Nanotechnology’s Wonder Material: Synthesis of Carbon Nanotubes - Hierarchical Nanostructures for Energy Devices - page 45

highly preferred above the eutectic point with an iron catalyst, and
solidification of the catalyst can potentially terminate growth. Recent
development of in situ TEM techniques has enabled the direct observation
of the catalyst phase during growth, revealing that CNTs grow from
catalyst particles remaining in a solid phase at relatively low temperatures
(600-650 1C). 22,68,69 Although these studies unambiguously demonstrated
that the VLS mechanism might not hold for CNT growth, there remains the
possibility that CNTs can grow by the VLS mechanism at higher growth
temperatures. Up to this point, VLS growth of CNTs has not been directly
observed yet, so the debate about this growth mechanism continues.

d n 3 r 4 n g | 6

3.2.3 Growth Kinetics
Despite the large amount of empirical observations describing different
aspects of the growth process, the understanding of the growth mechanism
of CNTs is still incomplete. However, studies on the growth kinetics can tell
a lot about the underlying mechanism since each growth mechanism pro-
duces its own kinetic trend. Researchers typically assume that the mech-
anism contains a rate-limiting step. 70 Fortunately, the longitudinal length of
CNT arrays has some correlation with growth kinetics (at least for the longest
CNTs in the array) and it is relatively easy to observe. Moreover, the growth
rate observed in the CVD growth of CNTs is generally within the measureable
range (up to a few micrometres per second) for in situ growth monitoring
instruments. The following section introduces kinetic models for the CVD
growth of CNTs and discusses their validity based on the experimental
evidence.

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3.2.3.1 Kinetic Model of CNT Growth
The driving force for the conversion of the carbon from the gas phase into
the carbon nanotube is equal to the chemical potential difference
(Dm ¼ m g m NT ) between the gaseous carbon (m g ) and the carbon in a nano-
tube crystal (m NT ). To build a generalized model of the CNT growth we can
use an equivalent electric circuit (Figure 3.8). Here the electric current cor-
responds to the mass flux of carbon. This circuit includes contributions
from three different resistances: the gas-phase diffusion resistance of the
CNT forest to the catalyst site (R 1 ); resistance associated with the carbon
adsorption to the catalyst surface and any further reactions happening there
(R 2 ); finally, a diffusion resistance of carbon adatoms through the catalyst
particle to the CNT growth site (R 3 ). In practice, carbon can be consumed
into non-graphitic carbon such as amorphous carbon deposits on the cata-
lyst. We can incorporate this process into the equivalent circuit as a current
leak. However, for a well-tuned CNT growth, the amount of such a leak is
negligible compared to the main current (i.e. the production of amorphous
carbon is much slower than the amount that gets incorporated into the
growing nanotube array), thus the following analysis will not consider it.