3.2.2. Adsorption Kinetics

Kinetic experiments were carried out on the Bi-MIPs, Bi-NIPs, Si-MIPs and Si-NIPs with a chrysin solution with an initial concentration of 1.0 mg/mL and the results are shown in Figure 5. The adsorption of chrysin on the Bi-MIPs showed excellent characteristics of the adsorption kinetics. The adsorption capability is increased with the increase in the adsorption time, and the adsorption rate decreased gradually with increasing adsorption time. At any time, the Bi-MIPs have the highest adsorption capacity of chrysin compared with the Bi-NIPs. As for the Bi-MIPs, the adsorption process can be divided into the fast adsorption stage (0–105 min) and the slow adsorption stage (105–240 min). The adsorption capacity in the fast adsorption stage accounted for 76% of the equilibrium adsorption capacity. As for the Si-MIPs, the adsorption capacity in the fast adsorption stage (0–75 min) accounted for 64.7% of the equilibrium adsorption capacity. The chrysin absorption capacity of Bi-MIPs reached equilibrium after 240 min, which indicates that the specific cavities of the adsorbent formed by binary functional monomers promote the adsorption effect. At the same time, the chrysin absorption capacity of the Bi-MIPs, Bi-NIPs, Si-MIPs, Si-NIPs and MIPs exceeds the NIPs, which further indicates that Si-MIPs and Bi-MIPs have successfully synthesized imprinted pores.

The pseudo-first-order (PFO) and pseudo-second-order (PSO) kinetic models were used to investigate the kinetic behaviors of the Bi-MIPs, Bi-NIPs, Si-MIPs and Si-NIPs during chrysin adsorption. The kinetic data of different initial melanoidin concentrations were fitted using the following models [50–54].

PFO kinetic equation:

$$
\ln(\mathbf{Q\_c - Q\_t}) = \ln \mathbf{Q\_c - \frac{\mathbf{k\_3}}{2.303}} \tag{6}
$$

PSO kinetic equation:

$$\frac{\text{t}}{\text{Q}\_{\text{t}}} = \frac{1}{\text{k}\_{\text{4}}\text{Q}\_{\text{e}}^{2}} + \frac{1}{\text{Q}\_{\text{e}}} \tag{7}$$

where k3 (1/min) represents the rate constant of PFO kinetic adsorption, k4 (mg/(g·min)) represents the rate constant of PSO kinetic adsorption, Qt represents the amounts of chrysin adsorbed (mg/g) at time t, and Qe represents the amounts' equilibrium time.

**Figure 5.** (**a**) Adsorption kinetics curves of the Bi-MIPs, Bi-NIPs, Si-MIPs and Si-NIPs; (**b**) PFO kinetic mode of the Si-MIPs and Si-NIPs; (**c**) PSO kinetic mode of the Si-MIPs and Si-NIPs; (**d**) PFO kinetic mode of the Bi-MIPs and Bi-NIPs; (**e**) PSO kinetic mode of the Bi-MIPs and Bi-NIPs.

The experimental data were fitted to the PFO kinetic and PSO kinetic to obtain the corresponding fitting curves (Figure 5) and kinetic parameters (Table 2). It is known from Table 2 that the correlation coefficient (R2) values of the PSO and PFO kinetic models of the Bi-MIPs are R<sup>2</sup> = 0.9903 and R2 = 0.9153, respectively. The PSO kinetic model creates better experiments with the adsorption behavior of chrysin onto the Bi-MIPs than the PFO kinetic model; this phenomenon also indicates that chemisorption is the principal mechanism involved in the sorption process. The results indicate that the Bi-MIPs are beneficial to the adsorption of chrysin, and these results further prove the potential applications in the separation of chrysin by the Bi-MIPs.


**Table 2.** Kinetic data of the PFO and PSO kinetic models.

3.2.3. Adsorption Thermodynamics

Adsorption isotherm experiments were performed at the same initial chrysin solution and at different temperatures of 10, 20, 30, 40 and 50 ◦C. The fitting results of the adsorption isotherms are presented in Figure 6. As shown in Figure 6a, the adsorption ability of chrysin by the Bi-MIPs is the highest, followed by the Si-MIPs. This is due to the specific cavities of the Bi-MIPs and Si-MIPs, which have specific adsorption on chrysin.

**Figure 6.** (**a**) Thermodynamic curves of the Bi-MIPs, Bi-NIPs, Si-MIPs and Si-NIPs; (**b**) Selective adsorption of the Bi-MIPs, Bi-NIPs, Si-MIPs and Si-NIPs.

With the temperature increase from 10 to 30 ◦C, the absorption capacity of the adsorbents increased, which due to increases in temperature accelerate the movement of the molecules in a methanol solution. Therefore, the probability of albumin binding to the adsorbent adsorption site is enhanced. As the temperature increased from 30 to 50 ◦C, the Qe of chrysin on the adsorbents decreased. Due to the hydrogen bonds of the adsorbents being broken with the increase in temperature, the adsorption capacity of chrysin by the adsorbents is weakened. From the point of view of economic and industrial applications, 30 ◦C is chosen as the optimum temperature. The energy consumption of the adsorption process is reduced, which builds the foundation for the large-scale extraction and separation of the binary functional monomer polymers in natural products.
