Download ENERGY BALANCE OF DC ARC DISCHARGE WITH CLOSELY

OPTICS
ENERGY BALANCE OF DC ARC DISCHARGE
WITH CLOSELY SITUATED ELECTRODES*
N. KOPRINAROV, M. KONSTANTINOVA
72 Tzarigradsko shose, 1784 – Sofia, Bulgaria
E-mail: [email protected]
Received September 14, 2010
Arc discharge is commonly used for producing carbon nanostructures. Geometry
of electrodes, the distance between them and ambient temperature are important factors,
which determine the quantity and the variety of the formed carbon structures. Usually,
two electrodes of different cross-sections (i.e. a thin anode and a thick cathode) are
placed far away from each other, allowing a large vapour stream to be obtained, which
then creates the nanostructures in the working chamber. However, if the two electrodes
were placed closely together, carbon vapour would leave deposits on the cathode. These
deposits consist of amorphous carbon and low quantities of carbon nanotubes. The later
approach has not been widely studied although it has potential to be used for film
depositions. The goal of this study is to understand how the distance between the
electrodes influences the temperature and to determine the underlying processes, as
well. Energy balance has been determined for two electrodes of equal cross-sections of
7.5 mm2. The experimental data needed for the calculation has been obtained for a
distance of 0.5 mm between the electrodes.
Key words: Arc discharge, carbon nanostructures.
1. INTRODUCTION
Arc discharge is commonly used and feasible to make different kinds of
carbon nanoparticles [1, 2, 3, 4, and 5]. The carbon vapour required for this process
is obtained by sublimation (it is disputable if carbon sublimates or evaporates) of
the anode heated up to a high temperature and the energy comes from the arc
discharge. In case composite electrodes are used, the ratio of the materials in the
bulk is preserved in the obtained vapour. This is used in the synthesis of carbon
nanostructures, also, where the catalyst is incorporated in the anode. In contrast to
the commonly used approach, when the two electrodes are placed at a relative big
distance, in the case of tight gab between them the temperature interaction between
*
Paper presented at the 11th International Balkan Workshop on Applied Physics, July 7–9, 2010,
Constanţa, Romania.
Rom. Journ. Phys., Vol. 56, Nos. 9–10, P. 1167–1172, Bucharest, 2011
1168
N. Koprinarov, M. Konstantinova
2
electrodes will become considerable. The discharge area will be constrained, which
will stimulate the generation of current carriers. Additionally, vapour stream will
be directed towards the cathode and not towards the working chamber.
2. EXPERIMENT AND DISCUSSION
A sketch of the set up for arc discharge with closely situated electrodes is
shown in Fig. 1. The electrodes of cross-section 7.5 mm2 are made of pure carbon
(99.999). The connected to a current source electrode ends are water cooled. The
arc discharge takes place in a stainless steel container, which is evacuated to high
vacuum and afterwards filled with Ar to a pressure of 3х104 Ра and pumping has
been stopped. Since the anode is used up as a result of its sublimation, the distance
between the electrodes is kept at 0.5 mm by continuously moving the anode. So,
due to the distance permanent controls the conditions for the arc discharge remain
constant.
Fig. 1 – A scheme of a set up for discharge with closely electrodes.
During an arc, the electric current flowing through the electrodes equals the
current flowing through the arc zone. Studies show that its local properties depend
on different simultaneous physical processes, which cause non-homogeneity
between the longitudinal and transversal directions. This is the result of the
different amounts and behaviors of the negatively and positively charged carriers.
This non-homogeneity combined with the specificity of each electrode (its
material, size, thermal conductivity, thermal dissipation through the ambient
atmosphere and the bulk) determines its temperature. This temperature, despite of
being very high, can be measured by spectral emission amount and characteristics.
However, in the case of closely situated electrodes, this is difficult and even
impossible. Therefore, some other way to measure the temperatures is needed,
which will also allow the underlying processes to be determined.
3
Energy balance of arc discharge by closely situated electrodes
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A DC source is used for the arc, which provides 16.7 V at a current of 18.5 A.
This corresponds to ne = 1.15 1020 carriers. Because of the electrode proximity, the
cross section of the discharge is practically comparable to their diameter. Hence,
the volume of the arc equals to 3.75 х 10-3 см3. At a pressure of 3 х 104 Ра, the
number of Ar molecules is calculated to be N = 2.72 1015. Considering the potential
between the electrodes to be 11.52 V, one can conclude that the conditions for
impact ionization are not fulfilled. Moreover, even if all the Ar atoms were
completely ionized, their number would not be enough to provide the above
number of carriers. Therefore, we need to look more carefully which other carriers
may be involved and how they get generated.
The electrode high temperature suggests that electrons can be these carriers if
the temperature was high enough to allow their thermal emission. The energy
barrier w which they need to overcome depends on the cathode material and
structure. For a carbon cathode, the barrier is 4.7 еV for amorphous material, 4.8-5 eV
for highly oriented pyrolitical graphite [6], 4.9 ± 0.3 eV for multi-wall nanotubes
(MWNT) and 3.7 ± 0.3 eV for single wall nanotubes (SWNT) [7]. The material
used for electrodes in our experiment is a granular one. Therefore, w is assumed to
be 4.7 еV.
As mentioned earlier, the proximity between the electrodes does not allow
the temperatures to be directly measured (the high temperature area is situated in a
very small and tight zone). This measurement would have allowed us to determine
whether there is thermal emission at the cathode and sublimation at the anode. To
solve this problem, we assume that all the carriers are electrons obtained by
thermal emission. The energy balance equations for the anode and the cathode are
respectively:
QR (I, l, S, ρ) - QL(l, S, T) - QG(l, S, T) - QS(λ, l, S, T) + Qe(I) + QI = 0
(1)
QR (I, l, S, ρ) - QL(l, S, T) - QG(l, S, T) - QS(λ, l, S, T) - Qe(I) = 0,
(2)
Qe (I) = I(w + 2kTg)/e,
(3)
and
where
QR is the energy released due to arc discharge current flow through the electrode
(considered as a resistor); QL is the energy emitted in form of radiation, QG is the
energy transferred to the working gas; QS is the energy dissipated through the bulk
of the electrode, Qe is the kinetic energy transferred by the electrons from the
cathode to the anode and transformed there in heat, QI is the energy of the
electrons accelerated by the field between the electrodes; l is the length of the
electrode; S is its cross-section, λ is thermal conductivity; ρ is the specific material
resistance; w is the work function of the cathode, I is the electric current, e is the
electron charge, k is the Boltzmann`s constant and Tg is the electron gas temperature.
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In our experiment, the electric power of the arc is determined to be 212.3 W,
based on the measured current and the calculated potential between the electrodes.
According to Eq. (3), energy Qe transferred by the electrons from the cathode to the
anode in the form of heat equals to 86.95 W, which accounts for 41% of the
consumed total arc energy. The transfer of this energy causes the cathode to be
cooled and the anode to be heated.
It should be mentioned that the estimation of the melting and boiling points
of carbon is difficult. Due to its nature, carbon decomposes its lattice not atom by
atom but in whole clusters. Therefore, some scientists talk about carbon
sublimation though others assume the existence of a liquid phase and fixed melting
and boiling points. Here, it is assumed that carbon goes through a liquid phase
(with a very low or even no sublimation at all) at a temperature Tc, which is in the
range 3500–4000 0С, and a state of high sublimation at a temperature Ts, which is
between 4300–5100 0С. This is based on various sources [8, 9, 10] and agrees well
with the results of our experiment.
If the thermal conductivity λ of carbon was known (λ = 1.29 W/cmK), one
could calculate the temperature increase ∆Та = 2696 0С of the anode due to the
energy Qe, transferred in the form of heat from the cathode by using the equation:
∆Та = l.Qе/λ.S,
(4)
Accordingly, cathode temperature must decrease by the same amount and the
difference between both electrodes should be 5392 0С. However, such a high value
is not realistic. The reason is that sublimation (evaporation) of the anode is not
taken into account. The anode begins to sublimate when the temperature reaches Ts
and its temperature does not rise anymore. At this point, all of the additionally
transferred energy is used to increase the sublimation rate. The temperature of the
cathode remains almost fixed, too, due to the physical process thermal emission.
For to have a thermal emission at a current of 18.5 A, the cathode temperature
needs to be 3495 K (3222 0C), which can be derived from the relationship:
i = BT2exp(- w/kT),
2
(5)
2
where i is the current density and B = 120 [A/cm .deg ].
The obtained temperature T is lower than Tc, which means that under these
conditions the cathode does not sublimate. This temperature is, also, lower than the
condensation temperature of carbon vapour. As a result, all the carbon atoms which
reach the cathode will stick to it and build a deposit.
Knowing the temperature of the cathode and the temperature range of the
anode, it can be concluded that the temperature difference between the cathode and
anode is not greater than 1605 0C. To be able to calculate this temperature
difference and to determine Ts, one should take into account all the factors,
including the energy balance of the electrodes. Considering that outer ends of both
the electrodes are cooled by water to a temperature of Te = 15 0C, the energy
5
Energy balance of arc discharge by closely situated electrodes
1171
transferred from the arc to the cooled ends of the anode and the cathode are,
respectively:
QR = (Ts-Te). λ.S / l
(6)
QR = (Tc-Te). λ.S / l.
(7)
and
The energy radiated by both the electrodes can be calculated by using the
Stefan-Boltzmann law about black body radiation:
QL = σTs4
(8)
4
(9)
QL = σTc
-12
2
4
where σ = 5.71 10 W/ сm .K
Equations (1) and (2) do not take into account the sublimation of the anode,
the deposition on the cathode and the energy transfer from the one electrode to the
other through radiation. The experiment shows that anode sublimation rate is
77 mg/min. By considering that evaporation energy of carbon is 355.8 kJ/mol, it
can be calculated that 38.1 W are needed to evaporate the above amount.
The energy balance of the cathode can be calculated similarly. It should be
mentioned that in addition to the energy transferred through electrons, there are
losses due to emission and energy dissipation through the cathode bulk. On the
other hand, energy is also transferred to the cathode due to carbon vapor
condensation and radiation originating from the anode. The rate with which carbon
atoms leave the anode due to sublimation, reach the cathode, and get deposited is
33 mg/min, which corresponds to an energy transfer of 16.31 W (due to condensation).
Because of the fact that the cathode and the anode surfaces are very close to
each other, one can assume that almost the whole energy emitted by the cathode
reaches the anode and vice versa. Calculations of the energy balance for two
electrodes with an area of 7.5 x 7.5 based on the above considerations and
equations (1) and (2) show that all the conditions are fulfilled for a sublimation
temperature of Ts = 4300 0K. Hence, one can conclude that this is the real
sublimation temperature. The fact that according to literature this is the lowest
temperature, at which sublimation can take place, can be explained by the granular
structure of carbon used for the electrodes.
3. CONCLUSION
Our calculations for DC arc discharge between two closely situated
electrodes in Ar show that the computed potential between the electrodes and the
gas molecule amount are not sufficient to explain the measured arc parameter.
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Moreover, even if all of the Ar atoms were completely ionized at pressure of 3 х
104 Ра, their number would not have been enough to justify the observed current.
This suggests that the main current carriers are electrons generated by thermal
emission. The proximity of the electrodes does not permit direct temperature
measuring. Measurements of the anode sublimation rate and the cathode deposition
rate allow to calculate the electrode energy balance and to estimate the temperature
on their surface. The derived relatively low sublimation temperature of Ts = 4300 K
can be explained by the granular structure of the carbon used for electrodes. The
calculation shows also that under our experimental conditions, the thermal
emission of electrons, which makes energy to be transferred from the cathode to
the anode, accounted for 41% of the energy used to maintain the discharge. 43%
from the transferred energy produce vapour which gets deposited on the cathode
and allows this approach to be used for depositions on conductive materials used as
cathodes.
Acknowledgments. This work was supported by the Bulgarian Science Foundation (contract №
DOO2-241/18.12.2008) which is gratefully acknowledged.
REFERENCES
1. R. R. Schlittler, J. W. Seo, J. K. Gimzewski, C. Durkan, M. S. M. Saifullah, M. E. Welland, Single
Crystals of Single-Walled Carbon Nanotubes Formed by Self-Assembly, Science 292 1136–1139
(2001).
2. M. Nishio, S Akita, Y.Nakayama, Cooling effect on the growth of carbon nanotubes and optical
emission spectroscopy in short-period arc-discharge, Thin Solid Films 464–465 304–307
(2004).
3. F. J. M. Rietmeijer, A. Rotundi, D. Heymann, Fullerenes, nanotubes and carbon nanostructures,
12 No. 3 659–680 (2004).
4. H. Kathyayini, N. Nagaraju, A. Fonseca, J.B. Nagy, Catalytic activity of Fe, Co and Fe/Co
supported on Ca and Mg oxides, hydroxides and carbonates in the synthesis of carbon
nanotubes, Journal of Molecular Catalysis A: Chemical 223 129–136 (2004).
5. Z. Yu, De Chen, B. Totdal, T. Zhao, Y. Dai, W.Yuan, A.Holmen, Carbon nanofiber based catalyst
supports to be used in microreactors: Synthesis and characterization, Applied Catalysis A:
General 279 223–233 (2005).
6. M. Shiraishi, M.Ata, Work function of carbon nanotubes, Carbon 39 (2001) 1913–1917.
7. http://www.snf.ch/nfp/nfp36/progress/schlapbach.html Electron Emission from Carbon Nanostructures
O. Groening, L. Nilsson, E. Maillard-Schaller, O. M. K¸ttel, P. Ruffieux, P. Groening and
L. Schlapbach, University of Fribourg, Physics Department, PÈrolles, 1700 Fribourg
8. http://en.wikipedia.org/wiki/Carbon
9. http://www.webelements.com/carbon/physics.html
10. А. М. Балдин, Б. А. ВВеденский, С. В. Вонсовский, Б. М., Физический энциклопедический
словарь 5 222-223 (1996).