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Synthesis and Characterization of Single-Walled Carbon Nanotubes

Derek Pulhamus, Gregory Savich, Krishanu Shome, Josh Winans

Abstract: Single-walled carbon nanotubes (SWNTs) are being used to expand and enhance

many of today’s current technological capabilities. SWNTs were grown using chemical

vapor deposition (CVD) and then characterized with resonant confocal micro-Raman

spectroscopy. A unique chirality assignment was made for each semiconducting SWNT

found.

I. Introduction

A single layer of carbon atoms bound together in a hexagonal pattern is defined as a sheet

of graphene. When a section of this material is rolled into a seamless tubular shape it becomes

known as a single-walled carbon nanotube. If two or more layers of stacked graphene are rolled

we have a multi-walled carbon nanotube (MWNT). As we’ll see, the orientation with which the

graphene is rolled to form the SWNT will have an important effect on the tube’s electrical

properties. It is just these electrical properties that make SWNTs such an interesting focus of

research.

MWNTs were discovered over fifty years ago [1], but for a multitude of reasons they

went largely unnoticed by the greater scientific community [2]. Except for a small subset

seeking to eliminate them from coolant channels in nuclear reactors, no one cared about carbon

nanotubes. Not until 1991, even though multiple publications on the subject had preceded them,

did the “discovery” of MWNTs make a significant impact on the research community. With a

newfound fervor researchers delved into the subject of carbon nanotubes and by 1993 we had the

first discoveries of SWNTs [3,4]. (Ironically both teams made their discoveries by failing to

create MWNTs filled with transition metals.) Regardless of discussions about who-did-what, no

one disputes the potential for SWNTs to have a huge impact on current technology because of

their highly unique properties.

SWNTs have diameters on the order of 1 nm while their lengths can span into the

millimeters. Depending on the exact structure of the tube it can act as metal or a semiconductor.

Some basic properties being exulted by those interested in the field of carbon nanotubes include

a tensile strength at least 22 times higher than steel alloys, a density twice as low as aluminum,

predicted heat transmission values nearly two times that of pure diamond, a current carrying

capacity one thousand times greater than copper and the potential for ballistic electron transfer.

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Excitement over these potentially revolutionary properties must be tempered by a cost roughly

150 times that of gold [5]. Price not withstanding, research continues into possible applications

such as ultracapacitors [6], hydrogen and ion storage, nanotube tipped atomic force microscopes,

enhanced scanning probe microscopes, nanotweezers, displays, and yes, even tennis racquets.

II. Physical Properties of SWNTs

As previously stated, a SWNT is a single layer of graphite rolled up into a hollow

cylinder. The microscopic structure of the nanotubes is closely related with graphene, and hence

is labeled in terms of graphene lattice vectors [7]. Fig 1 shows the honeycomb lattice of

graphene. The vector c connects two crystallographically equivalent sites, each of which is a

carbon atom located at vertices of the honeycomb structure. The carbon nanotubes are rolled up

along this vector given by c=na1+ma2, where n and m are integers and a1 and a2 are the primitive

lattice vectors. The rolling takes place in such a way that c becomes the circumferential vector

of that particular tube. This vector, usually defined in terms of integers (n,m), is called the chiral

vector and uniquely defines the diameter and chirality of a particular tube. Properties such as

band structure or spatial symmetry group depend strongly on this chiral vector. The direction of

the chiral vector is measured by the chiral angle θ, this is the angle between a1 and the chiral

vector c. The chiral angle can be derived from the following expression,

cos θ = a1.c/a1|.|c|=(n + m/2)/√(n2+nm+m

2) (1)

Fig 1: Honeycomb lattice of Graphene with the chiral vector shown[7]

c

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There are two kinds of tubes that have mirror symmetry, one is the zigzag nanotubes with

indices (n,0), the other is the armchair nanotubes with indices (n,n). All other nanotubes are

called chiral nanotubes and have axial symmetry. The zigzag, armchair and chiral nanotubes

have chiral angles corresponding to θ =0o, θ =30

o and 0

o≤|θ |≤30

o respectively.

The diameter of a (n,m) nanotube, d, is given by

d= a0 √(n2+nm+m

2)/π (2)

where a0 is length of the basis vector |a1| = |a2| = a0 = 2.461 Å for graphene.

The smallest graphene lattice vector perpendicular to c, which defines the translation

period of distance a along axis of the tube as shown in the Fig. 2 is defined as a. This translation

period a can be determined from the chiral indices (n.m) as [8]

a = a0√3(n2+nm+m

2) / nR, (3)

where R=3 if (n-m)/3n is integer and R=1 otherwise.

Fig 2: Translation vector for armchair,zigzag and chiral Nanotubes[8]

III. Electronic Properties of Single-Walled Carbon Nanotubes

The one-dimensional (1D) electronic density of states is given by the energy dispersion

of carbon nanotubes. This energy dispersion is obtained by zone folding of the two-dimensional

(2D) energy dispersion relations of graphite. Here the σ bonds are not critical because they are

far away from the Fermi level. In contrast, the bonding and anti bonding π bonds cross the Fermi

level at the K point as in Fig 3. They make graphene and one third of the SWNT's metallic or

quasi metallic.

To construct the Brillouin zone of SWNT we consider the Brillouin zone of graphene as

shown in Fig 3. In the direction of tube axis which is defined as z axis, the reciprocal lattice

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vector kz corresponds to the translation period a, with its period given by

kz = 2π / a. (4)

When the tube is regarded to be infinitely long then the electronic states along the kz direction are

Bloch functions as in 3D crystals. Along the circumference c of the tube, the allowed wave

vectors are quantized. The quantized wave vectors k┴ and the reciprocal lattice vector kz can be

found from the conditions

k┴ . c = 2π k┴ . a = 0 (5)

where k┴,p=(2 / d). p, with p being an integer.

These periodic boundary conditions for a SWNT with (n,m) indices gives N discrete lines

of length 2π/a and distance 2/d parallel to the z axis. Here N denotes the number of hexagons in

the graphite honeycomb lattice that lie within the nanotube unit cell and is given by,

N= √2 (n2+nm+m

2)/d. (6)

These lines are plotted onto the Brillouin zone of graphene as shown in Fig 4. This approach is

called zone folding.

Fig 4: The wave vector for 1D SWNT is shown in the 2D Brillouin zone of graphite (hexagon),

(a) and (b) corresponds to metallic and semiconducting case respectively[9].

Fig 3: The energy dispersion relations for 2D graphite. The inset shows the energy

dispersion along the high symmetry line between the Γ, M and K points[9].

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For a particular (n,m) nanotube, if the cutting line passes through the K point of the 2D

Brillouin Zone, then the 1D energy bands have a zero energy gap. Since this degenerate point

corresponds to the Fermi energy, and the density of states are finite, the SWNTs with zero band

gap are metallic. When the K point is located one-third of the distance between two adjacent kz

lines, then a finite energy gap appears resulting in a semiconductor tube. Therefore, for a

nanotube to be metallic it must satisfy n-m=3q, where q is an integer [10].

The density of states (DOS) is a critical quantity which comes up when one studies the

application of the electronic properties. The DOS depends inversely on |∂E/∂kz| [11] near the

Fermi level. So the DOS becomes large when the energy dispersion relation becomes flat as a

function of k, as is shown in Fig 5.

Fig 5: Dispersion relations (left) for the 1D electronic bands and the corresponding DOS (right) of metallic (a), and semiconducting (b), single-

walled carbon nanotubes close to Fermi energy.[12]

IV. Resonant Raman Spectroscopy

Vibrational spectroscopy can be used to find specific properties of the SWNTs like tube

diameter, tube orientation and identification of whether the tube is metallic or semi-conducting in

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nature. SWNTs have a large Raman signal even for single tubes. Resonant confocal micro

Raman spectroscopy (RCMRS) not only provides a wealth of information it is also a noncontact,

nondestructive in situ method.

Confinement of electrons along the radial direction, results in spikes at the DOS. These

spikes are called Van Hove's singularities. When the energy of the incident light matches exactly

the energy difference between spikes, Raman scattering becomes a resonant process.

A Raman spectrum of SWNTs is generally divided into different bands, as shown in Fig

6. The first one corresponds to the radial breathing mode (RBM). The out of plane translation,

an acoustic mode in graphene, transforms into the RBM in carbon nanotubes with nonzero

frequency at the Γ point. This line is not present in graphite, yet much of the experimental

information about the properties of the SWNT originates from this line. All the carbon atoms in

the nanotube move in phase in the radial direction creating a breathing like vibration of the entire

tube. The forces needed for a radial deformation of a nanotube increases as the diameter

decreases as

ωRBM = C1 / d, (7)

where C1= 248 cm-1

[13]. This equation can be used to measure the diameter of the tube.

The second important band is the Tangential Mode (TM) or the G mode. It is also sometimes

called the high energy band. This mode corresponds to the stretching modes in the Graphite

plane. Other than this, the Defect mode or D mode is also present. It originates from defect

induced double-resonant Raman scattering, which involves phonons from the graphite K-point

and lies between 1200 cm-1

and 1400 cm-1

. This D mode shifts with energy of the exciting laser.

The presence of the RBM clearly indicates carbon nanotubes while the occurrence of multiple

peaks at the G band confirms the existence of a SWNT.

Fig 6 : Raman spectrum of a SWNT [8]

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V. Growth

The carbon nanotubes characterized in this experiment are grown using chemical vapor

deposition (CVD) (Fig 7). The process begins with a CVD catalyst consisting of 60 mg of

Iron(III)nitrate nonahydrate (FeNO3), 60 mg bis(acetylacetonato)-dioxomolybdenum(VI)

(Mo[acat]), and 10 mg of aluminum oxide (Al2O3) nanopowder. These solids are dissolved in

10mL acetone and allowed to evaporate overnight. 10mL of water is then added to the dried

catalyst. 300 L of this solution is diluted with 10 mL of water and finally .5mL of this solution

is dropped onto a quartz cover slip being spun at 3000 RPM.

Next, the quartz slip is placed into the furnace, which is then evacuated to 10-5

mbar to

purge out the system. The sample is then heated in the vacuum for 20 minutes at 750˚C. Next,

the rotary pump is turned on and the turbo pump turned off to achieve a pressure of 10 mbar in

the chamber. After opening the butterfly valve, hydrogen gas (H2) is allowed to flow at 200 sccm

for 10 minutes. The furnace is turned up to 1005˚C and placed at position B (1 meter from the

sample) for 25 minutes. Next, the butterfly valve position is adjusted to change the chamber

pressure to 7 mbar. At this point ethanol is allowed to flow into the chamber while the hydrogen

gas is turned off. The furnace is then set to 915˚C and moved to its original position for 10

minutes. By flowing hydrocarbons over the heated molybdenum catalyst we can disassociate the

ethanol vapor passed over the slip. The metal nanoparticles in the catalyst then become saturated

with the free carbon. Precipitation of carbon from the saturated metal nanoparticles form into

nanotubes on the surface of the catalyst. The carbon forms into tubular structures rather than

other structures (such as sheets) because it takes less energy. Now that the nanotubes have

grown, the ethanol flow is stopped and the butterfly valve closed. The pressure is then adjusted

to 10-2

mbar using turbo pump. Since the growth is over, the furnace is turned off then vented to

allow airflow to the sample. The nanotubes now need at least three hours to cool before they can

be characterized. After cooling the sample, the nanotubes that grew over the catalyst drop onto

the cover slip [12].

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Fig 7 : Schematic of CVD Growth Apparatus.

VI. Characterization

Fig. 8 represents the experimental setup used to locate and characterize SWNTs. Laser

light of wavelength 785nm is used to excite the sample. Scattered light from the sample is

initially passed through to the avalanche photodiode (APD) recording the G band intensity, to get

a comparatively broad field of view. Once the nanotubes are identified, then the Raman spectra

are taken by the spectrograph.

Fig 8 : Experimental setup for characterization of SWNTs

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VII. Data and Analysis

After the nanotube sample was processed, two portions of the sample were investigated in the

characterization test bed. Each area considered was a 40μm square. Fig 9 shows a broad image

of each area investigated.

(a) (b)

Fig 9: Broad area image of nanotube sample for both region one (a) and region two (b). Both images are 40μm by 40μm in area.

The carbon nanotubes that are resonant at the laser excitation wavelength are scattered among

the bright regions of the images. The circled regions contain nanotubes that were studied and

characterized. There are many other nanotubes in these two regions alone, but not every bright

spot is a resonant nanotube. Many of the bright regions are deposits of amorphous carbon. It is

important to note that the nanotubes that show up on the images are not the only carbon tubes in

these regions. In fact these tubes are not nearly the majority of those found on the sample. Only

tubes that are resonant at the excitation wavelength and are oriented in the proper direction with

respect to the polarization of the laser light are seen on the sample. As the tubes do not grow

perfectly straight, it is likely that the bright regions identified as carbon nanotubes do not

represent the total length of these tubes, but rather the length of the tube that is positioned in the

proper orientation. Fig 10 shows two close-up images of nanotubes in the first region.

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(a) (b)

Fig 10: Close-up image of example nanotubes. Nanotube two (a) and nanotube three (b). Each image encompasses an area of 5μm by 5μm.

Each image encompasses an area 5μm by 5μm. The spectra of the tubes were taken near the

center of the bright regions. From these spectra the RBM frequency can be measured. Fig 11

shows the spectra of the nanotubes shown in Fig 10.

(a) (b)

Figure 11: Spectra of nanotube two (a) and nanotube three (b).

The RBM frequency is represented by the highest intensity peak in both cases. In inverse

centimeters, the frequency peaks of nanotubes two and three are found to be 12510.41cm-1

and

12520.35cm-1

respectively. Following the work of Jorio et. al [13], we can relate this to the

ωRBM frequency, and then determine the diameter of each nanotube, dt, using equation (7).

This empirical formula allows the characterization of nanotubes excited at a wavelength of

785nm, the wavelength used in our experiment. From the calculated values for the tube

diameter, we can determine the likely chiralities of the tubes in question [13]. Once the values

for n and m are determined, it is easy to determine the translation vector and other general

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properties of the nanotubes. Table 1 shows the ωRBM and calculated parameters for nine

nanotubes studied.

All of the nanotubes we characterized were of the semiconducting variety, although metallic

tubes could have been a possibility [14]. Also, note that we only found tubes with chiral vectors

(11,4), (14,1), and (14,2) rather than a random assortment of different tubes. This means that the

growth process was consistent and well controlled.

VIII. Conclusion

Carbon nanotubes are an increasingly prevalent topic of research and have many potential

future as well as current applications. This study focused on the growth and characterization of

SWNTs. Using CVD SWNTs of a variety of chiralities were grown. These SWNTs were

characterized with Raman Spectroscopy to take advantage of their inherent resonances.

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