Chemistry Reference
In-Depth Information
Langmuir isotherm describes the surface coverage in terms of pressure of
the gaseous precursor.
y
¼
s
bP
1
þ
bP
s
0
¼
(3
:
8)
d
n
3
r
4
n
g
|
6
where s is the number of occupied sites and s
0
is the maximum number of
available sites. b is a constant that is related to residence time of the
adsorbate on the surface.
According to Langmuir-Hinshelwood kinetics, the surface reaction rate is
proportional to the surface coverage (y). Then, the reaction order comes
between 0 and 1 with respect to the precursor pressure. Apparently, the
surface reaction becomes linear with respect to P when the pressure is low
(P
{
1) or the residence time of the adsorbed molecule is very short (b
{
1). In
contrast, when the pressure is very high, the molecules cover a large area,
eventually saturating the catalyst surface with the adsorbates. If this is the
case, the reaction order approaches zero, thereby the surface reaction
becomes constant regardless of a further increase in the precursor pressure.
3.2.2.5 Diffusion through Catalyst and Carbon Incorporation
Carbon adatoms can find their way to the growing carbon nanotube end via
two pathways: bulk diffusion and surface diffusion. Generally, surface dif-
fusion has a lower activation barrier than bulk diffusion, so surface diffusion
should be prevalent.
60
However, bulk diffusion is not negligible at high
temperatures and especially for the growth of multi-walled carbon nano-
tubes (MWCNTs) since the multiple inner nanotube cylinders are not easily
accessible to surface carbon adatoms.
61
The diffusivity and solubility of carbon in a catalyst greatly depends on the
physical phase of the catalyst during growth, which has been a controversial
topic in CNT growth research. The vapor-liquid-solid (VLS) mechanism
62,63
postulates that precursor gas molecules adsorb and form a solid solution at
the eutectic point. As carbon accumulates in the catalyst, the carbon content
reaches the point of supersaturation. Subsequently, an island of carbon cap
nucleates and grows into the tip of a nanotube. Then, continuous feeding of
carbon lifts the tip cage and drives elongation of the nanotube.
While it has been widely accepted that the other types of catalyst-assisted
growth of nanowires such as silicon nanowires follows the VLS mechanism,
the state of the nanotube catalysts during growth is not obvious. The melting
temperatures of general nanotube catalysts (Fe: 1538 1C, Co: 1495 1C, Ni:
1455 1C) are much higher than growth temperatures. However, the high
surface-to-volume ratio of the catalyst nanoparticles can modify the ther-
modynamics of the melting process, reducing the melting temperatures.
64
Researchers also argued that eutectic mixtures formed by carbon addition
can also contribute to an early change in the phase of the catalyst in several
simulation studies.
65,66
Harutyunyan et al.
67
.
claimed that CNT growth is
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