Download Three–dimensional Modelling of dc Arc Discharges for Carbon Nanostructure production

st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
3D Modelling of dc Atmospheric Arc Discharges
E. Tam1, A. B. Murphy1
CSIRO Materials Science and Engineering, Lindfield 2070, NSW, Australia
1
Abstract: The simulation results of an arc discharge, using a three-dimensional fluid model
and a modified version of Patankar's SIMPLER algorithm is presented in this work. The
physical parameters used here correspond to a system using graphite electrodes immersed in a
helium/carbon background gas. The effects of the inflow rate of He, the inter-electrode gap
and the arc current are explored in the context of optimizing the arc for the growth of various
carbon nanostructures such as graphene and carbon nanotubes.
Keywords: arc discharge, carbon nanotubes, graphene, modeling, computational fluid dynamics
1. Introduction
Carbon nanostructures, such as carbon nanotubes and
graphene nanoribbons, have unique properties that have
motivated many researchers to attempt their integration
into advanced new devices. Potential applications include,
but are not limited to, drug and gene delivery, hydrogen
storage and electron field emission [1,2].
Arc discharges generally produce large volumes of high
quality nanostructures, because the manufacturing process
occurs at very high temperatures when compared to other
methods [3,4]. However, even though arc discharges are
already used to produce nanostructures commercially for
scientific purposes, there are still challenges that must be
overcome for applications outside the laboratory. These
challenges include controlling the environment to minimize the large temperature gradients typically seen in an
arc discharge, optimizing the energy inputs so that the arc
produces just enough heat to ablate the electrodes and
nucleate the nanostructures and, as with all other fabrication methods, controlling the growth of the desired
nanostructure (such as diameter and chirality of single–walled carbon nanotubes).
2. Model
A schematic of the system modelled in these simulations can be seen in Fig. 1. The computational domain is a
rectangular prism. Room-temperature helium is pumped
into the system at a constant rate around the graphite anode. The graphite cathode is roughly twice the diameter of
the anode.
The plasma is assumed to be incompressible and can be
approximated with local thermal equilibrium (LTE). The
heat transfer boundary conditions given by Tanaka and
Lowke for a thermionic cathode and an anode were used
[5]. In addition, the cooling effects associated with the
latent heat of vaporization were taken into account.
The standard conservation and continuity equations,
adapted from those of conventional computational fluid
dynamics to take into account thermal plasma phenomena,
are used. These include the mass continuity equation,
charge continuity, the Navier–Stokes equation and energy
conservation [6-11].
Figure 1: Schematic of the system modelled.
An equation for conservation of the carbon vapour
mass fraction is also required. This is [10]
(1)
where
is the mass density of the plasma,
is the
plasma velocity,
is the mass fraction of carbon in the
plasma,
is mass flux of the carbon vapour,
is the
source term for the ablated carbon vapour and t is the
time.
The carbon mass source term used in Eqn (1) is approximated to be [12]
(2)
at the plasma–electrode interface and 0 elsewhere. The
variables
,
and
are the mass of a carbon
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
atom, the vaporization (or ablation) flux and the deposition flux respectively.
The Hertz–Knudsen relation [12]
(3)
ture at which graphite ablates. On the other hand, the
electrodes in Fig 2 (b) never exceed 4200 K, less than
10% greater than the ablation temperature, which shows
that the ablation has an important cooling effect on the
electrodes.
is used to determine the vaporization flux, where
is
the saturation vapor pressure of carbon, determined by
Clausius–Clapeyron relation[12]
(4)
where
is the latent heat of the graphite and
specific gas constant for carbon
.
The deposition flux is calculated using [12]
is the
(5)
In this binary gas system, the diffusive mass flux of
carbon, relative to the mass–average velocity in a helium
plasma, was determined using the combined diffusion
coefficient method [9-11]:
(6)
3. Results
Figure 2 shows the temperature profile of the systems
with and without ablation.
When vaporization and deposition of carbon vapour is
included, there are significant changes in the plasma flow.
Without ablation, the temperature appears to be evenly
distributed in the z direction as the plasma flow is primarily driven by the magnetic pinch force. This leads to flows
which forms eddies and recirculate around the arc, leading to the temperature profile seen in Fig 2 (a). On the
other hand, when ablation is included, the flow is primarily driven by the rapidly expanding carbon as it forms a
gas. Also, as graphite is a thermionic emitter, the cathode
is significantly cooler than the anode at the surface. Recalling from Eqns (3) and (4) that the rate of ablation has
an exponential dependence on temperature, the hotter
anode therefore ablates more rapidly, leading to a plasma
flow which predominantly flows away from the anode,
producing the temperature distribution seen in Fig 2 (b).
The maximum temperature of the arc is observed to be
higher when ablation is included, however the temperature drops off much more rapidly and the arc appears to
be more constricted with the inclusion of ablation. More
importantly, the temperature of the electrodes differs
greatly between the two cases. In Fig 2 (a), the anode
temperature can be seen to reach approximately 6000 K,
which is approximately 2000 K higher that the tempera-
Figure 2: Temperature field of an (a) arc with no carbon ablating
from the electrodes and (b) arc with carbon ablating and depositing on to the electrodes. Temperature units are kelvin.
Figure 3 shows the mass density of the carbon species
(C, C2, C+, etc) in two different extreme cases. In Fig 3 (a),
a large He inflow rate of 38.4 L/min is used. In this system, the He inflow is very clear. An almost complete absence of carbon is seen in the blue region, corresponding
to where helium enters the system, with the colour beginning to turn green as the gas passes the electrodes where
carbon is ablated. Fig 3 (b), on the other hand, uses a
large current of 200 A, resulting in the rapid ablation of
the electrodes and a much higher average carbon mass
density in the system in general. The higher carbon density away from the electrodes, near the walls of the
chamber, is due to two effects: the cooler gas temperature,
which leads to a denser gas, and the fact that carbon molecules are taken into account in this model (up to C5).
The isolines overlaid in both Fig 3 (a) and (b) represent
the carbon saturation ratios ( ) of 0.01, 1 and 100. The
carbon saturation ratio is the ratio of the partial pressure
of the carbon species to the saturation carbon vapour
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
pressure. Solid carbon cannot nucleate when
, and
will typically form for S ~ 10, so this ratio is a good indicator of where carbon nanostructures will nucleate and
grow. In Fig 3 (a), these lines are very close to each other,
and the density of carbon species is low. This indicates
that only very small nanoparticles will form, since growth
of the carbon nuclei by condensation will be weak. On the
other hand, Fig 3 (b), with a high current density and relatively low He inflow rate shows saturation isolines that
are more widely spaced. Further, the region between the
isolines of 1 and 100 has a much higher density of carbon
species, and therefore larger carbon nanostructures can be
expected.
Figure 3: Carbon mass density of arc systems with an inter-electrode gap of 4 mm and; (a) total current of 50 A and helium in-flow rate of 38.4 L/min and; (b) total current of 200 A
and helium in-flow rate of 2.4 L/min. The isolines represent the
carbon saturation ratios of 0.01, 1 and 100 respectively. Carbon
mass density units are g/cm3.
4. Summary
The effect of the inclusion of carbon mass conservation
on a dc arc discharge has been investigated using a
self-consistent code that includes the electrodes in the
solution domain. Comparisons to results obtained for a
pure helium plasma with no carbon vaporization show
differences in the plasma flow, current densities and temperature distribution of the plasma. By including ablation,
the maximum temperature of the electrodes is kept close
to the ablation temperature of graphite. Results demonstrate that both the total current and the He inflow rates
have a strong influence on the carbon mass density and
the carbon saturation ratio, which will strongly affect the
size of the carbon nanostructures that are formed.
5. References
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