As shown in Figure 2, different times were required for the adsorption of biphenyl and phenanthrene onto the four different types of sorbents to reach equilibrium. The kinetic data plotted in Figure 2 were modeled using Equations 1 and 2. The plots of ln (qe − q) versus t from the kinetic data were nonlinear (data not shown), indicating that the PFOM is not suitable for the simulation of these data. The PFOM has been widely used in the case of one-site-occupancy adsorption (that is, one adsorbed molecule occupies one adsorption site) 22. As explained by Rudzinski and Plazinski 22, in the case of one-site-occupancy adsorption, the Lagergren kinetic equation leads to Langmuir equation at equilibrium. In our previous work 10, we demonstrated that the adsorption of organic compounds on the adsorbents used in the present study did not follow the Langmuir model but was fitted well with the Freundlich model, because the adsorption sites on these carbons are not energetically homogeneous. The empirical Freundlich equation well described the general features of the adsorption systems with different geometric and energetic surface heterogeneity.
Figure 2. Uptake versus time profiles of biphenyl (BP) and phenanthrene (PNT) on the four carbons. ACF10 = phenol formaldehyde-based activated carbon fiber; HD4000 = coal-based granular activated carbon; SWNT = single-walled carbon nanotube; MWNT = multiwalled carbon nanotube; S = sonication; L = low initial concentration; LS = low initial concentration coupled with sonication; H = high initial concentration; HS = high initial concentration coupled with sonication.
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All t/q versus t plots showed very good linearity (data not shown). As summarized in Table 1, the regression coefficients of t/q versus t plots were higher than 0.99 for the adsorption of both compounds on all carbons, indicating that the PSOM provided good fits to the experimental data.
Table 1. The pseudo-second order kinetic parameters for biphenyl (BP) and phenanthrene (PNT) adsorption on the four carbons
The better description of the adsorption kinetic data with the PSOM rather than with the PFOM might be because of the mathematical nature of the PSOM, and may not indicate a general pseudo-second order adsorption process 24. However, the successful description of the kinetic data with the PSOM provided some valuable insight into the adsorption process. The parameters in Table 1 demonstrate several factors.
First, ultrasonication of the CNT suspensions significantly accelerated their adsorption kinetics but had no effect on their equilibrium capacities.
Second, the k2 and h values showed different orders for the four carbons. Because k2 is dependent on solid phase concentration, the comparison of kinetic processes based on k2 values alone can be problematic 24. Therefore, a modified parameter, k2* (defined as k2qe, /h), was used to describe and compare adsorption kinetics 24. The modified pseudo-second order rate constants (k2* values) of the four carbons followed the order of MWNT > SWNT > ACF10 ≈ HD4000, indicating that the sorbents with a larger pore size and higher external surface areas possess faster sorption kinetics.
Third, the adsorption rate was faster at higher concentrations in comparison with low concentrations, as shown by all three parameters, k2, h, and k2*, of phenanthrene adsorption on MWNTs performed at two concentration levels. This phenomenon might be explained by the external mass transfer process—the diffusion of phenanthrene through the film surrounding the MWNT particles to the exterior surface of the MWNT is directly proportional to the linear concentration gradient across the film. A reverse trend was reported for the adsorption of 17α-ethinyl estradiol and bisphenol A on an MWNT and an SWNT; that is, a negative relationship existed between the k2* and the qe of 17α-ethinyl estradiol and bisphenol A on the CNT 18. The authors explained that porelike structures (inner pores and interstitial channels) may not contribute to the overall adsorption; therefore, diffusion was not a rate-controlling step in the adsorption of 17α-ethinyl estradiol and bisphenol A on CNT 18. The MWNT used in the above-mentioned work and in the present study have nearly identical structural characteristics. This indicates that both adsorbent and adsorbate properties should be considered in the investigation of adsorption kinetics. The two organic compounds selected in the present study do not have functional groups and have a small molecular size, making them ideal probe molecules to investigate adsorption kinetics. The role of diffusion in the adsorption of the organic compounds on the four types of carbons will be revisited in the next section.
Finally, the adsorption rates on CNTs were faster for biphenyl than phenanthrene. The three-dimensional molecular structures of the organic compounds, as discussed in the literature 18, could be attributed to the difference in their adsorption kinetics. Molecular structures determine the molecular diffusivity and hydrophobicity. Molecular diffusivity is inversely proportional to one-third the power of molar volume. The molar volume of biphenyl is smaller than that of phenanthrene (155.45 vs 167.67 cm3/mol), giving an advantage to biphenyl over phenanthrene in their adsorption on CNTs. Hydrophobic effect plays a significant role in the adsorption of organic compounds on CNTs. The qe values of biphenyl on CNTs were lower than those of phenanthrene at the same initial concentrations, because the hydrophobicity of biphenyl is lower than that of phenanthrene (the logarithms of octanol–water distribution coefficients of biphenyl and phenanthrene are 3.98 and 4.68, respectively). Molecular diffusivity impacts the rates in steps one to three of the adsorption process, whereas hydrophobicity is predominant during the final surface reaction step. Therefore, the faster adsorption of the nonplanar biphenyl than the planar phenanthrene indicated that the adsorption process of the two organic compounds on CNTs was diffusion-controlled and that their molecular configurations played a role in the adsorption kinetics.
Adsorption rate-limiting mechanism
The IPDM modeling of experimental data is shown in Figure 3. Piecewise linear regression method has been applied in the model fitting of these data. The linear segments were numbered as one to three to indicate the different adsorption stages. An obvious difference was seen between the Weber-Morris plots of biphenyl on CNTs and those on activated carbons. The plots of biphenyl on CNTs had positive intercepts, whereas the plots for biphenyl on activated carbons passed through the origin, suggesting that different mechanisms were involved in the adsorption. Various observations and interpretations in the application of IPDM to kinetic data 25 have been reported as follows: the regression of q versus t1/2 is linear and passes through the origin, in which intraparticle diffusion is the sole rate-limiting step; the regression of q versus t1/2 is linear, but it does not pass through the origin, suggesting that the adsorption involves intraparticle diffusion but it is not the only rate-limiting step; and the q versus t1/2 plot is multilinear, suggesting that two or more steps are involved in the process.
Figure 3. Weber-Morris plots of biphenyl (BP) and phenanthrene (PNT) adsorption on the four carbons. The linear segments are numbered with 1, 2, and 3 to indicate the different stages. Dots = experimental data; lines = intraparticle diffusion modeling; ACF10 = phenol formaldehyde-based activated carbon fiber; HD4000 = coal-based granular activated carbon; SWNT = single-walled carbon nanotube; MWNT = multiwalled carbon nanotube; S = sonication; L = low initial concentration; LS = low initial concentration coupled with sonication; H = high initial concentration; HS = high initial concentration coupled with sonication.
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The intercept θ has been used widely as an index reflecting the thickness of the boundary diffusion layer 24, 26–28. However, interpretations have not been consistent in the literature. McKay et al. 26 stated that “extrapolation of the linear portions of the plots back to the axis provides intercepts which are proportional to the extent of the boundary layer thickness, i.e., the larger the intercept, the greater the boundary layer effect.” This is based on experiments performed at different mixing intensities, in which increased agitation led to decreased intercept on the time axis of the Weber-Morris plot. Because the effect of an increased mixing rate is to decrease the boundary layer and therefore the film resistance to external mass transfer surrounding the adsorbent particles, the results indicated that the boundary layer had a retardation effect on the intraparticle diffusion. However, the intercepts referred by the researchers were on the time axis, and the intercepts on the q axis were negative. McKay and co-workers' interpretation has been widely cited by other researchers. However, in some studies, the intercepts on q axis reported in the literature were positive 27, 28. In a recent report 28, the intercept values (1.935–27.296 mg/g) were found to increase with increasing temperature (273–333 K), and the increase in intercept was attributed to an enhanced boundary layer effect. In fact, this is probably because of an increase in the external mass transfer with temperature rather than the increase in the thickness of the boundary layer, because increasing temperature should promote external mass transfer rather than increasing the thickness of the boundary layer; that is, the larger the positive q intercept, the larger the contribution of external surface adsorption or instantaneous adsorption. Conversely, a negative q intercept indicates the boundary layer effect, as observed by McKay et al. 26.
The Weber-Morris plots of biphenyl adsorption on activated carbons, though not linear, passed through the origin, suggesting that intraparticle diffusion is a rate-limiting step in the adsorption of biphenyl to activated carbons. The positive intercepts of the Weber-Morris plots of biphenyl/phenanthrene adsorption on CNTs demonstrated that intermediate adsorption occurred in the adsorption of organic compounds onto CNTs. For adsorption without sonication, the kinetic data could be divided into three stages, whereas the adsorption on CNTs after sonication was composed of two (for MWNTs) or three (for SWNTs) stages. Moreover, the θ values of stage one in biphenyl and phenanthrene adsorption on sonicated CNTs were significantly higher than those on unsonicated CNTs. Before sonication, both the SWNT and the MWNT had agglomerated structures. Sonication dispersed the MWNT in the solution well, whereas no observable change was seen for the SWNT. The possible reason might be that the sonication treatment used in the present study was not powerful enough to overcome the van der Waals forces among the SWNT, which were higher than those among the MWNT. The change in the aggregation structure of the MWNT did not impact its adsorption capacities for the two organic compounds; however, it altered the relative contributions of the four different adsorption sites. More outermost surface and inner cavities were available, whereas peripheral grooves and interstitial channels were lost after sonication. Because the molecular sizes of the studied organic compounds were several times smaller than the inner diameter of the MWNT, the inner cavities of the MWNT with a cylindrical shape acted more as a curved surface rather than as pores for the adsorption of organic compounds. The interstitial channels were porelike structures, which may contribute to intraparticle diffusion in the adsorption process. Thus, the disappearance of stage 2 in the sonicated MWNT solutions suggested that stage 2 was attributable to intraparticle diffusion. Although the inner cavities of the SWNT were slightly larger than the organic compound in terms of size and theoretically could serve as porelike adsorption sites, the intraparticle diffusion in the adsorption on the SWNT occurred mainly in the interstices rather than in the inner cavities, because most of the individual SWNTs were close-ended, as characterized in our previous work 9. Thus, the difference between the adsorption sites of CNTs and activated carbons was that outer surface predominates in CNTs, whereas the space in the inner pores constitutes the main available adsorption sites in activated carbons. As a consequence, the adsorption of biphenyl on activated carbons was dominated by intraparticle diffusion, whereas intermediate adsorption played an important role in the adsorption of biphenyl on CNTs.