*3.4. Adsorption Kinetics of Dencichine on the RCMs and RPMs*

The adsorption kinetics curves of dencichine on the RCMs and RPMs at initial concentrations (0.1 mg/mL) are represented in Figure 6a. The adsorption of dencichine on the RCMs and RPMs showed excellent characteristics of the adsorption kinetics, the adsorption capacity increased with the increase in the adsorption time, and the adsorption rate decreased gradually with increasing adsorption time. As for the RPMs, the fast adsorption stage appeared within the first 15 min, while the slow adsorption stage appeared at 15 to 60 min and the adsorption equilibrium appeared after 150 min. As for the RCMs, the fast adsorption stage appeared within the first 45 min, while the slow adsorption stage appeared at 45 to 90 min and the adsorption equilibrium appeared after 240 min. Compared with RPMs, the RCMs have different adsorption kinetics behavior. This is because dencichine molecules are adsorbed on the 4-VP surface of the RPMs and RCMs during the initial stages. Then, over time, it becomes increasingly difficult for the dencichine to enter the RCMs.

**Figure 6.** Adsorption kinetics of dencichine on the RCMs and RPMs. (**a**) Adsorption kinetics curves; (**b**) Pseudo-first-order adsorption kinetics model; (**c**) Pseudo-second-order adsorption kinetic.

To determine the mass transfer mechanisms and rate controlling, adsorption kinetics of dencichine onto the RCMs and RPMs are evaluated using fitting pseudo-second-order (PSO) and pseudo-first-order (PFO) models [49–53].

PFO adsorption kinetics models:

$$
\ln(\mathbf{Q\_e} - \mathbf{Q\_t}) = \ln \mathbf{Q\_e} - \frac{\mathbf{K\_1}}{2.303} \mathbf{t} \tag{7}
$$

PSO adsorption kinetics models:

$$\frac{\text{t}}{\text{Q}\_{\text{t}}} = \frac{1}{\text{K}\_{2}\text{Q}\_{\text{e}}^{2}} + \frac{1}{\text{Q}\_{\text{e}}}\text{t} \tag{8}$$

where Qe represents the adsorbed amount at equilibrium (mg/g), Qt represents the amounts adsorbed at time t (mg/g), K1 represents the PFO adsorption kinetics models rate constant (min<sup>−</sup>1) and K2 represents the PSO adsorption kinetics models rate constant (g/(mg min)).

The corresponding kinetic parameters calculated by Origin are shown in Table 1. The PFO kinetic model is based on the assumption that adsorption controls diffusion and the PSO kinetic model assumes that the adsorption rate is controlled by the chemisorption process.

**Table 1.** Kinetic data of PFO kinetic model and PSO kinetic model.


Figure 6b shows the relationship between ln (Qe − Qt) and time (t), and Figure 6c shows the relationship between t/Qt and time t. It can be seen from the kinetics parameters of both adsorbents presented that the coefficient of determination of PFO kinetics R2 (the RPMs) and R<sup>2</sup> (the RCMs) are 0.9082 and 0.8235, respectively, and that of PSO kinetics R2 (the RPMs) and R<sup>2</sup> (the RCMs) are 0.9999 and 0.9992. The results indicate that the PSO kinetics model fits well with experimental data, and the R2 values of the PSO kinetics model are higher than that of the PFO kinetics model. This phenomenon also indicates that chemisorption is a dominant role in the adsorption process.
