st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Homogeneous nucleation of graphene nanoflakes (GNFs) in
thermal plasma: Tuning the 2D nanoscale geometry
J.-L. Meunier1, N.-Y. Mendoza-Gonzalez1, R. Pristavita1, D. Binny1, D. Berk1
1 Plasma Processing Laboratory, Department of Chemical Engineering, McGill University,
Montreal, Canada
Abstract: Analysis is presented on the 2D structural evolution of the graphene flakes
during nucleation. The spherical initial cluster model is applied to the specific
crystalline graphitic-based geometry. The conditions and time scales of the carbon
nucleation allow assigning to this crystalline initial cluster differential growth rates for
in-plane and out-of-plane growth. The influence of parameters such as the reactor
design and the injection rate of carbon precursor are accounted to the tuning of the
process and possibly a control of this 2D structure.
Keywords: thermal plasma, graphene, CFD modeling, nucleation, carbon nanoflakes,
carbon nanoparticles.
1. Introduction
Pure graphene nanoflakes (GNF) are produced as a
support frame to replace Pt-based catalyst materials in
polymer electrolyte membrane fuel cells (PEM-FC). This is
made using iron dispersed at the atomic level, the
dispersion and catalytic availability of Fe follows a
chemical structure mimicking the blood heme structure
[1,2]. The GNFs act as a support for pyridinic nitrogen
functional groups, the nitrogen structure coordinating Fe
and making it available for the oxygen reduction reaction
(ORR). Thermal plasma generated GNF structures showed
exceptional properties in terms of stability in the PEM-FC
because of their very high crystallinity, as well as the
exceptionally high N-doping levels attained. A “properly
designed” ICP thermal plasma reactor enabled a very good
control of the flow and energy fields and complete
elimination of recirculation zones. This design leads to a
fine control of the nanoparticle nucleation fields and of the
history of this nucleation [2]. Experimental results
effectively produced very pure GNF structures within a
narrow structural thickness range averaging around 10
graphene layers (range: 5-20 layers/2-7 nm) and in-plane
lengths between 50-100 nm. Assuming through modeling
of the particle nucleation fields that the primary particles
created after nucleation are spherical, this work aims at
analyzing the formation of the 2D graphene layered
structure, and develop reactor design aspects for controlling
the thickness and width of this 2D structure. We show
through modeling that not only the very pure GNF
synthesis can be understood and controlled, but also that the
2-dimensional (2D) shape and evolution of the
nanoparticles can be modeled with good comparison with
experimental results.
2.Model
The model presented in this study is applied to the case
of a 35 kW inductively-coupled thermal plasma (ICP) torch
system used at PPL. The ICP torch is attached to a conical
water-cooled reactor having 50 cm in length and a 14 o total
opening angle [1]. This geometry provides a symmetric
flow pattern within the reactor avoiding recirculation that
would lead to uncontrolled thermal history and growth. The
plasma gases used are Argon and Nitrogen. The methane
carbon precursor is injected axially and the effective plasma
power kept constant at 10 kW, reactor pressure varying
between 14 kPa and atmospheric pressure [1]. These
conditions give temperatures upwards of 10,000 K in the
plasma core where the methane is instantly dissociated, the
resulting carbon atoms nucleating homogeneously from the
rapid quenching downstream within the reactor. The GNFs
are formed through a well-controlled homogenous
nucleation. The resulting product is extremely pure, with
GNFs consisting of 5-20 graphene planes of often
rectangular planar dimensions typically around 100nm X
50nm. The production rate of GNFs is around 0.4 g within
30 minutes of reaction time [3].
The present model discussion focuses on the reactor
section only. The calculation of fluid flow is coupled with
the General Dynamic Equation (GDE) to account for
particle nucleation and growth. The following assumptions
are used [4]: two dimensional (2D) model with fully
axisymmetric configuration; steady state flow neglecting
gravity effects; turbulence effects are included using the
Renormalization Group (RNG) k-epsilon model; diluted
particle system formed by argon plasma and carbon gas;
mixture properties are those of an argon plasma; the
1
condensable vapor is not involved in any chemical reaction;
particles are assumed spherical with the same temperature
as the gas; formation of particles is by nucleation, and
growth by condensation and coagulation; transport of
particles is by convection and diffusion; the particle size
distribution (PSD) follows a logarithmic representation; the
three first moments of the PSD are considered for the
solution of the GDE.
The formation of particle nuclei with critical size rc
(critical radius) is followed by surface condensation growth
to provide the final size of particle. In the present model
we consider the local high temperature and residence time
to generate a fully crystalline carbon structure in the shape
of a cylindrical stacking of graphene layers (Fig. 1). By
symmetry, we suppose the cylinder diameter ac and height
hc to be the same and equal to the critical cluster size 2 rc.
Once the GNF cluster is formed, a lateral growth of the
particle from condensation provides the final values of af
and hc, where af is the lateral growth based on an equivalent
final volume of the condensed phase forming the graphene
and the spherical particle The final thicknes length hf =hc as
condensation is assumed not to increase the number of
graphene sheets, while the final sheet length is calculated
as:
Nucleation, condensation and coagulation mechanisms
are integrated to the GDE. The "kinetic" nucleation rate I is
written according to Girshick and Chiu (1990) [5]:
I
11ns2 S
12


4 3 
exp 
2
2
27ln S  

(1)
af 
This equation uses the saturated vapor in equilibrium as
reference for the calculation of the energy of formation of
clusters, where β11 is the Brownian coagulation coefficient
between two monomers,   s1 k BT the dimensionless
surface tension, S  n1 ns is the supersaturation ratio, n1 is
the vapor concentration (m-3), ns the vapor concentration at
saturation (m-3), σ the surface tension of the condensed
phase (J/m2), s1 the surface of a monomer (m-2), kB
Boltzmann's constant (J/K) and T the gas temperature (K).
The coefficient of condensation growth in the free
molecular regime is calculated with:
B1  36 
13
16 rx3,t
(4)
3rc
Where rx,t is the radius after condensation and rc is the
critical radius after nucleation.
12
 kT 
n v  B 
 2m1 
23
s 1
(2)
Where v1 and m1 are the volume (m3) and the mass (kg) of
one monomer. The coagulation coefficient
between spherical particles containing, respectively, i and j
monomers of one single chemical species is given in the
free molecular regime by (Flagan and Seinfeld 1988) [6]:
 v 
ij   1 
 4 
16
6k BT  1 1  1 3 1 3
   i  j
 p  i j 


2
Fig. 1 Control for GNF morphology [2].
(3)
The temperature and velocity boundary conditions for the
reactor inlet are extracted from the plasma flow model [1]
at 55kPa and 10kW. Initial carbon vapor mass fraction
concentration is set to 10-3 kg/kg with a parabolic profile.
The water cooled reactor walls are set to 300 K as in the
experimental setup. Axial gradients at the reactor outlet are
assumed to be zero for all variables, while the centerline
condition is set to zero radial gradients and zero radial
velocity. Transport and thermodynamic properties of the
plasma gas as a function of temperature are obtained from
Boulos et al. [7].
p is the particle density, kg/m3.
The preceding assumptions lead to the simplification of
the conservation equations for momentum, energy
equations and the solution of the three moments of PSD
(Table 1). The resulting elliptical partial differential (EPD)
equations are solved using the sequential solver of the CFD
finite-volumes commercial code Fluent-Ansys 14.5.
Table 1 Equations to solve the Particle growth.
The nucleation rate and particle growth are function of
the physical properties of the condensable element, in this
case carbon: density for the temperature range of 4765–
4965K is taken from [8]. Special attention has been put to
2
the surface tension which was originally for C60 and
interpolated to carbon black [9]. Carbon vapor pressure in
the range 3450 to 4500 K and evidence for melting at
approximately 3800K is taken from [10]. To solve the
model an underlying computational grid is created with a
total of 21,760 quadrilateral cells, thereby assuring that a
high computational grid density and numerical accuracy
were attained.
3. Results
The model solution allows tracking the flow fields,
particle spherical growth and lateral planar growth. Three
cases are analyzed, the first one constitutes the base case
where the reactor wall has a 7o angle expansion to the
central axis, and a diluted mass fraction of carbon gas
injection of 10-3 kg/kg. The effective plasma power and the
pressure are kept constant at 10kW and 55.3 kPa
respectively. Two other cases are analyzed with angle
expansion of 12o and mass fraction concentration to 10-2
kg/kg respectively.
The summary of the simulated
conditions is given in Table 2.
Fig.2 Temperature (left) and velocity (right) contours for
the base case.
Fig. 2 shows the velocity and temperature contours for
the base case. The stream function lines are superimposed
to the velocity magnitude to show the paths the particles
follow in the absence of diffusion or other external force
field. The flow field influences the properties of the final
particles since the transport of particles is due to
convection, while the temperature affects all other
equations and the final size distribution of particles. The
particle nucleation (from supersaturation ratio of carbon
vapor), the rate of condensation and coagulation are
temperature dependent. As we can see from Fig. 2, the gas
enters the reactor at around 8 000 K and this temperature
decreases very gradually down. Evidence for carbon
melting is at approximately 3800 K according to [10] and
the formation of Carbon species are expected in the 30005000 K range from equilibrium thermodynamic
calculations.
There is practically no influence of the coagulation
mechanism due to the absence of flow recirculation. The
thickness (number of graphene layers) and lateral size can
be calculated using the diameters obtained from the present
model. The critical radius rc size is obtained from the
diameter of particle after nucleation which is the same for
the three cases studied (3E-10).
The first growth mechanism is the nucleation burst,
followed by a rapid growth by condensation
and
coagulation. Fig. 3 shows the contours of particle mean
diameter and the condensation coefficient which is
responsible of the final particle size. The final size of the
particle is given by the mean particle diameter which is
defined as
where d1 is the atomic size of a
carbon particle, M4/3 and M1 are calculated moments of the
particle size distribution function (PSDF). Once the carbon
vapor enters the reactor, particles of 1nm start to grow
immediately close to the walls. The growth of a particle
starts below 5000 K and follows the condensation
mechanism to reach a final size of 11 nm very rapidly.
Fig. 3 Contours of condensation coefficient (left) and mean
diameter (right) for the base case.
3
When the carbon concentration is increased to 10 -2 kg/kg,
flow fields and the residence times remains the same as the
base case. However the increase of mass fraction of carbon
increases the available carbon vapor to condense and bigger
particles will form. Large differences in the final particle
size appear because the carbon vapor concentration is
coupled to nucleation and condensation mechanisms.
Comparison of the model results with the experimental
findings where the thickness range is around 10 graphene
layers and in-plane widths between 50-100 nm [1], allow to
believe we are capturing some of the 2D growth dynamics.
Influence of parameters: Fig.4 shows the zy plot of
temperature for the base case (7o) and with a larger angle
expansion (12o). Very small differences are observed.
Similar results are found for the velocity profiles. However
one needs to consider these very small variations for
evaluating the changes in the GNF geometry, these changes
occurring at the nanoscale and atomic level. Focussing on
the 3000-5000 K window, the 12o design conserves higher
temperatures over longer distances e.g., the 5000 K location
is 1.5 mm further than the base case, and at 3000 K it is 8
mm. The residence time analyzed on the streamline 2x10-4
kg/s in the temperature window (3000-5000K) is 15 ms for
7° and 19 ms for 12°. The particle growth is affected by the
residence time in the zone of condensation and is confirmed
by the model where the final size is 15 nm resulting in a
difference of 4 nanometers between both cases. Table 2
summarizes these results.
4. Conclusions
The temperature, flow fields, condensation, mean diameter
and lateral growth of the 2D GNF particles were analyzed
in three cases affecting the particle nucleation and growth
zones. The temperature and velocity fields show only small
variations in the nucleation/growth regions. These are
however enough to modify the 2D structure of the GNF.
Comparison with experimental results shows a good
agreement particularly in the number of the graphene
layers. This study paves the way for tuning the 2D GNF
structure produced by thermal plasma through a
manipulation of the reactor design and operating
conditions.
5. References
[1] R. Pristavita, N.-Y. Mendoza-Gonzalez, J.-L. Meunier,
D. Berk, Plasma Chem. Plasma Process., 31, 6, 851-866
(2011).
[2] J-L Meunier, R. Pristavita, N.-Y. Mendoza-Gonzalez,
D. Binny, D. Berk, ICOPS 2012, Edinburg UK, July 8-12
(2012).
[3] D. Binny,, J.-L. Meunier, D. Berk, IEEE NANO
Conference Proceedings (2012).
[4] N.Y. Mendoza-Gonzalez, M. El Morsli, P. Proulx,
Journal of Thermal Spray Technology, Vol. 17, No. 4, pp.
(2008).
[5] S.L. Girshick and C.P. Chiu, J. Chem. Phys.,93 (1990)
[6] Flagan, R. and J. Seinfeld, ISBN 0133325377, (1988)
[7] M.I. Boulos, P Fauchais, and E. Pfender, ThermalPasmas Fundamentals and Applications, Vol. I, Plenum
Press, New York (1994).
[8] Chemical Properties Handbook, McGraw-Hill (1999).
[9] M.B. Khedr et al. Molecular Physics Vol. 107, no. 13
(2009).
[10] Whittake, Arthur G, report for the aerospace corp El
Segundo CA material sc. lab. (1981).
Fig. 4 Temperature zy plot for the base and angle expansion
cases.
Table 2. Sumary of results
Base
Angle
Carbon
case
expansion
increase
7o
12o
7o
-3
-3
10
10
10-2
Angle exp.
Mass fract.
[kg/kg]
Residence times in 3000-5000 K range
Axis
12 ms
14 ms
12 ms
Streamline 2E-4
14 ms
19 ms
14 ms
Spherical diameter
Final size
11nm
15 nm
19nm
Lateral GNF growth (# graphene layers for hf)
Thickness hf
7 layers
10 layers
12 layers
Lateral size af
77 nm
122 nm
175 nm
4