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).