Optical visualization and polarized light absorption of the single-wall carbon nanotube to verify intrinsic thermal applications

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The predicted extraordinary properties of carbon nanotubes (CNTs) from theoretical calculations have great potential for many applications. However, reliable experimental determination of intrinsic properties at the single-tube level is currently a matter of concern, and many challenges remain because of the unhandled and nanoscale size of individual nanotubes. Here, we demonstrated a prototype to detect the intrinsic thermal conductivity of the single-wall carbon nanotube (SWCNT) and verify the significant non-resonant optical absorption behavior on tiny nanotubes by integrating the nanotube and ice into a new core-shell design. In particular, a reversible optical visualization method based on the individual suspended ultra-long SWCNT was first developed by wrapping a nanotube with ice in the cryogenic air environment. The light-induced thermal effect on the hybrid core-shell structure was used to melt the ice shell, which subsequently acted as a temperature sensor to verify the intrinsic thermal conductivity of the core-like nanotube. More interestingly, we successfully determined for the first time the thermal response phenomenon of the tiny absorption cross section in SWCNT in the vertical-polarization configuration and the significant non-resonant absorption behavior in the parallel-polarization configuration. These investigations will provide a better understanding for the unique optical behaviors of CNT and enable the detection of intrinsic properties of various one-dimensional nanostructures such as nanotubes, nanowires, and nanoribbons. Growing ice on a carbon nanotube not only enables the nanotube to be optically imaged but also permits its thermal properties to be measured. Isolated single-walled carbon nanotubes with diameters of just a few nanometres are usually impossible to observe using an optical microscope. Now, Xiao Zhang and other scientists in China have discovered a non-destructive and reversible way to optically observe carbon nanotubes and measure their thermal properties. Their method involves growing a few-micrometre-thick layer of ice on a suspended nanotube by placing it in a cryogenic environment. The researchers then melted the ice by irradiating the ice-coated nanotube with a laser beam, while inferring the nanotube s temperature from a shift in its Raman signal. From this information, they could determine the intrinsic thermal conductivity and the light absorption behavior of the nanotube.

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## ORIGINAL ARTICLE

# Optical visualization and polarized light absorption of the single-wall carbon nanotube to verify intrinsic thermal applications

Xiao Zhang 1, Li Song 2, Le Cai 1, Xuezeng Tian 1, Qiang Zhang 1, Xiaoying Qi 3, Wenbin Zhou 1, Nan Zhang 1,
Feng Yang 1, Qingxia Fan 1, Yanchun Wang 1, Huaping Liu 1, Xuedong Bai 1, Weiya Zhou 1 and Sishen Xie 1

Keywords: carbon nanotube; optical visualization; polarized laser; resonant absorption

INTRODUCTION
The extraordinary thermal and electrical properties of carbon nanotubes (CNTs) have been extensively investigated in the last decade for
applications in various devices. Despite its obvious importance, a
reliable experimental determination of the intrinsic properties of
SWCNTs, particularly at the single-tube level, remains a challenge
because of the tiny sectional area and enormous difficulty in nanotube
manipulation, which in fact hampers its wide use. From the theoretical
side, an equilibrium molecular dynamic (MD) simulation has suggested that the lattice thermal conductivity of a (10, 10) SWCNT
reaches the maximum value of approximately 37 000 W (K?m) 21 at
100 K and decreases to approximately 6600 W (K?m) 21 at 300 K 1 .
However, because of the diversity of measuring methods and sample
qualities, the experimentally measured thermal conductivity value (k)
significantly varies from 200–25 000 W (K?m) 21 2–5 . Moreover, in
most previously reported measurements, the crystal structure of
CNT was not adequately characterized. Consequently, it is predictable
that the obtained thermal conductivity values may contain errors
that result from the uncertainty in the actual SWCNT cross section,
let alone the relationship between structure and thermal property.

Furthermore, experimental results 6,7 of the polarized optical
absorption cross section of SWCNTs in bulk samples provide
some direct confirmation of the absorptive process theory 8,9 .
Considering that the surrounding environment of CNTs (particularly the substrate and adjacent tubes 10,11 ) may remarkably affect
the properties of CNTs, a reliable experimental determination of
the intrinsic properties at the single-tube level is currently a matter of concern. Recent light absorption investigations of individual nanotubes have focused on different resonant and nonresonant modes using spatial modulation spectroscopy 12, polarization-based homodyne microscope 13, and photoconductivity
spectra 14 . However, to avoid the optical detection difficulty from
the small cross section of SWCNTs, the light-induced thermal
effect was considered a suitable method to study the thermal
and optical properties of CNTs, which is also significant to both
the function of optical devices 15 and SWCNT species control 16–18 .
In arrays of nanotubes with mixed structures and chirality,
unusual laser-induced ‘‘heat trap’’ phenomena have recently been
observed 19,20 . However, intrinsic thermal response study on individual nanotube remains missing because individual CNT’s

1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; 2National Synchrotron Radiation
Laboratory, University of Science and Technology of China, Hefei 230029, China and 3 National Center for Nanoscience and Technology, Beijing 100190, China
Correspondence: Li Song, Email: song2012@ustc.edu.cn; Sishen Xie, Email: ssxie@aphy.iphy.ac.cn
Received 8 November 2014; revised 1 April 2015; accepted 2 April 2015; accepted article preview online 9 April 2015

X Zhang et al

manipulation and visualization are challenging. Recently, a flowguided synthesis method was reported to grow ultra-long nanotubes with perfect crystalline structure (maintaining the chirality
without any change for more than hundreds of micrometers 21 ).
Therefore, the ultra-long nanotube is considered an ideal object
to characterize intrinsic nanotube properties, particularly the suspended nanotube with unique superiority in avoiding any effects
from the substrate 12,22 .

Moreover, optical microscopic imaging resolution has a theoretical
limit of approximately 200 nm within the visible-light spectrum
because of the far-field diffraction limit, which prevents the technique
from being used to directly observe nano-objects 23 . If individual ultralong nanotubes can be observed under an optical microscope through
a facile and reversible method, nanotube characterization and manipulation will tremendously benefit its fundamental investigations and
various specific applications.

In this contribution, the individual and suspended ultra-long
SWCNT is successfully synthesized to cross over an as-patterned
optical slit. Then, its chirality is characterized using high-resolution
transmission electron microscopy (HRTEM), electron diffraction
(ED) and Raman spectra. More interestingly, a facile method was
proposed to make such suspended SWCNTs visible by depositing
ice around them to form a new core-shell structure. We demonstrate
that when irradiated by lasers, the ice-enclosed SWCNT can be heated,
which melts the ice around it. By analyzing this ice melt strategy and
the inferred temperature from the SWCNT’s Raman peak shift, we
propose a prototype to directly identify the intrinsic thermal conductivity of the individual suspended SWCNT. With its structure and
chirality, which are obtained from the analysis of ED and
Raman spectra, the relationship between the nanotube structure
and its thermal property is further verified. Furthermore, we use laser
polarization absorption experiments to reveal, for the first time, the
thermal response evidence of a tiny absorption cross section of
SWCNTs in the vertical-polarization configuration and its significant
non-resonant absorption behavior in the parallel-polarization
configuration.

MATERIALS AND METHODS

Suspended CNT sample preparation
To study the core-shell structure, first, we prepared the individual
suspended SWCNTs using a previously described method 24 .
3 mg mL 21 hemoglobin (Hb) solution was spin-coated on silicon
wafers with a 500 nm thick thermally oxidized layer as the catalyst substrates. Before the growth procedure, the catalyst substrate was
annealed in air at 800 6 C for 20 min and subsequently pretreated at
950 6 C in H2 for 5 min to effectively reduce the catalyst. The nanotube
growth was initiated by introducing 25 sccm H2 and 10 sccm CH4
at 950 6 C. After 20 min growth, the sample was cooled in Ar to room
temperature. The entire preparation process was performed at atmospheric pressure.

Raman and melting experiments
We performed the optical experiment on a HORIBA HR800 microRaman spectroscopy equipped with a Linkam model THMS600
heating and cooling microscope stage to maintain the sample at different constant temperatures in air. The optical setup also includes
503 objective (N.A. 5 0.5), 1800 grating, and lasers with excitation
energy of 2.41 eV (514.5 nm), 1.96 eV (632.8 nm), and 1.58 eV
(785 nm). The largest laser power on the sample is 2.4, 4.9, and
7.5 mW, respectively (measured using an optical power meter).

Substrate preparation and chiral index (n, m) characterization
Because of the sensitivity of nanotube’s properties to atomic configuration, a reliable method to determine the nanotube structures is
indispensable. We determined the atomic structure of each CNT from
HRTEM and the ED pattern 25 using nanofocused electron beams in an
FEI Tecnai G2 F20 U-TWIN TEM and JEOL 2010F TEM. To avoid
conceivable large drifting and optical experiment uncertainty, which
are induced by electron irradiation damage, as illustrated in Figure 1a
and 1b, a homemade substrate was used as a receiving substrate on
which the suspended nanotubes were directly grown. Using this new
receiving substrate, the electron beam and laser beam can pass through
the narrow TEM slits (5 mm 3 200 mm with location marks) and wide
optical slit (100 mm 3 200 mm) respectively. This design enables the
combination of TEM ED and optical spectroscopy techniques to
investigate both the chiral index and the optical, thermal properties
of the same individual suspended SWCNTs.

RESULTS AND DISCUSSION
Visualization of SWCNTs via a hybrid ice-SWCNT coreshell design
To form the core-shell structure, the substrate with suspended ultralong SWCNTs was loaded into the heating and cooling microscope
stage (Figure 1c). When the temperature of the stage decreased, the
individual suspended SWCNTs gradually became visible as a wire
across the slit under an optical microscope, as shown in Figure 1d
and 1e. We identified the Raman spectrum of the shell, which had
an O-H stretching vibration mode at approximately 3200 cm 21 . Thus,
we ascertained that, as long as the temperature was sufficiently low, the
supercooling water vapor in the surrounding would rapidly condense
onto the nanotubes to form a unique SWCNT-ice core-shell structure
of a few micrometers. The hybrid structure enables the individual
SWCNT to be visualized as a wire under the optical microscope,
although the CNT has a notably tiny diameter of approximately 2 nm.

Similar efforts have been reported to make CNT visible under an
ordinary optical microscope to easily manipulate CNTs, such as electroplating Au nanoparticles 26 and depositing TiO2 particles 27 .
Compared with the previous methods, in our strategy, the visualization process is reversible because the nanotube will recover to its
naked form without any change in structure when it returns to room
temperature (proven by comparing the TEM feature and ED pattern
before and after the melting process). Very recently, Wang et al.
developed a technique to observe nanostructures using an optical
microscope with water vapor condensation 28 . Here, we want to point
out that in our method, the nanotube attached to the substrate can also
be reversibly visualized probably because ice nucleation was facilitated
by the nanotubes in comparison to the surrounding flat substrate.
However, a remarkable difference between our method and that of
Wang et al. is how to construct a supercooling water vapor environment. Thanks to this distinction, our method can maintain the
visibility of the CNTs as long as the temperature is sufficiently low.
More importantly, this distinction endows the ice-CNT structure
some further intriguing functionalities as follows.

Polarization laser-induced melt experiment
The most intriguing phenomenon is that when exposed to a parallelpolarized laser with intensity of several mW mm 22, the wire began to
gradually vanish from the irradiated position to two ends and formed
a melt section, as shown in Figure 2a and 2b. The melt section was
always much larger than the laser spot, which is calculated using the

l
diffraction limit (1:2 N:A: , which is calculated to be 1.2, 1.5, and

X Zhang et al

a CNT growth b

Optical slit

TEM slits

SEM view

Programmable cryogenic platform

Linkam THMS600
Temperature controlled stage (-190~400°C)

Optical view

Optical
microscope

Lid window
objective

Air atmosphere at 1 bar

Ice

SiO2 Ice

SiO2

100 µm
1.0kV 8.6mm ×1.00k SE(M) 50.0 µm

Figure 1. (a–b) A schematic illustration of the controllable preparation of an individual suspended SWCNT sample using a flow-guided chemical vapor deposition
method. (c) The illustration shows the formation of the new core-shell structure by depositing ice around the SWCNTs, when the temperature-controlled stage
maintained a cryogenic air environment. (d) An SEM image of suspended nanotubes that cross over the optical slit (indicated by white arrows) and three TEM slits
(indicated by blue arrows). (e) Suspended nanotubes coated with ice became visible under an optical microscope as wires across the optical slits.

1.9 mm for 514, 633, and 785 nm lasers, respectively). The margin
between the ice-enclosing part and the naked part, which we call the
melt edge, would reach a steady site after several minutes of exposure.

To determine whether the laser-inducing melt phenomenon originates from the heating of the CNT instead of the ice itself, we rotated the
sample by 90 6 to make the axis of the SWCNT perpendicular with the
incident laser polarization. Because of the deep sub-wavelength and
highly anisotropic dimensions of SWCNTs, the interaction between
SWCNTs and light strongly depends on the orientation of the electric
field with respect to the SWCNT axis. In contrast, the environment and
ice aroundthe SWCNT feels nodifferencewith the laserpolarization. As
shown in Figure 2c, almost no melt can be observed after the middle of
the suspended core-shell structure was irradiated with laser for 15 min.
However, after adding a l/2 retardation plate to turn the laser polarization parallel to the SWCNT axis and irradiating the wire for 5 min, an
obvious melt section was clearly observed around the laser spot as

shown in Figure 2d, despite the decrease in laser intensity with the l/
2 retardation plate in the light path. According to the above observations, the melt phenomenon undoubtedly originates from heating the
SWCNT despite its nanoscale size.

We have looked into our samples using an optical microscope and
estimated the thickness range of the ice shell, which is approximately
1–2 mm. In other words, the ice shell is notably thick (almost three
orders larger than that of the SWCNT diameter). Thus, we suggest that
the ice shell should have a notably lower degree of polarization effect
than SWCNT.

Theoretical basis
As previously mentioned, the enclosed SWCNT in ice was heated by the
laser.The ice began togradually meltfrom the irradiatedposition totwo
sides until a dynamic equilibrium was established. Then, the power of
the laser input to SWCNTs was offset by the power loss transferred from

X Zhang et al

b c

20 µm

20 µm 20 µm

Figure 2. (a) A schematic illustration of the heat-induced melt of an SWCNT-ice
core-shell wire from laser irradiation. (b) A laser-induced melt section was experimentally formed around the irradiated spot, when the SWCNT-ice core-shell wire
was exposedto a parallel-polarized 785nmlaser with a power of7.5 mWfor12min.
(c) In the vertical-polarization configuration, no melt section can be observed even
after laser irradiating for 15 min. (d) In the parallel-polarization configuration, an
obvious melt section can be directly observed near the laser spot with a much
weaker laser intensity than that used for the vertical-polarization configuration.

SWCNTstothe surrounding gas moleculesor ice out of the melt region.
Meanwhile, because the nanotube temperature decreased to nearly the
surrounding temperature within a short distance from the laser spot, we
could neglect the heat lost through the ends of the SWCNT.

Therefore, the spatial temperature profile can be analyzed using two
sectionalized stationary one-dimensional (1D) heat diffusion equations, which describe the naked and enclosed sections, respectively.

The naked part can be expressed in Equation (1):

where g9 represents the heat transfer coefficient between ice and
SWCNT. Similar to the aforementioned statement, the SWCNT temperature of the melt edge is TM. Because the nanotube temperature
declines to nearly the surrounding temperature within a short distance
(usually within several micrometers), we obtain T (‘) 5T0. Using the
above boundary conditions, the solution of Equation (3) is as follows:

T(x)~DTMe {m’x zT 0

and m’ ~

rf f i f f i f f i ffi ð4Þ

g’P

Because the temperature profile along the SWCNT is differentiable,
the first derivatives of above two solutions must be equal at the melt
edge. Thus, we obtain:

{m’ DT Me {m’ | 0 ~ mae mxM {mbe {mxM ð5Þ

The solution of Equation (5) is

sf f i f f

g’

DT M
DT H

s f f

z DT M

DT H

z DT M

DT H

Y 2 {2Yz {

f f i f f
g’

ð6Þ

j pdjd~npd½djz(n{1)d�,

k d d 2 x T2

gP A (T{T 0)~0 ð1Þ

d2T

dx 2 { gP A

where T, T0, g, P, A, and k represent the local temperature of SWCNT,
ambient temperature of the surrounding gas environment, heat transfer coefficient between SWCNTs and the gas, SWCNT’s perimeter,
cross-sectional area, and thermal conductivity, respectively.

We assumed that the temperature of SWCNT at the margin of the
laser spot was TH. Here, ice was actually considered a temperature
sensor, which had a fixed temperature TM at melt edge xM. Using these
boundary conditions, we obtained the solution of Equation (1):

ð2Þ

r f f f

, a~ DTM{DTHe{mxM

T(x)~ae mx zbe {mx zT0 and m~

f f i f f i f f
gP
kA

M{DTHe{mxM,

e mxM {e {mxM

and Y~e mxM

Based on the above analysis, we obtain the relationship between
DTH, xM, and k, which can be used to measure its thermal conductivity
and analyze the light absorption ability of SWCNTs.

Thermal conductivity measurement
According to the Equation (6), the thermal conductivity of SWCNT
can be calculated based on g’, g, DTM, DTH, xM and the geometry of
tube, P and A.

As mentioned above, P is the outside perimeter of the CNT, which
transfers heat to the surroundings, and A is the cross-sectional area
of the CNT, which transfers heat along the axis of the CNT. A is

calculated in previous reports 29 . A: j pdjd~npd½djz(n{1)d�,

where n is the number of shells in the CNT, dj is the diameter of the
j-th nanotube shell, and d 5 0.335 nm is the interplanar spacing of
graphite.

For SWCNT, the upper equation reduces to A 5 pdd and P 5 pd.
The A of SWCNT also accounts for the cross-sectional area of each
shell in double-wall carbon nanotube (DWCNT) and multi-wall carbon nanotube (MWCNT) samples.

It is worth noting that although the laser power is the heat source of
the melting, we avoid measuring or calculating the transferred laser
power to the CNTs, which was proven to be difficult in previous
reports. Instead, DTH was measured and calculated based on the
heat-induced Raman G band red-shift 24, which is frequently used to
identify the temperature of carbon nano-materials. In addition, DTH
has a positive correlation with the transferred power.

The fixed melt temperature TM can be identified by directly notably
slowly increasing the temperature of the programmed stage until
the ice-CNTs structure becomes invisible again. As previously mentioned, TM 5 287 6 C, so DTM 5 13 K when T0 5 2100 6 C. Because
of the symmetrical configuration, xM can be calculated by subtracting
the calculated laser spot radius from half of the melt length, which is
measured under an optical microscope.

We characterized the atomic structure of each CNT from the
HRTEM (Figure 3a) and ED pattern 25 (Figure 3b and 3c). The
HRTEM observations indicated that the diameter of the as-grown
SWCNTs is 1–3 nm. We characterized the nanotube structure at both

b~ DT HemxM {DT M

HemxM {DT M, DT H~T H{T 0, DT M~T M{T 0

e mxM {e {mxx

The enclosed part can be expressed in Equation (3):

k d d 2 x T2

A ’P (T{T 0)~0 ð3Þ

d2T

dx 2 { g A ’P

a d

–2.22 nm 2.98 nm

10 nm 10 nm

b c

X Zhang et al

2800 3000 3200

Raman shift (cm –1 )

1588.60

1589.00

1600 1650

Ice

3400

1300

1350 1400 1450

High Intensity

Cumulative fit line
of high intensity

Low Intensity

Cumulative fit line
of low intensity

×20

1500 1550

Raman shift (cm –1 )

Figure 3. (a) High-resolution transmission electron microscopy images of two individual SWCNT with diameters of 2.22 and 2.98 nm. The wall numbers and diameter
of all samples were determined from the ED pattern and verified using the HRTEM image. (b–c) Standard and experimental ED pattern of a (21,4) nanotube. (d) D and
G bands of the Raman spectra for the (21,4) nanotube, which was excited by 514 nm laser with high and low intensity. The negligible D band at approximately
1320 cm 21 illustrates the perfect crystalline of the as-grown suspended ultra-long SWCNT. All peaks were fitted by a Lorentzian curve to distinguish the G band
frequency and heat-induced red-shift (inset). Raman spectra of the ice O-H stretching vibration mode.

higher and lower narrow slits to guarantee that nanotubes preserve its
chirality without any change in ED patterns. We further verified its
atomic structure using its Raman resonant condition based on the G
band intensity. In other words, if Elaser lies in the G band resonance
window of Eii, the G band intensity will be enormously enhanced, not
vice-versa. In addition, there are also DWCNT and bundles of
SWCNTs, of which the ED patterns come from all inner nanotubes.
Therefore, it is difficult to accurately determine the SWCNTs in
DWCNT and bundles.

In Table 1, we listed all CNT structures or chirality, and the corresponding reported Eii30 To study the light-induced melt pheno

ponding reported Eii30 To study the light-induced melt pheno
menon, we also repeated the above melt experiment using 514, 633,
and 785 nm lasers and concluded the melt condition in Table 1.

As the temperature coefficient of red-shift, av~( dv

dv

dT )100 K=v100 K,

Therefore, it is suitable to take k as a constant for each individual
CNT in our calculation.

The thermal boundary conductance (TBC) between the surface of
the CNTs and various molecules has been theoretically investigated in
several reports. Because the diameter of the SWCNT is in the nanometer scale, the TBC calculation should be based on the kinetic
theory of molecules instead of free convection or other continuum
approximations. Hu et al. simulated the TBC between a CNT and air as
0.1 mW (m 2 ?K) 21 at 1 atm 32, which is consistent with additional MD
simulations using a simple gas kinetic model. MD simulations
have predicted the TBC of a SWCNT surrounded by liquid molecules as 1.6 mW (m 2 ?K) 21 33 . Here, we use g < 0.1 mW (m 2 ?K) 21 and
g9 < 1.6 mW (m 2 ?K) 21 .

Based on the above discussion, we proposed a prototype to calculate
the thermal conductivity of each CNT and summarized the results in
Figure 4. As shown, the thermal conductivity of SWCNTs is approximately 4000 W (K?m) 21 at approximately 250 6 C in our original steps.
We attribute this appealing value to the following factors: (i) ultralong SWCNTs that are grown using the flowing mechanism have a
nearly ideal crystalline structure, which eliminates unnecessary scattering by defects; (ii) the suspended naked SWCNTs have an increase
in thermal conductivity of over 30% compared with the supported
SWCNTs because of the elimination of scattering at the substrateSWCNT interface 34 ; (iii) our method avoids difficult measurements
of the input power and thermal boundary resistance (TBR); and (iv)
possible overestimation of g’ in our ice-enclosing configuration.
Moreover, k is reported to decrease with increasing temperature
because of anharmonic interactions that produce phonon–phonon
Umklapp scattering 31 .

does not change at specific temperature. DTH can be calculated from
the G band red-shift frequency. Using this method, we can prevent
large-heat capacity objects from touching the SWCNTs for the local
temperature measurement. However, it is noteworthy that the G band
would be red-shifted when the nanotubes were wrapped in ice, which
we believe to originate from the stretch of the nanotube by the ice
gravity. To avoid the effect of ice, we first irradiated the wire with the
highest laser intensity for more than 10 min to form a steady melt.
Then, we acquired the red-shifted Raman G band signal at the identical laser intensity. After the SWCNTs cooled, the normal G band was
acquired again with a laser intensity smaller than 0.1 mW mm 22 to
avoid the thermal effects (Figure 3d). The calculated DTH of each CNT
is shown in Table 1 (the values in the parentheses). As shown in
Table 1, the temperature range of our experiments is 170–350 K, where
the value of k changes notably slowly as previously reported 31 .

X Zhang et al

Table 1. Structure property and melt condition (temperature rise) under 514, 633, and 785 nm laser irradiation in the parallelpolarization configuration

Melt length (DTH) under

Melt length (DTH) under Melt length (DTH) under

633 laser/ mm (/K) b 785 laser/ mm (/K) b

785 laser/ mm (/K) b

No. Chirality d/nm Eii/eV a

Melt length (DTH) under Melt length (DTH) under

514 laser/mm (/K) b 633 laser/ mm (/K) b

a (21,4) 1.82 0.58, 0.99, 2.09, 2.29, 3.59 4 (32) 5 (N.A.) 7 (N.A.)
b1 c (18,15) 2.24 1.23, 1.25, 2.36, 2.41, 3.36 8 (85) 10 (N.A.) 18 (N.A.)
b2 c (18,15) 2.24 1.23, 1.25, 2.36, 2.41, 3.36 6 (46) 4 (N.A.) 14 (N.A.)
c1 c (18,15) 2.24 1.23, 1.25, 2.36, 2.41, 3.36 13 (170) 7 (N.A.) 18 (N.A.)
c2 c (18,15) 2.24 1.23, 1.25, 2.36, 2.41, 3.36 12 (165) 4 (N.A.) 14 (N.A.)

d (29,13) 2.91 0.36, 0.68, 1.29, 1.64, 2.13, 2.56 6 (45) 10 (24) 20 (N.A.)

e (24,20) 2.98 0.36, 0.66, 1.27, 1.57, 2.12, 2.43 7 (29) 7 (N.A.) 19 (310)
f e (37,15) 3.68 7 (32) 10 (3) 11 (85)
Bundle-a Bundle of 2 SWCNT,4.0 f 5 (28) 3 (N.A.) 23 (N.A.)
Bundle-b Bundle of 2 SWCNT,4.4 f 12 (63) 13 (66) 13 (157) d

DWCNT-a DWCNT,1.5 f 10 (47) 7 (N.A.) 13 (N.A.)

a Eii (lists from E11 to E55 or E66) of each SWCNT is applied to room temperature.30

b The numbers outside the parentheses are the melt lengths, which were measured under an optical microscope. The numbers in parentheses are the relative temperature
increase of the CNT at the margin of the laser spot. DTH values that are expressed as N.A. cannot be acquired because the G band does not resonate with the photon energy. All
melt length and temperature increase data are the average results of repeated melt and measurements.
c c1 and c2 come from one identical ultra-long SWCNT but different optical slits. The same is true for d1 and d2.
d Operated at 2120 6C.
e This SWCNT’s diameter is so large that we have not found its Eii value in previous reports.
f Outer diameter of the DWCNT or bundles under HRTEM.

Another controversial thermal conductivity factor is its diameter
dependence. In Figure 4, we can see that k tends to increase with the
increase in SWCNT diameter in our prepared samples, which coincides with new theory reports 34,35 (the diameter-dependent thermal
conductivity difference is mainly because of the curvature-induced
phonon relaxation time shortening 34, or it is attributed to the presence
of additional low- and moderate-frequency radial breathing modes in
larger-diameter nanotubes 35 ).

It is noteworthy that for DWCNT and SWCNT bundles, whose ED
patterns come from all inner nanotubes, an accurate determination of
all SWCNT indices is difficult. Without an accurate estimation of the
cross-sectional area and surface area of these CNTs, the thermal con

6,000

514
785

5,500

5,000

4,500

4,000

3,500

3,000

2,500

2,000
1.6 2.0

2.4 2.8 3.2

Diameter (nm)

3.6 4.0 4.4

ductivity cannot be derived. Further elaborate experiments are in
progress.

Because the diameter of the prepared SWCNT is confined between
1.8 and 4.0 nm, and the number of samples is limited, a more comprehensive conclusion could only be made based on extra elaborate
experiments, particularly considering the following extra points:

Unlike previously reported methods, the ice melt strategy with
inferred temperature from the Raman shift can reflect the inherent
thermal response, which suppresses the measurement disturbance. In
addition, the tough measurement or calculation of the transferred
power of laser to CNT is avoided. Therefore, we suggest that this
prototype can be facile to verify the intrinsic thermal property of
nanotubes and lead to a more convincing result.

Furthermore, the melt distances may fluctuate during repeated melt
experiments. This deviation of the melt distance originates from (i) the
thickness difference of ice and (ii) the focus condition of the Gaussian
profile laser beam on the core-shell structure. Although this deviation
obstructs the assessment of the CNT absorption ability to some extent,
it will exert a negligible effect on the calculation of the thermal conductivity because the temperature of the SWCNT changes with the
melt distance, i.e., the self-adjusting property. In fact, a bad focus
condition can hardly be observed because of the visualization of iceCNTs structure.

We must admit that the proposed prototype to measure k is an
initial attempt, and there are some aspects to be improved. First, we
may use other volatile materials to replace ice to form a more controllable and thinner shell structure around 1D materials. Even the cryogenic environment can also be avoided. By adopting other volatile
materials, we can also enlarge the melt length by performing the measurement in vacuum 36 ; thus, the length measurement error can be
reduced. Furthermore, because the deviation of k mainly comes from
the error of DTH, the results will fluctuate less when the CNT reaches a
higher DTH (200–400 K is preferred). To attain this goal, a laser with
higher power is essential. It is predicted that this method can also be
used with other 1D nanomaterials.

Figure 4. Calculated thermal conductivity of each CNT vs. diameter. The different k of c1, c2, b1, and b2 under different lasers are within the measurement
uncertainties.

Resonant and non-resonant absorption
In recent years, significant studies have been conducted using CNTs
for broadband absorber coatings 37 . Previous theories and experiments demonstrated that optical transitions in SWCNTs arise from
excitons with strong binding energy instead of free electrons and holes.
Each of these optical resonances can be referred to as Sij or Mij depending on the nature of the nanotube (S for semiconducting and M for
metallic) and the corresponding valence (i) and conduction (j) subbands. When the incident light polarizes in parallel to the nanotube
axis, transitions occur between the sub-bands with i 5 j, and crosspolarized light addresses the transitions between sub-bands with

ji{jj~1. After the optical transition, the energy of the exciton is
efficiently transferred to the crystal lattice through strong electron–
phonon interactions, which increases the temperature of the
SWCNT 15 . It is noteworthy that although the listed Eii value in
Table 1 is applied at room temperature, Eii only increases by approximately 0.05 eV from room temperature to 2100 6 C 38, which has little
effect on the resonant condition.

As observed from the vertical-polarization melt experiment, there
was nearly no absorption when the laser polarization was perpendicular to the CNT axis. As recently reported 12,13, the perpendicular-polarization absolute absorption cross-sectional spectra show
small and finite perpendicular absorption (approximately 1/4 13 or
,1/10 12 of parallel polarization one), and they are largely featureless 13 . However, the parallel-polarization spectra show prominent
and different exciton transition peaks, which provide rich information on chirality-dependent nanotube photophysics. Our results
verified this conclusion in a thermal response method for the first
time. In particular, the difficult signal collection because of the
small cross section of the SWCNT can be avoided.

For the parallel-polarization configuration, the resonant SWCNT
tended to melt longer with higher DTH. We attributed this phenomenon to the larger absorption cross section when the photon energy
matched the gap between Van Hove singularities of the Density of
State, which is one of the reasons why identical nanotubes have different melt lengths under 514, 633, and 785 nm laser. However, the ice
also melted when the non-resonant absorption occurred, which
resulted from the continuum absorption (including band-to-band
transitions, phonon sidebands and higher-order exciton transition).
This non-resonant absorption is similar to graphene’s universal
absorption of approximately 2.3% in the visible and near-infrared
range 39 . Furthermore, we note that this continuum absorption constitutes a significant portion of the total nanotube absorption oscillator strength, which was recently appreciated 13 . However, as shown in
Table 1, the effect of the nanotube diameter on the heating length is
not obvious. Moreover, we did not notice any obvious difference in
either resonant or non-resonant absorption between metallic and
semiconducting SWCNTs.

The use of laser light to manipulate SWCNTs is an attractive challenge 40 . Because the photons directly access the electronic energy
structures of SWCNTs in a resonant manner, it may be possible to
selectively manipulate SWCNTs based on their chirality. According to
our results, to reduce the portion of metallic SWCNTs in a mixed
sample, we should consider two factors: (i) a proper laser photon
energy that matches the resonant absorption metallic SWCNTs
instead of semiconducting SWCNTs and (ii) an appropriate gas and
temperature that are conducive to make metallic SWCNTs susceptible
to oxidation 18 .

X Zhang et al

CONCLUSIONS
In summary, the facile and reversible optical visualization of individual suspended ultra-long SWCNTs was realized by wrapping
them with ice in a cryogenic air environment. When this core-shell
structure is irradiated with a high-power laser, the heated SWCNTs
melt the ice around it. By modeling this process and regarding ice as
a temperature sensor, a link among the melt length, rising temperature and thermal conductivity is established. With the calculated
temperature increase based on the Raman red-shift, our prototype
indicates that the intrinsic thermal conductivity of these perfect
crystalline SWCNTs is approximately 4000 W (K?m) 21 . Based on
the identified CNT’s structure and chirality with HDTEM and ED,
we find that k tends to grow with the increase in the SWCNT
diameter. Moreover, we also provide a perspective to further
improve our prototype. Finally, the thermal response evidence of
tiny absorption cross section of SWCNTs in the vertical-polarization
configuration and the significant non-resonant absorption in the
parallel-polarization configuration were discussed. The prototype
shown here can also be used with other 1D nanomaterials to provide
new insight into the unique fundamental comprehension of light–
matter interaction in quasi 1D nanomaterials and enable the absolute determination of their thermal properties.

ACKNOWLEDGEMENTS
This work was supported by the National Basic Research Program of China
(Grant Nos. 2012CB932302, 2014CB848900), National Natural Science
Foundation of China (U1232131, 90921012, 51172271, 51372269 and
11375198), ‘‘Strategic Priority Research Program’’ of the Chinese Academy
of Sciences (XDA09040202), Beijing Municipal Education Commission
(Grant No. YB20108000101), and Fundamental Research Funds for the
Central Universities (WK2310000035). Li Song thanks the recruitment
program of global experts and the CAS Hundred Talent Program of China.
The authors thank M. Habib from University of Science and Technology of
China for his useful discussion.

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