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

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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:

vikas.prakash@case.edu. 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)

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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)

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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)

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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)

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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)

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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)

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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)

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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.

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