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Table 2 Kinetic equations used for fitting experimental sorption data
Model equation
Description
a ¼ kt
Surface-controlled reaction with chemisorption being the RDS
Þ 1 = 3 ¼ kt
JMA nucleation and growth: three-dimensional growth of existing
nuclei with constant interface velocity
½ ln 1 a
ð
Þ 1 = 2 ¼ kt
JMA nucleation and growth: two-dimensional growth of existing
nuclei with constant interface velocity
½ ln 1 a
ð
Þ 1 = 3 ¼ kt
CV: three-dimensional growth with constant interface velocity
1 1 a
ð
Þ 1 = 2 ¼ kt
CV: two-dimensional growth with constant interface velocity
1 1 a
ð
1 2 3 1 a
Þ 2 = 3 ¼ kt
CV: three-dimensional growth with decreasing interface velocity
ð
Adapted with permission from Barkhordarian 2006
Fig. 10 Different kinetic
curves based on the equations
in Table 1 for magnesium
catalyzed with 1 mol%
Nb 2 O 5 and milled for 100 h
(T = 100 C). Reproduced
with permission from
Barkhordarian 2006
and Contracting Volume (CV) [ 87 ] model (Fig. 11 ). Both models make assump-
tions that may not be valid during growth of differing phases of nanoparticles. For
instance, the CV model makes the assumption that nucleation of the secondary
phases are instantaneous (the nucleation of MgH 2 , for example) and that the core/
shell morphology is quickly reached. As a result of the model not accounting for
the initial nucleation and growth, the fitting will likely have discrepancies for low
a values. In contrast, the fitting for JMA will likely have discrepancies for the high
a values. This is because the JMA model does not account for the overlap of the
growing phase that is likely to occur once, most of the material is transformed to
MgH 2 [ 70 , 88 ]. Due to the many assumptions made by these models, the exper-
imental data rarely fit well for a whole data set [ 70 ]. However, even though an
entirely acceptable fit may not be made, the nature of the mechanism can be
inferred through characterization of a portion of the full data set [ 70 , 81 ].
As mentioned earlier, the GCI method can be performed at constant pressure,
which is advantageous because pressure changes add even more complexity to
isothermal measurements. In addition to the difficulty of fitting the data, the PCI
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