thermal conductivity, the acid treatment enhances
electrical conductivity by a factor of ∼2.3. Further, the measured convective heat transfer coefficients range from 25 to 200 W
m−2 K−1 for all fibers, which is higher than expected for macroscale materials and demonstrates the impact of the nanoscale CNT
features on convective heat losses from the fibers. The measured thermal and electrical performance demonstrates the promise
for using these fibers and films in macroscale applications requiring effective heat dissipation.
KEYWORDS: carbon nanotubes, thermal conductivity, convective heat transfer, CNT macroscale assemblies, acid treatment
1. INTRODUCTION
homogeneous and uniform quality CNT-based structures that
fully exploit the excellent axial properties of individual CNTs.
Manufacturing CNTs into continuous, macroscale fibers is a
significant step toward integrating them into practical
applications. CNT fibers, produced by either wet-spinning
from CNT/acid or polymer solutions,7,8 dry-spinning from
Individual carbon nanotubes (CNTs) demonstrate excellent
mechanical (Young’s modulus up to 1 TPa),1 electrical (up to
106 S cm−1),2 and thermal (up to 3500 W m−1 K−1)3
properties. Many applications could benefit from CNT-based
materials, including high-strength and conductive nanocomposites, electrochemical devices, sensors, and probes.4−6 However,
practical applications require the extension of the superior
properties of individual CNTs up to the macroscale. This
remains a challenge due to the difficulty in synthesizing
© XXXX American Chemical Society
Received: April 6, 2016
Accepted: June 20, 2016
A
DOI: 10.1021/acsami.6b04114
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vertically aligned CNT arrays,9 or direct-spinning from CNT
aerogels formed in floating catalyst chemical vapor deposition
(FCCVD)10−15 are promising as novel lightweight, highstrength, and highly conductive materials. Compared with
commercial carbon and polymer fibers, CNT fibers demonstrate higher modulus and strength, better electrical and
thermal conductivities, and more flexibility.8,14−16 The effects
of fabrication processes17,18 and different post-treatment
methods8,14,16,19,20 on the morphology, mechanical, and
electrical properties have been systematically studied for several
years. But there are only a few reported experimental studies on
the thermal properties of CNT fibers,8,21−27 and the large
difference in reported thermal conductivities between these
similar fibers indicates a significant dependence on quality and
processing technique.
CNT fibers can be assembled directly from CNT aerogels in
FCCVD10,15 leveraging the ability to produce CNT fibers in
large scale efficiently with controllable CNT structures and
outstanding mechanical and electrical properties.10,14,15 This is
in contrast to the wet-spinning and array-spinning methods
where individual CNTs are first produced as powders or arrays
and require a separate postprocess of spinning to create the
fibers. Although the thermal conductivity of the CNT fibers
directly spun from FCCVD-synthesized CNT aerogels has not
yet been reported in detail, they are expected to have high
thermal conductivity.5,28 Despite years of research, the reported
effective thermal conductivities of CNT fibers are still much
lower than those of individual CNTs. High defect concentration and high thermal contact resistance between CNTs in
macroscale assemblies are commonly cited reasons for the low
performance of CNT-based networks.29 Chemical modifications to the CNTs, such as acid treatments, have been
demonstrated to improve CNT quality and manage the
interfacial interactions.30 For instance, soaking CNT fibers in
nitric acid increases their electrical conductivity.20,31 But little
thermal transport data exists for such modifications, and the
effect of acid treatment on the thermal conductivity of CNT
macroscale assemblies has not yet been experimentally
investigated.
In this work, we measure the thermal conductivity and heat
transfer coefficient by natural convection of CNT fibers and
thin films fabricated from CNT aerogels, which are grown by
FCCVD. We develop a steady-state Joule heating infrared
thermal metrology technique to study the thermal conductivity
and convective heat transfer for the CNT-based fibers. This
technique leverages infrared microscopy as a noncontact,
nondestructive, fast thermal characterization tool to measure
the two-dimensional temperature maps in the CNT fibers and
films self-heated by Joule heating. As opposed to conventional
measurement techniques, the sample thermal conductivity can
be extracted in air and without need for microfabrication.
Further, the steady-state technique developed here enables a
direct measurement of thermal conductivity (independent of
density and specific heat) while simultaneously measuring
convective heat transfer coefficient. The technique is applicable
to a broad class of electrically conductive samples ranging from
metallic wires to CNT fibers. Here, the impact of micro/
macrostructure (collecting time, diameter, and density) on the
thermal conductivity and the convection coefficient for the
CNT fibers is investigated for the first time. These data
complement previous work characterizing the mechanical and
electrical properties of the CNT fibers directly spun from CNT
aerogels in CVD.13,14 Moreover, we demonstrate a simple,
effective acid treatment approach to enhance the electrical and
thermal conductivities of the CNT fibers and films. The acidtreated specimens demonstrate up to a factor of ∼3 for the fiber
and ∼6.7 for the thin film improvement in the thermal
conductivities than the as-prepared samples due to the
purification and densification during the acid treatment,
which results in less defective structure and reducing contact
resistance between nanotubes.
2. EXPERIMENTAL SECTION
Fabrication of CNT Fibers and Films. The CNT fibers are
fabricated from CNT films, which are synthesized by the floating
catalyst vapor deposition method.13 In a reducing hydrogen
atmosphere, the nanotubes form an aerogel in the hot zone of the
furnace (1200 °C) and the aerogel is stretched into cylindrical hollow
socks. The CNT sock is pulled out of the furnace by a stainless rod
and continuously collected on a paper roller to form a CNT film. CNT
films collected for 1, 5, and 10 min are mechanically rolled from one
end to the other to fabricate the CNT fibers with various diameters
and densities.13 In order to study the effects of acid treatment on the
thermal conductivity, the CNT fibers and films are immersed in 65 wt
% nitric acid (HNO3, Sigma-Aldrich Pte Ltd.) at room temperature for
30 min and washed in deionized water.
Morphology Characterizations. The structures of the specimens
are observed using a field emission scanning electron microscope (FESEM, Model S-4300, Hitachi), a transmission electron microscope
(TEM, JEOL JEM-3010), and a Horiba Jobin Yvon Modular Raman
Spectrometer. Nitrogen adsorption/desorption tests to determine the
distribution of pores in the specimens before and after acid treatment,
are conducted using a Nova 2200e Surface Area and Pore Size
Analyzer (Quantachrome). To measure the bulk density of the
specimens, the masses of the specimens are obtained with an analytical
balance in accuracy of 0.01 mg and the dimensions of the specimens
are measured by an Olympus optical microscope. The CNT volume
fraction ( f) is calculated from the bulk density of the CNT fiber or
film, ρ, as
f=
ρ
× 100%
ρCNT
(1)
where ρCNT = 2.1 g cm−3 is the density of an individual CNT.
Electrical Properties of the CNT Fibers and Films. Electrical
resistances of the CNT fibers and films are measured by four-wire
method using a Keithley 2420 source meter. For better electrical
contacts, the two ends of the specimens are fixed on two separate glass
slides with silver paint. The electrical conductivity (σ) and specific
electrical conductivity (σ′) is then calculated from eqs 2 and 3,
respectively,
σ=
L
(S cm−1)
RA
(2)
σ′ =
σ
(S cm 2 g −1)
ρ
(3)
where R, A, and L are the resistance, cross-sectional area, and length of
the specimen.
The temperature coefficient of resistance (TCR or α) is measured
by four-wire electrical resistance measurements across the temperature
range of 295−350 K. The average TCR of the as-prepared specimens
and acid-treated specimens was 0.001 15 ± 0.000 25 and 0.002 65 ±
0.000 40 K−1, respectively.
Thermal Properties of the CNT Fibers and Films. Each CNT
fiber is suspended between two pairs of copper blocks working as
electrodes as shown in Figure 1a. For the CNT fiber samples, the
length of suspended portion is ∼1 cm; while for the film samples, the
suspended portion is 2 cm in length and 0.5 cm in width. Current
flowing through the sample heats the specimen. A Keithley 2420
source meter (Figure 1b) is used to source the current and measure
the voltage drop across the sample. The temperature profile along the
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where k, A, L, and α are the thermal conductivity, cross-sectional area,
length, and TCR of the specimen, respectively, h′ is the convective
heat loss per unit length to the air (with units of W m−1 K−1), T(x) is
the temperature profile along the length of the specimen, T0 is the
room temperature (295.15 K), TL/2 is the temperature of the ends of
the specimen, p′ = I2R0/L is the heat generation per unit length in the
specimen, and I and R0 are current amplitude and the electrical
resistance of the specimen at T0, respectively. The analytic solution of
eq 4 is
⎞
⎛
p′ ⎜ cosh(mx)
⎟
−
1
⎟ + (TL /2 − T0)
h′ − αp′ ⎜ cosh mL
⎠
⎝
2
T (x) = T0 −
( )
cosh(mx)
( mL2 )
cosh
Figure 1. Experimental setup and example data from the steady state
Joule heating infrared metrology technique. (a) Optical image of a
CNT fiber suspended between two copper electrodes that also serve as
heat sinks. (b) Schematic of the experimental setup. The Keithley
2420 source meter sources current through the sample leading to an
increased temperature throughout the fiber, which is measured by the
infrared microscope. (c) Example infrared microscope image of a CNT
fiber during Joule heating for a sample with a measured density of 0.28
g cm−3. Note the one-dimensional heat transfer along the length of the
fiber as indicated by the nearly uniform temperature in the direction
perpendicular to the axis of the fiber. (d) Temperature profile along
the axis of the fiber. Solid lines indicate temperature measured along
three selected rows of pixels between the center and edge of the fiber.
Blue crosses indicate data points averaged from each column of pixels
in the 2D image. The bold solid red line indicates the best fit to the
experimental temperature profile with an extracted thermal conductivity of 9.5 W m−1 K−1 and convection coefficient of 37 W m−2
K−1.
where m = (h′ − αp′)/kA, when h′ − αp′ > 0. We fit eq 6 to the
experimental temperature profiles to measure the thermal conductivity
k and convective heat transfer coefficient h. Figure 1d shows an
example of the best fit curve with an example experimental
temperature profile. The traditional convection coefficient (h in
Watts per squared meter per Kelvin) was then calculated from
where P is the perimeter of the cross section of the specimen.
Note that the analytical solution in eq 6 assumes a constant
convective coefficient along the length wire. As the maximum
temperature of the wire is limited to a few Kelvin above the set
base temperature, the variation in the natural convection coefficient is
small. Essentially, the extracted heat transfer coefficient can be
considered an average value for the fiber. This assumption is validated
in detail in the Supporting Information.
The proposed method was first verified by measuring the thermal
conductivity of the bare nickel chromium resistance (BNC) wires
(AWG 30, Consolidated Electronic Wire & Cable, United States). As
shown in Table 1, all experimental values are very close to the values
provided by the manufacturer, with standard deviations of less than
10%. Thus, the experimental setup and methods employed in the
present work were considered to be valid and extended to the CNT
fiber and film samples.
3. RESULTS AND DISCUSSION
3.1. Electrical Properties of CNT Fibers. Figure 2 shows
the effect of the volume fraction of CNTs on the electrical
conductivity determined according to eq 2. When the volume
fraction increases from 5.5% to 41.4%, the electrical
conductivities of the fibers increases from 150 to 1050 S
cm−1. While there is a clear increase in the electrical
conductivity with increasing volume fraction, the specific
electrical conductivity, defined as the ratio between fiber
electrical conductivity and bulk density, is nearly independent
of the volume fraction varying in the range of 1000−1500 S
cm2 g−1. The average specific electrical conductivity is ∼1200 S
cm2 g−1 obtained by linearly fitting the data for electrical
conductivity as a function of fiber bulk density. A similar trend
of increasing electrical conductivity with volume fraction, but
constant specific electrical conductivity, was previously
observed by Miao17 for array-spun CNT fibers. Here, the
measured specific electrical conductivity is comparable with
d2T (x)
+ p′[1 + α(T (x) − T0)] − h′(T (x) − T0) = 0
dx 2
(4)
with the boundary condition of
⎛
L⎞
T ⎜x = ± ⎟ = TL/2
⎝
2⎠
(7)
h = h′/P
specimen is measured by an infrared temperature measurement
microscope system (InfraScope, Quantum Focus Instruments
Corporation), as shown in Figure 1c. The high spatial resolution
(11.7 μm/pixel at 1× magnification) of the infrared microscope
enables hundreds of temperature data points along the length of a 1
cm long specimen, as shown in Figure 1d. The one-dimensional (1D)
heat transfer along the length of the fiber is confirmed by the nearly
uniform temperature in the direction perpendicular to the axis of the
fiber as illustrated in Figure 1c and d and is further validated in detail
in the Supporting Information. All measurements are performed under
ambient environment at room temperature (295.15 K). The range of
currents tested is limited to ensure the average temperatures of the
specimens do not exceed 303.5 K (near room temperature). The
emissivity of the samples is 0.86 ± 0.02 measured through a calibration
procedure described in the Supporting Information.
Heat transfer along the specimen is governed by the steady-state 1D
heat diffusion equation:32,33
kA
(6)
2
(5)
Table 1. Data Sheet and Experimentally Measured Properties of Bare Nickel Chromium Resistance (BNC) Wires
diameter (μm)
value provided by manufacturer
experimental value
254
255 ± 5
resistance (Ω cm−1)
TCR (K−1)
0.2215
0.2195 ± 0.005
0.00015
0.000146 ± 0.00002
C
thermal conductivity (W m−1 K−1)
13
13 ± 1
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5, and 10 min-films are 13 ± 1.2, 12.5 ± 1.5, and 13.7 ± 2.0 W
m−1 K−1, respectively, which are nearly independent to the
diameter and collecting time.
In contrast to diameter and collecting time, the volume
fraction of CNTs has a great influence on the fiber thermal
conductivity. Figure 3b shows the thermal conductivities of the
CNT fibers as a function of volume fraction. When the volume
fraction of CNT increases from 5.5% to 41.4%, the thermal
conductivities of the fibers increase from 4.7 ± 0.3 to 28.0 ± 2.4
W m−1 K−1. Similar to the specific electrical conductivity, the
specific thermal conductivity (k′) is also nearly independent of
the volume fraction as illustrated by the nearly linear
relationship between the volume fraction and the thermal
conductivity. The average specific thermal conductivity is
estimated to be 32 W m2 kg−1 K−1 by linearly fitting the
thermal conductivity as a function of the fiber bulk density.
Heat conduction in carbon materials is usually dominated by
phonons due to the strong covalent sp2 bonding resulting in
efficient heat transfer by lattice vibrations. Here, we predict that
the electronic contribution to the thermal conductivity (ke) is
less than 5% of the total measured conductivity for all the
specimens, as calculated via Wiedemann−Franz law: ke/σ = LT,
where σ, L, and T are electrical conductivity, Lorenz number,
and temperature, respectively.36
The CNT fiber can be regarded as a two-phase system
consisting CNTs and air with thermal conductivities of kCNT
and kair (0.0259 W m−1 K−129). A simple model considering
nanotubes conducting heat parallel with the air predicts that the
thermal conductivity increases linearly with volume fraction of
CNTs ( f):6
Figure 2. Electrical conductivity and specific electrical conductivity of
the CNT fibers as a function of volume fraction. Note that the
electrical conductivity increases approximately linear with volume
fraction indicating a nearly constant specific electrical conductivity.
previously published result on CNT fibers synthesized from
aerogels (1600 S cm2 g−1)34 and one measurement of CNT
fibers synthesized from aligned CNT arrays (1300−1400 S cm2
g−1).35 But it is much higher than the specific electrical
conductivities of several other studies of CNT fibers
synthesized from aligned CNT arrays (370−900 S cm2
g−1).17,21,22
The average temperature coefficient of resistance (TCR)
near room temperature for the CNT fibers is 0.00115 ±
0.00025 K−1. Reported values of the TCR of CNT fibers near
room temperature vary from 0.001 to 0.002 K−1.8,9,19,21 Note
that the TCR of the CNT fibers in this research is
approximately half that of the TCR of copper (∼0.004 K−1)
and aluminum (∼0.0043 K−1), which is a promising result for
further developing these CNT fibers into potential applications,
such as electrical cables.5
3.2. Thermal Conductivities of CNT Fibers. In this work,
thermal conductivities of CNT fibers with different collecting
time (1, 5, and 10 min) and volume fractions (5.5%−41.4%)
are measured with a steady state Joule heating infrared
metrology technique. First, in order to investigate the effect
of collecting time and diameter, fibers with the same volume
fraction (∼17%) are made from 1, 5, and 10 min-films. As
shown in Figure 3a, the diameters of the fibers increase with the
increasing collecting time. Larger fiber volume is expected
because the longer collecting time leads to increased
accumulated CNT mass while the volume fraction is kept
constant. The thermal conductivities of the fibers made from 1,
kspecimen = fk CNT + (1 − f )kair ≈ fk CNT
(8)
A linear fit to the data in Figure 3b provides an estimate of 68
W m−1 K−1 for the thermal conductivity of the individual
nanotubes in the fibers. This is within the reasonable range for
individual MWNTs. Previous researchers have reported 34 W
m−1 K−1 for the MWNT with a diameter of 14 nm and 160 W
m−1 K−1 for the MWNT with a diameter of 11.4 nm.38
However, it is much lower than other previous measurements
of individual MWNTs.39−44
Previous research suggests that the density of nanotubes is
not the only factor influencing the thermal conductivity of
nanotube-based systems. The low apparent thermal conductivity of the CNT fibers compared to that predicted from
the high values of thermal conductivity of the individual CNTs
Figure 3. Impact of (a) collecting time and (b) volume fraction on thermal conductivity. The thermal conductivity of the fibers is independent of
collecting time and fiber diameter but increases approximately linearly (blue dotted line) with volume fraction indicating an effect individual CNT
thermal conductivity of ∼68 W m−1 K−1. The green solid line indicates the best fit of the model of Chalopin et al.,37 which enables estimation of the
CNT−CNT contact conductance of GCNT−CNT ∼ 13−130 pW K−1.
D
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reported in literature can be explained by the impact of
contacts, as well as the quality and morphology of the CNT
fibers.
Thermal contact resistance leads to temperature jumps at the
interfaces between contacting nanotubes. The contact points
may also introduce additional phonon scattering or damping
phonon modes within a nanotube reducing the effective
thermal conductivity of each nanotube.6 Although the coupling
in nanotube bundles significantly increases the contact area, it
may also lead to the deformation of nanotube shape due to van
der Waals force between adjacent nanotubes.45 The deformation could lead to suppression of optical phonon modes42 and
increased inter-CNT contact resistance,46 which results in
substantially reduced thermal transport abilities for the
individual CNT.
The CNT−CNT contact conductance (GCNT−CNT) in this
work is estimated to be on the order of 13−130 pW K−1,
extracted by fitting the model of Chalopin et al.37 to our
experimental results (see Figure 3b):
kspecimen
0.18L ρspecimen
≈
GCNT − CNT
2πD ρgraphene
Figure 4. SEM images illustrating (a) the overall alignment of CNTs
within the in the fibers and (b) the inhomogeneity of the structure that
may depress the measure valued of thermal conductivity.
critical for accurate predictions of temperature and device
performance.
Figure 5a shows the convection coefficients of the CNT
fibers with various collecting times (tc) and diameters vary from
26 to 193 W m−2 K−1, which is higher than the typical values
for the natural convection coefficient at the macroscale (2−25
W m−2 K−1). In general, most thermal conductivity measurements of fibers require a high vacuum environment to eliminate
convection losses, which increases the experimental complexity.
As a result, there are fewer studies (see Figure 5b) on the
mechanism of convective heat transfer at microscale than at the
macroscale. Li et al.52 reported convection coefficient of 1039−
1143 W m−2 K−1 for CNT fibers an order of magnitude smaller
in diameter than our fibers (d ∼ 36−43 μm compared to
∼150−800 μm in this work). Hsu et al.53 found the heat
transfer coefficient between an individual single-walled nanotube (SWNT) and the surrounding air molecules ranged from
1.5 × 103 to 7.9 × 104 W m−2 K−1. Other studies on free
convection from other microscale materials showed that the
convection coefficient varies from 100 to 7000 W m−2 K−1
depending on the diameter of the microwire.50−52,54−56 Our
observation is consistent with these results in the literature,
suggesting that the convection coefficient for CNT fibers is also
strongly influenced by scaling effects, as well as other structural
and environmental factors.
As shown in Figure 5a, for fibers with the same collecting
time (e.g., 10 min), the convection coefficient decreases with
increasing diameter. This trend is consistent with the results
calculated by the correlation of Churchill and Chu29 for free
convection on long horizontal cylinders:
(9)
where ρgraphene = 7.6 × 10−7 kg m−2 is the surface mass density
of graphene. Note that this model was developed for randomly
oriented nanotube mats instead of aligned CNT films or fibers,
and neglects the finite thermal conductivity of the individual
CNTs. But, essentially, this value can be considered an upper
bound to the thermal resistance for the contacts and it is
comparable to the few reported experimental and simulation
works (ranging from ∼3−50 to >100 pW K−1).37,47,48
Mesoscopic models for aligned CNT macroscale assemblies,
which can fully model the interactions between the individual
CNT properties, specimen morphology including CNT length,
diameter and alignment and CNT−CNT contacts on the
thermal conductivity, are required in the future to better
understand the heat conduction in CNT macroscale assemblies.
In addition to contact resistances, thermal conduction within
nanotube fibers and films is complicated by CNT quality and
the morphology of the nanotubes. MWNTs grown by CVD are
generally more defective than those grown by arc-discharge or
laser ablation methods.49 Simulations and measurements of
individual CNTs with defects showed that the thermal
conductivity decreased significantly with increasing defect
concentration. CNT fibers or films consisting of longer
nanotubes may exhibit even lower conductivity than the one
consists of shorter nanotubes because of higher probability of a
defect occurring within a longer tube.6 Additionally, the
structural inhomogeneity of the CNT macroscale assemblies
strongly impacts their apparent thermal conductivity.21,42 As
shown in Figure 4, even though CNTs are assembled into
bundles with high orientation preference (Figure 4a), we still
observe dangling ends and interweaving in the structure (Figure
4b). These inhomogeneities may prevent the overall thermal
conductivity from achieving the performance expected from
that of individual CNTs.
3.3. Convective Heat Transfer in CNT Fibers. Natural
convection from the CNT fibers is also investigated in this
same experiment. The physics of solid to gas heat transfer
changes considerably with size50 and environmental factors like
temperature and pressure.51 Since most microelectronic and
microelectro-mechanical devices operate in air, understanding
the mechanism of convective heat transfer at microscale is
⎧
⎫2
⎪
⎪
⎪
⎪
0.387RaD1/6
⎬
NuD = ⎨0.60 +
8/27
⎡
⎪
⎪
0.559 9/16 ⎤
1 + Pr
⎪
⎪
⎢
⎥
⎣
⎦
⎩
⎭
(
for RaD ≲ 1012
)
(10)
where NuD = hD/kair , RaD, and Pr are the Nusselt number,
Rayleigh number, and Prandtl number, respectively. Note that
the correlation of Churchill and Chu is for free convection at a
constant temperature, while the temperature distribution along
the CNT fiber shows a cosh-shape. Since the average
temperatures of the specimens were controlled within a small
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Figure 5. (a) Impact of diameter and collecting time on the convection heat transfer coefficient. The trend of decreasing convection coefficient with
diameter agrees well with the correlation of Churchill and Chu (calculated at 299.15 K),29 (dashed line), although exact values differ. Note that for
the same diameter, a higher collecting time indicates more CNTs within the same outer fiber diameter. (b) Measured convection coefficients of this
work compared with literature data52,55,56 and predictions50 for microwires. Note that the convection coefficient for CNT fibers is not only strongly
influenced by scaling effects but also by other structural and environmental factors. (c) Effect of volume fraction on the convection coefficient.
(inset) Cross-section of a CNT fiber with different volume fractions. (d) Convection coefficient of the CNT fiber as a function of effective diameter.
The red hollow circles in part c and the solid red line in part d indicate the calculated convection coefficient using the Churchill−Chu correlation and
the effective diameter of the fiber.
Assuming a fixed outer diameter and a fixed convection
coefficient on CNT bundle surface, a fiber with higher volume
fraction consists of more CNT bundles and thus could have a
larger effective surface area for convection. This results in more
total heat loss and a higher effective convection coefficient
because only the outer perimeter (P = πD) is used to calculate
h in eq 7. For a better understanding of the convective heat
transfer in a porous structure like the CNT fiber here, we
suggest to consider an effective diameter (Deff (m)), which
combines both the outer diameter (D (m)) and volume
fraction (f (%)) by the following empirically obtained equation:
range (296.15−303.15 K), no significant impact of spatially
varying convection coefficient is expected (see Figure S3 in the
Supporting Information). Thus, a typical average fiber temperature (299.15 K) is chosen for use in the Churchill−Chu
correlation. As shown in Figure 5a, most of our experimental
results are larger than the corresponded calculated values,
although the diameter scaling effect has been taken into
account in this correlation.
In addition, the correlation of Churchill and Chu29 indicates
that the convection coefficient monotonically decreases with
the increasing diameter, independent of other fiber properties.
However, the convection coefficients of the CNT fibers in
Figure 5a are also affected by the collecting time, which
determines the number of CNTs inside the fiber. This suggests
that the porous structure of the CNT fibers may affect the
convective heat transfer considerably. Since it is difficult to
count the number of individual CNTs inside a fiber, here we
investigate the effect of the volume fraction, reflecting the
number of individual CNTs per unit volume. As shown in
Figure 5c, the convection coefficient increases with increasing
of volume fraction. Previous studies report that surface area to
volume ratio demonstrates great impact on heat transfer
coefficient.51,57 Unlike solid materials, the effective surface area
of CNT fibers is difficult to calculate. The insets in Figure 5c
show illustrations of the cross-section of a CNT fiber. The
structure of the CNT fibers can be regarded as numerous CNT
bundles consisting of aligned individual CNTs. Open pores,
between the CNT bundles, interconnect the air inside and
outside of the fiber. Thus, the free convection can be
considered on not only the outer surface but also the surface
of each or some CNT bundles inside. The convection
coefficient reflects the degree of heat loss per unit area.
Deff = D(0.000268D−1.6f −1.8 + 0.061)
(11)
As shown in Figure 5c and d, the corresponding convection
coefficients calculated by eqs 10 and 11 have a good
consistency with the experimental data. To a certain extent,
this estimate of effective diameter indicates synergistic effects
between the outer diameter and the number of CNT inside the
fiber on the convective heat transfer in these porous CNT
fibers. The actual convection between CNT fibers and the air is
complicated due to the interaction of many environmental
variables, as well as the complex structure of the CNT fiber.
Ultimately, a more detailed correlation may include many
factors including CNT length, bundle size, bundle entanglement, pore size, and gas flow inside the pore structure.
The mechanism of heat transfer between microscale
materials and air or other gases is also controversial. Some
research assumes that the dominant mode of heat transfer at
the microscale is conduction through the air, instead of the
classic notion of advection, such that natural convection effects
could be neglected at microscale.57 Models considering the
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scaling effect and the microstructure of the CNT fiber are
required in the future to further study the mechanism of heat
transfer in CNT based assemblies.
3.4. Effects of Acid Treatment on Thermal Conductivity. To study the effects of acid treatment on the
thermal conductivity, both CNT fibers and the CNT films from
which they were fabricated are immersed in 65 wt % HNO3 at
room temperature for 30 min. The effects of acid treatment on
physical properties of CNT fiber and films are summarized in
Table 2. After acid treatment, the electrical conductivities of the
Table 2. Effects of Acid Treatment on Physical Properties of
CNT Fiber and Films
as-prepared
sample
−3
density (g cm )
electrical conductivity
(S cm−1)
specific electrical
conductivity (S cm2 g−1)
thermal conductivity
(W m−1 K−1)
specific thermal conductivity
(mW m2 kg−1 K−1)
BET surface area (m2 g−1)
acid-treated
fiber
film
fiber
film
0.67
700
1.19
1988
0.71
1622
1.60
4666
1045
1670
2285
2916
25
113
74
759
37
104
94
474
78
124
specimens are enhanced by a factor of 2−3, while their thermal
conductivities are enhanced by a factor of 3−6. Additionally,
the specific electrical and thermal conductivities are enhanced
by factors of ∼2 and ∼4, respectively. For the as fabricated
samples discussed previously, the specific electrical and thermal
conductivities are nearly independent of density. However, acid
treatment significantly improves the specific conductivities
indicating that the intrinsic conductivity of the CNTs or the
interfacial resistance have been modified during the acid
treatment.
Such significant improvements on both electrical and thermal
conductivities of the specimens can be related to structural
modifications, which are investigated using Raman spectroscopy based on the ratio ID/IG. As shown in Figure 6a, ID/IG
decreases from 0.26 to 0.21 after acid treatment, suggesting that
CNTs become less defective after this treatment. Chemical
processing of CNTs by concentrated nitric acid induces several
modifications to the structure including purification (i.e., to
eliminate amorphous carbon adhering to the CNTs),
functionalization, and decapping of the CNTs.30 Functionalization typically requires elevated temperature or long times (90−
120 min or more),20,30,31 which may result in an increase in the
ratio ID/IG after acid treatment.20,31 Unlike those studies, in this
work, the CNT fibers and films are treated for just 30 min at
room temperature and purification is expected to be the
dominant effect in this initial short period of acid treatment.
The impact of the nitric acid is further elucidated by TEM
images, as shown in Figure 6c and d. Before the acid treatment,
many small particles could be observed adhering to the CNT
surface. These particles are believed to be amorphous carbon.30
After 30 min acid treatment, the CNT surface becomes cleaner
and thinner, which proves that the short acid treatment odes
impact the purity of the structure. Furthermore, there is an
enhancement of 50% for the BET surface area of the acidtreated specimen (Table 2). The pore size distribution of
specimen is also modified during the treatment (see Figure 6b).
Although the majority of the pores range from 2 to 4 nm for
Figure 6. Effects of acid treatment on (a) Raman spectra and (b) pore
size distribution. TEM images of CNT (c) before and (d) after acid
treatment. Note the amorphous carbon at the surface of the assynthesized CNT in part c, which is not observed in the acid-treated
sample in part d.
both the as-prepared and acid-treated specimens, there is a wide
peak in the range of 15−30 nm for the as-prepared specimen.
After acid treatment, two smaller peaks around 7 and 10 nm are
observed. The work of Edwards et al.58 revealed that the
concentrated HNO3 treatment was not effective for purification
of the iron within the CNTs that serve as catalyst nanoparticles,
although amorphous carbon can be eliminated. Thus, here, the
increase in the BET surface area and the change of pore size
distribution is attributed to the etching of the carbon-based
defects, such as amorphous carbon and very short, highly
defective CNTs, in the CNT fibers and films resulting in
smaller pores and increasing specific surface area. These results
further support the purification effect of acid treatment. As
discussed in the previous sections, amorphous carbon, short
CNTs and dangling ends, serving as resistances to thermal
conduction and may prevent the overall thermal conductivity
from achieving the expected performance. More effective
contacts between nanotubes and less defective structure after
purification greatly enhance the electrical and thermal
conductivities.
Additionally, the densities of the acid-treated CNT fibers and
films are larger than the as-prepared ones (Table 2), indicating
densification of the macroscale structure as another effect of
acid treatment. Figure 7 shows the SEM images of the fracture
morphologies of the as-prepared and acid-treated CNT films.
After acid treatment, the CNTs assembled into thicker bundles
with more compacted structure with larger densities. Since the
contact resistance depends strongly on the contact angle and
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increasing density and the specific thermal conductivity remains
nearly constant in the density range of 0.11−0.87 g cm−3. This
indicates some nonlinearity in the thermal conductivity with
increased density in a wider density range (e.g., the density of
the as-prepared film is around 1.2 g cm−3). The nonlinearity in
the thermal conductivity with increased density was also
reported by Marconnet et al.64 in their study of the thermal
conductivity of aligned CNT−polymer nanocomposites as a
function of varying CNT volume fraction. The lower specific
conductivity may be ascribed to the structure of the CNT fiber
and the inter-CNT contact resistance. Since the CNT fiber was
rolling from the CNT film, it can be regarded as a cylinder
structure consisting of multiple layers of films. Aliev et al.21
studied the effect of multilayered structure on the thermal
conductivity of CNT sheets stacked on top of one another.
They found that increasing the number of layers decreased the
measured value of thermal conductivity, likely due to poor
interfacial transport between the sheets. The same effect of
decreasing thermal conductivity with increasing layers occurs
for graphene layers when they are stacked in graphite. In that
case, interlayer interactions quench the thermal conductivity by
nearly an order of magnitude. The lower conductivity of
multilayered structure indicates the presence of enhanced
scattering of heat carriers at the tube−tube interconnections
between layers. This result suggests that an improved
fabrication method is required in the future to obtain highly
dense CNT fibers with better intertube contacts and high
thermal conductivity. In addition, the thermal conductivities in
this work are measured near room temperature. For many
applications,65,66 it is of great importance to study the thermal
conductivity of the CNT fiber across a range of temperatures.
The technique developed here can be extended to enable
temperature-dependent measurements through control of the
base temperature of the fiber and the environment.
Figure 7. SEM images of as-prepared (a and b) and acid-treated (c and
d) CNT film at different magnifications. Note that the acid-treated
specimen has more compacted structure with thicker CNT bundles
compared with the more porous structure consisting thinner bundles
of the as-prepared samples. The denser structure contributes more
effective intertube contacts to the enhanced thermal conductivity.
intertube space,6 the considerable enhancement of conductivities also can be attributed to the improving CNT−CNT
contact conductance due to the better alignment, shorter
intertube space, and larger effective contact area after
densification.
Interfacial contact resistance can also be modified through
the covalently bonded nanotubes,59 and there may be some
slightly functionalized CNTs existing after the short time acid
treatment.20,30 However, thorough functionalization was
reported to suppress the electrical conductivity of the CNT
fibers20 and also decrease the intrinsic nanotube thermal
conductivity60 due to the destruction of the crystalline structure
of CNT, which can be observed by TEM. Based on our
characterizations of the structural modifications, functionalization is not the dominant reason for the observed enhancement
of conductivities.
As shown in Figure 8, the thermal conductivity and specific
thermal conductivity of our CNT fibers and films are
comparable to those of other CNT fibers and selected highly
conductive films.8,21−25,52,61−63 In particular, our acid-treated
CNT film combines both high absolute thermal conductivity
and high specific thermal conductivity, which is even higher
than the typical values of conventional heat-transfer metals
(copper, aluminum, and silver) and comparable to that of the
highest performing CNT fibers and films reported in the
literature. Interestingly, the specific thermal conductivity of our
CNT film is much higher than that of our CNT fiber, which
differs from the observation for the CNT fibers where the
thermal conductivity increases nearly linearly with the
4. CONCLUSIONS
We demonstrate a robust, fast electrothermal technique for
simultaneously measuring the thermal conductivity of and
convection coefficient from CNT fibers and films. The
measured thermal and electrical performance demonstrates
the promise for using these fibers and films in macroscale
applications requiring effective heat dissipation such as
electrical cables and multifunctional composites.
The thermal conductivity of the as-prepared fiber ranges
from 4.7 ± 0.3 to 28.0 ± 2.4 W m−1 K−1, which is much lower
than the expected from the high thermal conductivity of
individual CNTs, is comparable to other CNT-based structures
and rivals the specific thermal conductivity of metals. The
Figure 8. Thermal conductivity and specific thermal conductivity of this work compared with literature data for other CNT fibers and films made by
different processes.8,21−25,52,61−63
H
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Based on Electrospinning, Twisting, and Heating for Producing One-
major factors limiting the apparent thermal conductivity of the
CNT fibers are the interfacial contact resistance and structural
inhomogeneity in the fibers.
The convective heat transfer coefficient for the as-prepared
CNT fiber strongly depends on the diameter and volume
fraction. A correlation between CNT volume fraction, diameter,
and convective coefficient has been developed based on the
experimental data. New models considering the microstructure
of CNT fiber are required in the future for better understanding
the mechanism of heat transfer in CNT based assemblies.
Nitric acid treatment is demonstrated to be a simple, effective
approach to enhance the thermal conductivity of the CNT
fibers and films. The thermal conductivity and specific thermal
conductivity are enhanced by 670% and 450% respectively after
acid treatment. This great improvement is attributed to the
reducing CNT−CNT contact resistance, modified fiber
structure, and increased density after the acid treatment. The
acid-tread CNT film demonstrates thermal conductivity of 759
W m−1 K−1 and specific thermal conductivity of 474 mW m2
kg−1 K−1, which is even higher than the typical values of
conventional metals and comparable with the highly conductive
CNT assemblies reported in the literature. Compared to the
CNT films, CNT fibers exhibit lower thermal conductivity and
require the development of optimized fabrication method for
more compacted fiber structures with improved intertube
contacts to further improve thermal performance.
■
ASSOCIATED CONTENT
S Supporting Information
*
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acsami.6b04114.
Validation of one-dimensional heat transfer; method of
emissivity calibration and thermal image acquisition;
influence of variable local heat transfer coefficient on the
temperature profile; influence of temperature on
Churchill−Chu correlation; summary of the properties
of the CNT fibers (PDF)
■
AUTHOR INFORMATION
Corresponding Authors
*E-mail: mpedhm@nus.edu.sg (H.M.D.).
*E-mail: amarconn@purdue.edu (A.M.M.).
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
The authors would like to thank Temasek Laboratory@NUS
Singapore (R-394-001-077-232) for the financial support for
this project.
■
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