and V) and by analyzing the silicon leaching after the adsorption experiments (Papers I and III).
Regeneration performed by 1 or 2 M HNO3 did not significantly change the adsorption efficiency of EDTA/DTPA-functionalized silica gels or chitosans (Table 10 in Paper I and Table 1 in Paper II), indicating a very high stability. Moreover, the leaching of silicon from EDTA/DTPA-silica gels was significantly lower than that from the intermediate synthetic product APTES-silica gel (Figure 5 in Paper I), which was attributed to the stabilization of the materials by the surface bound chelating agents. The silicon leaching from EDTA-Chi:TEOS 2:60 was slightly higher than from EDTA-silica gel (Figure 2 in Paper III). Considerably lower leaching observed for EDTA-Chi:TEOS 2:30 and 2:15, however, confirmed their stability. Finally, comparison of the swelling of studied adsorbents showed increasing rigidity of the hybrid materials over the modified chitosan (see Figure S2 in Paper III), which can be attributed to the networking between silica and chitosan moieties (see Figure 6 and ref. [146]).
4.4 Modeling adsorption kinetics
4.4.1 Pseudo-second-order model
As presented in section 1.1.8 the PS2 model suggests that the adsorption rate is governed by the surface reaction. In papers I and II we applied linear fittings of both PS1 and PS2 models and found that the PS2 model sufficiently described the adsorption kinetics of modified silica gels and chitosans. In papers III and V non-linear regression was used instead. For comparison, both linear and non-linear fittings of PS2 model were conducted for Co(II) adsorption by all the studied adsorbents and results are shown in Table 11. For clarity, Table 11 shows results only for one initial concentration of Co(II) for each of the adsorbent and the results obtained for the other studied metals (Papers I-III) and Co(II)EDTA complex (Paper V) are not presented.
Table 11. Comparison of linear and non-linear regression of PS2 model for Co(II) adsorption by EDTA/DTPA-functionalized adsorbents. Dose: 2 g/L, pH: 2 for functionalized chitosans and pH:
3 for the other adsorbents. Uncertainty of the parameters obtained by Origin. Total differential used for linear equations.
aLinear data taken from Papers I and II, non-linear data recalculated
bNon-linear data taken from Paper III, linear data recalculated
Both linear and non-linear fittings provided similar qe values, which were also close to those obtained experimentally. In most cases, however, non-linear fitting provided rate constants around two times higher than linear fitting. In addition, the correlation coefficients were lower for non-linear fitting, indicating that the PS2 model might not be the best one for describing kinetic data. The differences between linear and non-linear fitting results may arise from the appearance of variable t on the both sides of Eq. (42). Despite that, calculated PS2 rate constants correlated well with the observations achieved in section 4.2.2 predicting the highest rate constants for the smaller particles and the highest ligand loading owing EDTA-chitosan. On the other hand, low adsorption kinetics for DTPA-chitosan can be attributed to its crosslinked structure.
In Paper V, the PS2 model was also applied to Co(II)EDTA adsorption by DTPA-silica gel and –chitosan at different temperatures. The first interesting observation was that we obtained
linear non-linear
Adsorbent C0
(mmol/L) qe,exp
(mmol/g) qe
(mmol/g) k2
(g/mmolmin) R2 qe
(mmol/g) k2
(g/mmol min) R2 EDTA-silica gel
5-20a 1.31 0.25 0.25 ± 0.01 0.36 ± 0.09 1.000 0.27 ± 0.01 1.03 ± 0.11 0.992 EDTA-silica gel
40-63a 1.31 0.26 0.27 ± 0.01 0.06 ± 0.02 0.999 0.25 ± 0.01 0.11 ± 0.02 0.957 EDTA-silica gel
63-200a 1.31 0.24 0.24 ± 0.01 0.05 ± 0.02 0.999 0.22 ± 0.01 0.09 ± 0.02 0.960 DTPA-silica gel
5-20a 1.31 0.24 0.24 ± 0.01 0.54 ± 0.24 1.000 0.24 ± 0.01 1.27 ± 0.12 0.997 DTPA-silica gel
40-63a 1.31 0.27 0.27 ± 0.01 0.06 ± 0.03 0.998 0.24 ± 0.01 0.15 ± 0.03 0.958 DTPA-silica gel
63-200a 1.31 0.26 0.26 ± 0.01 0.06 ± 0.02 1.000 0.24 ± 0.01 0.11 ± 0.02 0.955 EDTA-chitosana 1.64 0.70 0.70 ± 0.01 0.27 ± 0.08 1.000 0.71 ± 0.01 0.16 ± 0.02 0.993 DTPA-chitosana 1.64 0.71 0.72 ± 0.01 0.03 ± 0.01 1.000 0.70 ± 0.02 0.03 ± 0.01 0.989 EDTA-Chi:TEOS
2:60b 1.21 0.22 0.22 ± 0.01 0.17 ± 0.04 1.000 0.21 ± 0.01 0.26 ± 0.05 0.963 EDTA-Chi:TEOS
2:30b 1.15 0.41 0.41 ± 0.01 0.10 ± 0.02 1.000 0.38 ± 0.01 0.22 ± 0.04 0.964 EDTA-Chi:TEOS
2:15b 1.15 0.44 0.44 ± 0.01 0.11 ± 0.03 0.999 0.42 ± 0.01 0.22 ± 0.03 0.976
greatly improved non-linear fitting results for chelated Co(II) than for free Co(II) in the case of DTPA-silica gel (Figure 3a and Table 2 in Paper V), which was attributed to the direct chemical reaction of Co(II)EDTA with the outermost DTPA surface groups. Free Co(II) was able to diffuse inside the mesoporous structure of modified silica gel, however, which worsened the PS2 fitting. A clear increase of the PS2 rate constants with increasing temperature also supported the PS2 model applicability for Co(II)EDTA adsorption [64].
4.4.2 Intraparticle diffusion model
Intraparticle diffusion model (Eq. 44) was used in this study since most of the studied adsorbents had a mesoporous structure. Results for modified chitosan and hybrid materials can be found in Papers II, III, and V. For comparison, diffusion rate constants were determined for the modified silica gels as well and are compared to the other studied adsorbents in Table 12. As in Table 11, only results for one initial Co(II) concentration for each of the adsorbent are shown.
Table 12. Diffusion rate constants obtained from intraparticle diffusion plots for Co(II) adsorption by EDTA/DTPA-functionalized adsorbents. Dose: 2 g/L, pH: 2 for functionalized chitosans and pH: 3 for the other adsorbents. Uncertainty of the parameters obtained by Origin.
Adsorbent C0
(mmol/ L)
kdif,1
(mmol/g min1/2)
kdif,2
(mmol/g min1/2)
kdif,3
(mmol/g min1/2)
kdif,4
(mmol/g min1/2) EDTA-silica gel
5-20a 1.31 0.056 ± nd 0.0054 ± 0.0016 0.0012 ± 0.0001 0.00014 ± 0.00004 EDTA-silica gel
40-63a 1.31 0.022 ± 0.002 0.0077 ± 0.0006 0.0019 ± 0.0001 0.00001 ± 0.00001 EDTA-silica gel
63-200 a 1.31 0.018 ± 0.001 0.0052 ± 0.0001 0.0020 ± 0.0001 0.00070 ± 0.00010 DTPA-silica gel
5-20 a 1.31 0.057 ± nd 0.0176 ± 0.0008 0.0027 ± 0.0002 0.00015 ± 0.00006 DTPA-silica gel
40-63 a 1.31 0.023 ± 0.003 0.0059 ± 0.0005 0.0018 ± 0.0002 0.00081 ± 0.00045 DTPA-silica gel
63-200 a 1.31 0.023 ± 0.001 0.0071 ± 0.0002 0.0023 ± 0.0001 0.00040 ± 0.00014 EDTA-chitosanb 1.64 0.118 ± nd 0.0583 ± 0.0010 0.0003 ± 0.0001
DTPA-chitosanb 1.64 0.054 ± 0.010 0.0188 ± 0.0018 0.0025 ± 0.0006 EDTA-Chi:TEOS
2:60b 1.21 0.044 ± nd 0.0104 ± 0.0013 0.0039 ± 0.0004 0.00047 ± 0.00018 EDTA-Chi:TEOS
2:30b 1.15 0.060 ±0.001 0.0113 ± 0.0039 0.0048 ± 0.0008 0.00076 ± 0.00001 EDTA-Chi:TEOS
2:15b 1.15 0.071 ± nd 0.0247 ± 0.0029 0.0050 ± 0.0005 0.00003 ± 0.00001 aCalculated for comparison bTaken from Papers II and III, nd = not determined, line drawn from the origin to the first experimental point.
In Table 12, the first diffusion constant (kdif,1) can be attributed to the boundary layer or external film diffusion and the remaining constants to the diffusion in macro/meso/micro pores [80]. The kdif,1 visibly increased with decreasing particle size in modified silica gels, which can be attributed to the smaller diffusion layer thickness of smaller particles [147]. Furthermore, a linear relationship was seen between the concentration and kdif,1 (see Papers II, III, and V), which is consistent with the concept of surface “film diffusion” [148]. For hybrid materials, the fastest external film diffusion occured for the material with the highest ligand loading. In addition, the higher amount of active sites seemed to accerelate pore diffusion. Comparison of diffusion rate constants of modified silica gels and hybrid materials suggests that faster diffusion inside the pores was accomplished for materials with larger pore sizes (see Table 8).
In Paper II, we assigned different regions of intraparticle diffusion plots obtained for EDTA- and DTPA-chitosan to diffusion in meso- and micropores. The SEM-images obtained later, however, showed the non-porous structure of modified chitosans (Figure 7e) and measurements of surface properties a possible presence of macropores (Table 8). Therefore, the diffusion constant kdif,2 in this case should instead be assigned to the diffusion of metals in macropores or in regions, where active sites were harder to reach by metal ions due to the crosslinking between surface groups (see sections 4.2.1, 4.2.2).
Besides these observations, significance of pore diffusion was seen in the adsorption of Co(II)EDTA chelates by DTPA-functionalized silica gel and chitosan (Paper V). These results indicated that the large Co(II)EDTA molecules could not diffuse inside the mesopores of DTPA-silica gel as in the case of free Co(II) ions. For DTPA-chitosan, however, intraparticle diffusion plots showed different linear regions indicating diffusion also in the interior parts (macropores, crosslinked sections) of the adsorbent.