Nanotechnology’s Wonder Material: Synthesis of Carbon Nanotubes - Hierarchical Nanostructures for Energy Devices - page 51

In contrast, Puretzky et al. 86 explored a deactivation model based on the
growth kinetics of a poisonous carbon platelet. Their model involves several
differential equations with a large number of parameters. In brief, the poi-
sonous carbon layers are assumed to be nucleated and grow by carbon
adatom addition. The essential governing equation accounting for the
spread of the poisonous layer states that:

d n 3 r 4 n g | 6

dN L ðÞ
dt

¼ k C N C ðÞ (3 : 21)

where N L is the number of carbon atoms that make up the poisoning carbon
platelet, whereas N C is the number of carbon atoms produced by adsorption
of hydrocarbon feedstock gas. Recently, Lee et al. 84 suggested a simplified
model based on the same governing equations of Puretzky et al. Interest-
ingly, the final form turned out to be the exponential decay that is actually
consistent with Iijima's model (eqn (3.18), (3.19)).
While the exponential decay model has been widely adopted to
describe CNT growth kinetics, researchers should be aware that this model
does not consider the nucleation kinetics of the poisonous carbon platelet.
Rather, it describes immediate surface poisoning, for instance, by strongly
adsorbing gas molecules. Moreover, one of the characteristics of this
model is relatively gradual termination, therefore it fails to predict the
abrupt termination behavior that was consistently observed in a number of
studies. 18,82,83,87-89
An alternative treatment based on the Kolmogorov-Mehl-Avrami model to
describe the growth kinetics of the poisoning carbon platelets can reproduce
the abrupt termination behavior. 83,89 This model accounts for sporadic
events of carbon platelet nucleation, and the resultant expression gives the
following deactivation kinetics:

.

n

t
t

a ¼ exp (3 : 22)

In the case of 2D islands of surface carbon, n become 3 with t 3 ¼ pJ a v a = 3
where J a indicates nucleation rate and v a indicates linear expansion speed of
the platelet. Applying this model requires that the critical size (r c )ofa
platelet nucleus is suciently smaller than the catalyst size. Thus SWNT
growth from very small catalysts ( 1 nm) may not follow this model.

Ostwald ripening, which is another reason for growth termination, can be
described by the following empirical relation: 80

B

da
dt ¼ k rp a a 1

Þ n ð (3 : 23)

where a N is catalyst activity at a steady state, and k rp is a kinetic constant.
This model accounts for sintering kinetics of metal particles supported on
an oxide surface. Assuming the ripening is the main growth termination
mechanism, Latorre et al. 80 applied this equation to the description of the
deactivation kinetics. Nonetheless, it is still not clear how the collective