Table 1. Parameters and results of
SCM fitting.
Dp ’s were determined to be
4.50×10-4, 4.70×10-4 and
4.56×10-4 for 266, 1130 and 10400 ppbv respectively.
For 113 ppbv CH3I adsorption, limited by the nature of
low CH3I concentration, Dp was
not determined. As discussed previously, at low concentration, the
CH3I has not consumed all Ag on the surface of
Ag0-Aerogel pellet during the test time frame and
therefore no significant pore diffusion was observed. The averageDp was 4.59 ± 0.102 ×10-4cm2/s. Different from 3 similarDp ’s, ks ’s increase from
5.43×10-2 cm/s at 113 ppbv to
3.53×10-1 cm/s at 10400 ppbv. The
concentration-dependent ks is highly
questionable. Theoretically, for a given reaction, theks only depends on temperature and shall not
change with the reactant concentration.54 Therefore,
the orderly changed ks indicates an
nth order reaction instead of the assumed
1st order.
Discussion
Nth Order Shrinking
Core
Model
The nth order SCM cannot be used directly to fit an
adsorption curve becauseks*Cbnterm in Eq. 5 contains two variables
(ks* & n) and one
constant (Cb ). There exists an unlimited amount
of combinations to yield the desired value. Instead,ks* and n were
determined by plotting ks (cm/s) andCb (mol/cm3) using Eq. 10 and
11.
The reaction order and nth order reaction constant
were determined using Figure 5 and shown in Table 2. For
CH3I-Ag0-Aerogel adsorption system,n =1.37 and ks* = 1287
(cm/s)∙(mol/cm3)1-n. As mentioned
earlier, the SCM results can be applied to deep-bed adsorption analysis.
However, keeping the nth order reaction assumption may
introduce certain difficulties in calculations. Therefore, Eq. 10 can be
rewritten as Eq. 12 to calculate the
nth-order-compensated, concentration-dependentpseudo ks ’s (cm/s).