Journal of Minerals and Materials Characterization and Engineering, 2012, 11, 961-964
Published Online October 2012 (
Optimization of Electrical Parameters for Produc tion of
Carbon Nanotubes
Sayantan Chattopadhyay, Kalyan Kumar Singh
Department of Mechanical Engineering & Mining Machinery Engineering Indian School of Mines (ISM), Dhanbad, India
Received July 20, 2012; revised August 22, 2012; accepted August 30, 2012
For more than two decades, there had been extensive research on the production of carbon nanotubes (CNT) and opti-
mization of its manufacture for the industrial applications. It is believed that they are the strong enough but most flexi-
ble materials known to mankind. They have potential to take part in new nanofabricated materials. It is known that,
carbon nanotubes could behave as the ultimate one-dimensional material with remarkable mechanical properties. More-
over, carbon nanotubes exhibit strong electrical and thermal conducting properties. In the process of optimizing the
production in line with the industrial application, the researchers have found a new material to act as an anode i.e. coal,
which is inexpensive as compared to graphite. There are various methods such as arc discharge, laser ablation, chemical
vapour deposition (CVD), template-directed synthesis and the use of the growth of CNTs in the presence of catalyst
particles. The production of carbon nanotubes in large quantities is possible with inexpensive coal as the starting carbon
source by the arc discharge technique. It is found that a large amount of carbon nanotubes of good quality can be ob-
tained in the cathode deposits in which carbon nanotubes are present in nest-like bundles. This paper primarily concen-
trates on the optimising such parameters related to the mass production of the product. It has been shown through Sim-
plex process that based on the cost of the SWNT obtained by the arc discharge technique, the voltage and the current
should lie in the range of 30 - 42 V and 49 - 66 A respectively. Any combination above the given values will lead to a
power consumption cost beyond the final product cost, in turn leading to infeasibility of the process.
Keywords: Coal; Carbon Nanotubes; SWCNT; Simplex; Optimization
1. Introduction
In 1985, Drexler proposed a molecular bearing consisting
of two graphitic nanotubes of different diameter, which
are concentrically arranged. It was a virtual operation
inside a computer. This dream, however, has become
more realistic by the discovery of carbon nanotubes.
There had been revolutionizing researches on the pro-
duction of Carbon Nanotubes from last twenty years and
optimising its manufacture for the industrial applications.
It has been thought that they are the strongest but most
agile materials known to humankind, and thus have po-
tential to take part in new nanofabricated materials as
additives. It has been shown that carbon nanotubes could
behave as the ultimate one-dimensional material with
remarkable mechanical properties. Carbon nanotubes ex-
hibit strong electrical and thermal conducting properties.
Study of the past researches on the production of carbon
nanotubes from coal revealed that most of the researches
concentrate on producing CNT by arcing electrodes,
produced separately by mixing the crushed coal with coal
tar followed by molding process. However, the only
process till date that has shown a positive adaptation to
direct coal application is thermal plasma jet technique.
With the extensive research in the production of the
Carbon Nanotubes, the requirement of optimising the
process parameters are realised. This paper concentrates
on the optimising such parameters related to the mass
production of the product. It has been found through cal-
culation that the only determining parameter in the arc
discharge technique is the power of the equipment, in
terms of voltage and current, and it is seen that on opti-
misation of these parameters, the cost of the process re-
duces drastically.
2. CNT Production through Arc Discharge
Carbon nanotubes (CNTs) have been used in various
fields of research due to their unique properties. There
are various methods such as arc discharge, laser ablation,
chemical vapour deposition (CVD), template-directed
synthesis and the use of the growth of CNTs in the pre-
sence of catalyst particles [1]. Special ambient gas is re-
quired for the fabrication of CNTs, in order to prevent
the oxidation of carbon at high temperature.
Copyright © 2012 SciRes. JMMCE
The production of carbon nanotubes in large quantities
and other nanomaterials as by-products is possible with
inexpensive coal as the starting carbon source by the arc
discharge technique [2,3]. It has been found that a large
amount of carbon nanotubes of good quality can be ob-
tained in the cathode deposits in which carbon nanotubes
are present in nest-like bundles. In the past decades, vari-
ous alternate synthesis strategies and methods have been
explored and developed in the hope of mass-producing
cheap and high quality Single-walled carbon nanotubes
(SWNT). Compared to other methods, the arc discharge
is the simplest, cheapest and easy to implement and it has
been used because of its potential merits to make a mas-
sive production. The mineral matter in raw coals may
also play an important part in the formation process of
carbon nanotubes. An approach of production of Single-
walled carbon nanotubes (SWNT) had been adopted in
2004 [4] where the coal is crushed and sieved with 150
µm mesh and mixed with coal tar and molded to form
coal rods used for anode with a graphite cathode for the
arc discharge process. Similar approach had been made
by the same researchers for the production of Double-
walled carbon nanotubes (DWNTs) which were synthe-
sized from coal in large quantity by arc-discharge me-
thod in hydrogen-free atmosphere [5], and was system-
atically examined using scanning electron microscopy,
transmission electron microscopy, high-resolution trans-
mission electron microscopy and Raman spectroscopy. In
the case of coal-derived carbons, the breaking-up scheme
involved in the arc-discharge process significantly differs
from that of graphite because of the striking difference in
their textures. Coal or coal-derived carbons feature mac-
romolecular structures rather than the lattice structure of
graphite. In their chemical structures there exist many
weak binding linkages between carbon polymeric units
such as polymerized aryl structures. In the fast paralyses
process under arc plasma conditions, these weak linkages
would be broken up rather easily to release a variety of
reactive fragments of hydrocarbon molecules such as
alkynes and aromatic species. However, the production
of SWNTs has seen a typical use of an iron wire mesh
utilised between the electrodes and the carbonaceous
matter is found on the wire mesh.
A possibility of the production of carbon nanotubes
from heavy hydrocarbon resources had been proposed in
2008 [6]. Before the use of heavy hydrocarbons, pure
compound, toluene was used as the pure substrate to es-
tablish the reaction system for the production of carbon
nanotubes. Toluene was fed by a mist-spray feeding sys-
tem with a carrier gas as 9:1 mixture of nitrogen and hy-
drogen at 100 ml/min, and following the reaction at
750˚C catalysed by 9.8% (by weight) ferrocene, Carbon
nanotubes were found in the carbonaceous product de-
posited on inner wall of a quartz tube and at the exit of
the tube. The product was observed by scanning electron
microscopy and analyzed by temperature-programmed
oxidation experiments to identify the presence of carbon
nanotubes. Based on the reaction system and reaction
conditions with toluene, the production of nanotubes was
examined by using heavy hydrocarbons such as asphalt-
tene and maltene fractions from natural asphalt. Under
selected reaction conditions including the reaction tem-
perature and the amount of the catalyst, carbon nanotubes
with a diameter of 30 - 60 nm were found.
3. Optimisation of Voltage and Current Used
in the Carbon Nanotube Production
It is known that Voltage and Current constitute the Power
requirements for an electrically operated machine. Same
in the case of the production of CNT from the arc dis-
charge method, the electrical power signifies the charac-
teristics of the arc that is generated between the two elec-
trodes, in this case, one coal-based and the other, graph-
ite. For the optimisation process, the total cost of the input
materials must be lesser than that of the output product.
It is seen from the past experimental research works
[2,3,7-9], the work has been done on Bituminous and
An- thracite coal samples. From the domestic coal, cost
fixed by Coal India Ltd. the coal costs are as stated in
Table 1.
For Anthracite and Bituminous coal, we choose Grade
B and F respectively [10]. Therefore, the cost would be
Rs.3590 per tonne and Rs.1130 per tonne respectively, if
we take the maximum cost of the above grades from dif-
ferent companies, from the Table 1.
The coal-based electrode specifications for the arc dis-
charge process are found from the experimental works in
the past. With the aim of the maximum cost involved in
the production of the coal-based electrode, the electrode
with maximum volume is selected, as it is the electrode
that involves the maximum amount of coal and thus the
cost. Out of the several independent researches the speci-
fication of diameter 10 mm and length 200 mm is chosen
as it gives the maximum volume as compared to the
other electrodes in the other researches.
Therefore, electrode volume = 22
dl 
20015707 mm1.5710m
 2
Bank density of coal is 1346 kg/m3
So, Bank Weight of the powdered coal used = 1.57
101346 0.021
Maximum Cost of the coal is taken to be Rs.3.5/kg
Therefore, Cost of the coal used = 3.5 × 0.021 = 0.073
The cost of power is to be calculated next. In a typical
experiment [9], the current was taken to be 100 A and the
voltage was taken to be 36 V.
Therefore, Power = V × I = 30 × 100 = 3000 W = 3
Copyright © 2012 SciRes. JMMCE
Table 1. Basic price of run of mine non-long-flame non-
coking coal [11].
Cost of grades of coal in rupees/tonne
Field/Co. A B C D E F G
ECL 3690 3590 1680 1350 1010 790560
Mugma 3690 3590 1950 1610 1290 960620
ahal - - - - 1330 1130910
BCCL 3690 3590 1630 1350 1080 860610
CCL 3690 3590 1590 1300 1030 820590
NCL 3690 3590 1430 1200 960 750560
SECL 3690 3590 1370 1140 950 740560
MCL 3690 3590 1370 1140 950 740560
(A—Graphite/high quality anthracite; B—Anthracite (C:H > 30); C—An-
thracite (C:H ~ 26 - 30); D—Semi-anthracite; E—Semi-bituminous; F—
Bituminous; G—Low quality bituminous).
Table 2. Carbon nanotube price list [12].
(gram) High purity*
Arc CNT*
($) High purity* ($)
1 210 83 210
10 1600 700 1600
50 6850 3050 6850
100 12400 5500 12400
500 Call Call Call
1000 Call Call Call
*The High Purity CNT (more than 90% pure) is not achievable by Arc
Discharge Method, as per different researches, and thus the cost of the Arc
CNT, made from Arc Discharge Method, is always less than the former.
However, DWNTs are not the common by-product from the Arc Discharge
The rate of anode feed in the experiment is taken to be
10mm for 2 hrs. The length of the electrode in the ex-
periment is 75 mm. So, the total experiment time equals
15 hrs. For that time the 45 units of electricity is con-
sumed (1 KWhr = 1unit of consumed electricity).
As per the regulations of Calcutta Electricity Supply
Corporation (CESC), the rate is Rs.2.7/unit for the first
25 units consumed, then at the rate of Rs.3.3/unit for the
next 35 units.
Therefore, Total cost = 25 2.720 3.3
  Rs.133.5
So, the total input cost for the production of CNT is
Rs.133.5 (neglecting the cost of coal as too small as
compared to the power consumption cost)
Now, the cost of the Carbon Nanotubes as per stan-
dards are stated in Table 2.
The amount of CNT produced in experiment is about
20mg [9]. The cost above is given in $, so we consider
1$ = Rs 50 and the package unit is in grams.
Thus, the total cost comes to be 20 83 50
 
Therefore, it can be understood that as the input cost is
greater than the output cost, optimisation is essential in
this case.
Optimising the Power
Power = PVI
loglog logPVI
Taking, logP = x1; logV = x2; logI = x3
In all the experiments minimum voltage and current
are taken as 30 V and 50 A respectively.
log1.47, log1.69VI
1.47, 1.69xx
Therefore, 1232 3
1.47,1.6,9xxxx x
 
Considering the power consumption rate as 2.7/unit,
The total power can be calculated as 15 × 2.7 × P =
40.5 P
For optimum result,
40.5 83P
83 2.05 KW2050 W
log 3.31P
Applying Simplex Algorithm,
Min 3
Subjected to the constraints,
Solving by graphical method, we get the following
plotted and shown in Figure 1.
We plot the graph by taking equalities for the above
The arrows shown on the particular line denoted the
lesser-than-equal-to and greater-than-equal-to zone for
the particular constraint line. The area enclosed by the
three constraint lines gives the range of feasibility of the
Therefore, we can conclude that, the enclosed region
Copyright © 2012 SciRes. JMMCE
Copyright © 2012 SciRes. JMMCE
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Figure 1. Solution graph of simplex optimisation process.
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with the three lines, fit the feasible solution range.
Max 1.62
Max 1.82
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The optimal range of the voltage and current can be
defined as (by antilog of the results obtained):
29.5 ~41.68V
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4. Summary and Future Trends
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Vol. 81, No. 1, 2002, pp. 5-14.
An optimisation of the main process parameters i.e. vol-
tage and current, pertaining to the arc discharge process
discussed in the paper. The result focuses on the feasible
and optimum range of the parameters, based on the cost
of the SWNT obtained as the product. It can be certainly
perceived through calculation that if the voltage or the
current cross the optimal range, the power consumption
is increased and thus, the input cost is aggravated result-
ing in infeasibility of the production line.
[9] K. A. Williams, M. Tachibana, J. L. Allen, L. Grigorian,
S. C. Cheng, S. L. Fang, G. U. Sumanasekera, A. L.
Loper, J. H. Williams and P. C. Eklund, “Single-wall
Carbon Nanotubes from Coal,” Chemical Physics Letters,
Vol. 310, No. 1-2, 1999, pp. 31-37.
[10] M. S. Krishnan “Classification of Coal,” Geological Sur-
vey of India, Vol. 4, No.3, 1940, p. 552.
However, still more scopes remain, as the major as-
sumptions viz. the cost of power consumption is only
confined to the unit power consumption cost fixed by
CESC, can be made universal by programming the algo-
rithm mentioned above, and a detailed analysis of the
optimization by various other processes may lead to
many valuable information in this virgin field.
[11] “Domestic Coal Price Fixation,” Coal India Ltd., 2011.