3.2.3. Adsorption Kinetics

It was perceived from the adsorption kinetics (Figure 10A) that the adsorption of PGA by CLCNF-3 was a very fast process, and the adsorption saturation was almost reached within 2 min of the start of adsorption. Such a rapid adsorption process was not unexpected, as nanofiber adsorbents usually exhibited fast adsorption responses to water contaminants [17,20]. CLCNF-3 exhibited such a strong and fast adsorption capacity because of its large surface area and abundant quaternary ammonium groups as binding sites to adsorb PGA. After the equilibration time of 180 min, the surface of the adsorbent became saturated.

**Figure 10.** (**A**) Adsorption kinetics of PGA on adsorbents from CLCNF-3 (pH = 7; adsorbent dose, 0.5 g/L; initial concentration, 400 mg/L); Fits to (**B**) pseudo-first-order (PFO), (**C**) pseudo-secondorder (PSO), and (**D**) intraparticle diffusion (IPD) kinetic models.

By fitting pseudo-first-order (PFO) and pseudo-second-order (PSO) kinetic models to the experimental data (Figure 10B,C), this allows further description and understanding of the adsorption process. The equations of these two models are as follows [42]: PFO:

*log*(*Qe* <sup>−</sup> *Qt*) <sup>=</sup> *logQe* <sup>−</sup> *<sup>K</sup>*<sup>1</sup> 2.303 *<sup>t</sup>* (3)

PSO:

$$\frac{t}{Q\_t} = \frac{1}{K\_2 Q\_\varepsilon^2} + \frac{t}{Q\_\varepsilon} \tag{4}$$

where *Qt* (mg/g) and *Qe* (mg/g) represent the amounts adsorbed at time *t* (min) and at equilibrium, respectively, and *<sup>K</sup>*<sup>1</sup> (min–1) and *<sup>K</sup>*<sup>2</sup> [mg/(g·min)] represents the rate coefficients for the PFO and PSO kinetic models, respectively.

The kinetic parameters calculated from the fitted equations in these figures along with the regression coefficients are listed in Table 2. The R<sup>2</sup> value of the PSO rate equation (0.9999) is higher than that of the PFO rate equation (0.9727), indicating that the process of PGA adsorption by CLCNF-3 is more consistent with PSO kinetics. The excellent applicability of the PSO model to the adsorption kinetics of PGA onto CLCNF-3 implies that the ratecontrolling step of adsorption is the chemisorption between adsorbent and adsorbate.

**Table 2.** Parameters of pseudo-first-order, pseudo-second-order and intraparticle diffusion for PGA adsorption.


Since neither PFO nor PSO kinetic describe the process of diffusion, the Weber-Morris intraparticle diffusion model was also used to explain the adsorption process. The Weber-Morris intraparticle diffusion equation is as follows [45]:

$$Q\_t = K\_i t^{0.5} + \mathcal{C} \tag{5}$$

where *Ki* [mg/(g·min0.5)] is the rate constant of intraparticle diffusion; *<sup>C</sup>* is the constant related to the thickness of the boundary layer, which is in direct ratio to the effect of the boundary layer.

The fitted curve of the Weber-Morris intraparticle diffusion model is shown in Figure 10D, and the parameters are listed in Table 2. According to this model, the plots of *Qt* versus *t* 0.5 must pass through the origin and yield a straight line. However, in this study, the plots of Qt versus *t* 0.5 were not linear over the whole time range, and the fit was very low. This result shows that the Weber-Morris intraparticle diffusion model was not suitable for predicting the adsorption kinetics of PGA onto CLCNF-3 over the whole range. This suggests that intraparticle diffusion is not the rate-limiting step in the adsorption process [53].

## 3.2.4. Adsorption Isotherm

As the concentration of PGA in wastewater is often fluctuating, the adsorption capacity of the adsorbent at different concentrations was investigated. Figure 11 illustrates the adsorption of PGA as a function of initial concentration. Figure 11A shows the reduction in the percentage adsorption removals of PGA onto CLCNF-3 with increasing initial concentrations of PGA. This reduction can be attributed to the finite number of active sites available on CLCNF-3 that were occupied by adsorbed PGA, subsequently leading to a decrease in PGA adsorption. On the other hand, it was found that the maximum adsorption capacity of CLCNF-3 increased with increasing initial concentration until the initial concentration of PGA was increased to 550 mg/L. This is because a higher concentration provides a driving

force to overcome all the resistances of PGA between the aqueous and solid phases, thus increasing adsorption; moreover, as the initial concentration increased, so did the number of collisions between PGA and CLCNF-3, thus improving the adsorption process.

**Figure 11.** (**A**) Effects of initial concentration on the adsorption of PGA onto CLCNF-3 (pH = 7; adsorbent dose, 0.5 g/L; stirring time, 6 h; concentration range, 400–800 mg/L); (**B**–**D**) Fits to (**B**) nonlinear adsorption isotherms, (**C**) the Langmuir isotherm, and (**D**) the Freundlich isotherm.

The experimental data were fitted to the Langmuir model [54], which applies to monolayer adsorption, and the Freundlich model [55], which applies to multilayer adsorption, in order to identify the mechanisms of contaminant removal (Figure 11B–D). The respective equations for these models are:

Langmuir model:

$$\frac{C\_e}{Q\_t} = \frac{C\_e}{Q\_m} + \frac{1}{K\_L Q\_m} \tag{6}$$

Freundlich model:

$$
\ln Q\_{\mathcal{C}} = \ln k\_F + \frac{\ln \mathcal{C}\_{\mathcal{C}}}{n} \tag{7}
$$

where *Ce* and *Qe* are the PGA solution concentration (mg/L) and adsorption capacity (mg/g) at equilibrium, respectively, and *Qm* is the theoretical saturation capacity (mg/g). *KL* and *KF* are the Langmuir adsorption constant (L/g) and the Freundlich adsorption constant (L/mg), respectively, and *n* is the heterogeneity factor for the adsorption.

The fitting parameters are presented in Table 3. The R<sup>2</sup> value for the Langmuir model is 0.9994 compared to only 0.5520 for the Freundlich model, demonstrating that the adsorption process is more consistent with monolayer adsorption without lateral interactions between adsorbed molecules. Moreover, the maximum experimental adsorption value (i.e., *Qe* = 1054 mg/g) is very close to the calculated value of *Qm*, the maximum theoretical adsorption value of PGA uptake for CLCNF-3.


**Table 3.** Parameters of the Langmuir and Freundlich Adsorption Isotherms for PGA adsorption.

The value for *KL* can be calculated from the Langmuir equation which can then be used to determine the separation factor *RL* using:

$$R\_L = \frac{1}{1 + K\_L C\_0} \tag{8}$$

The relationship between the initial concentration *C0* and the separation factor *RL* is shown in Figure S2. *RL* can be used to determine the favorability and feasibility of an adsorption process. An *RL* value between 0 and 1 is favorable for adsorption and values greater than 1 are adverse for adsorption [56]. The *RL* values for CLCNF-3 are all between 0 and 1 indicating that the adsorption of PGA by CLCNF-3 is a favorable process. It should be noted that as the initial concentration increased from 400 to 800 mg/L, the *RL* value gradually decreased from 0.0030 to 0.0015, indicating that higher concentrations promote PGA adsorption by CLCNF-3.
