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catalysts. Computer simulations may help in the understanding of this
coupled non-linear numerical problem, yet reasonable solutions are still
highly challenging to obtain. Therefore, rather than pursuing a complete
analysis, most research focuses on the phenomenological aspects of GPRs in
the CVD growth of CNTs.
In general CVD, non-equilibrium processes are dominant in GPRs of
hydrocarbon pyrolysis, therefore the reaction time or residence time (t
r
)of
gas molecules is a key parameter along with other thermodynamic prop-
erties. The residence time can be estimated from the following expression:
d
n
3
r
4
n
g
|
6
t
r
¼
V
rt
Q
(3
:
3)
where V
rt
is the volume of the hot zone in CVD, and Q is the flow rate of
gases. Whereas a fast gas flow (or large Q) enhances the mass transport of
carbon precursors, it also sweeps gas molecules in a short time from the hot
zone where GPRs occur. Thus, the effect of the mass transfer enhancement
by a faster gas flow, and the effect of the GPRs, need to be decoupled.
Excessive pyrolysis can also generate non-graphitic carbon contaminants
such as aromatic soot precursors and amorphous carbon. These by-products
can be deleterious to the nanotube quality and yield.
56
This effect coupled
with the positive effect of GPRs leads to the existence of an optimum resi-
dence time (Figure 3.7).
57
In the case of a cold-wall reactor with a separated
gas pretreatment cell,
17
adjusting the pretreatment temperature can be an
effective way to optimize GPRs due to their high activation energy (
B
3.36 eV
for ethylene).
54
.
Figure 3.7 Effect of gas dwell time on growth yield of SWNT.
Reprinted with permission from ref. 57. Copyright 2011 American
Chemical Society.
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