Chemistry Reference
In-Depth Information
3.2.2.3 Mass Transport of Gas Precursors
In the CVD process, the main routes for supplying the carbon
precursors to the growth sites on the catalyst are convective and diffusive
transport. The convective flow of gases inside a long flow channel is a well-
established classical problem of a fully developed internal flow. As the
molecules approach the substrate, however, the convective transport
decelerates and a rather complex flow pattern starts to develop. The detailed
description of a flow pattern near the substrate is not simple since it de-
pends on the geometric shapes of the reactor, substrate, and other objects
inside the reactor. Nevertheless, a widely accepted notion has a thin
boundary layer on the substrate surface, across which temperature, flow
velocity, and gas composition change with an abrupt gradient.
Diffusive mass transport through this boundary layer is an important gas-
phase mechanism of carbon delivery. The deposition surface can be mod-
eled as a mass sink, while the free stream acts as a continuous supplier of
carbon precursor molecules. The concentration gradient acts as a driving
force of this transport process, and the transport rate can be expressed using
Fick's law:
d
n
3
r
4
n
g
|
6
N
g
N
c
J
c
¼
D
g
(3
:
4)
d
c
where J
c
is the molecular flux of the carbon precursors, D
g
is the mass dif-
fusivity of the precursor gas, d
c
is the thickness of the (concentration)
boundary layer, and N
g
and N
c
are molecular concentrations of the pre-
cursors in the free stream and very near the catalysts, respectively. Here, we
note that in this lumped relation, the boundary layer thickness (d
c
)isan
implicit parameter that can encompass all aspects of mass transport near
the surface.
At common CVD temperatures, gas-phase diffusion is considered very fast
compared to chemical conversion and other mass transport processes.
However, the gas-phase diffusion may become slower as the nanotubes grow
longer; especially, the nanotube forest (VACNTs) can act as a diffusion bar-
rier due to the very short inter-nanotube distances (10-100 nm).
58
We note
that this diffusion deceleration corresponds only to root growth of CNTs
where the catalyst remains on the bottom of VACNTs. The length scale of the
interstitial space is comparable to the mean free path of the gas molecules,
resulting in more frequent collisions of a gas molecule with CNT walls than
with other gas molecules. Then the diffusive transport undergoes a different
transfer mechanism: Knudsen diffusion. The Knudsen diffusivity (D
K
) takes
the following form:
.
1
=
2
D
K
¼
97r
e
E
v
t
T
M
(3
:
5)
Search WWH ::
Custom Search