## 3 Results and Discussion
### Kinetics  
Figure 8 shows the kinetic and intraparticle diffusion fitting curves of Ni\({}^{2+}\) adsorption by nZVI@ATP. The adsorption capacity of the nZVI@ATP on Ni\({}^{2+}\) in the solution gradually tended to equilibrium after 6 h (Figure 8a). The adsorption process was divided into three stages: 0-1 h was the fastest stage; 1-6 h was a slow stage; and 6-12 h was a stage wherein adsorption gradually tended to equilibrium. At the beginning of the adsorption, numerous active sites on the surface of the nZVI@ATP and the high concentration of Ni\({}^{2+}\) in the solution resulted in the fastest reaction rate. Further, as the reaction proceeded, the number of free active sites on the surface of the composite material gradually decreased; the pores on the material surface were blocked; and the adsorption rate gradually declined, which gradually attained equilibrium after 6 h.  
The time dependence curves of the adsorption capacity of nZVI@ATP on Ni\({}^{2+}\) were fitted using pseudo-first-order, PSO, and Weber-Morris models. The fitted equations are shown in Equations (4)-(6), and the fitted parameters are listed in Tables 2 and 3. The correlation coefficient R\({}^{2}\) of the pseudo-first-order kinetics was 0.7830, and the adsorption capacity gradually deviated from the actual capacity after 1 h as the reaction proceeded, indicating that the pseudo-first-order kinetics favored only the early stage of the reaction. The correlation coefficient of then PSO kinetics was 0.9729, significantly exceeding that of  
Figure 8: Fitting curves of Ni\({}^{2+}\) adsorption kinetics by nZVI@ATP (**a**); and intraparticle diffusion (**b**). Figure 7: Effect of pH on Ni\({}^{2+}\) adsorption by nZVI@ATP (initial concentration of 200 mg/L; temperature of 298 K; dosage of 1 g/L; and stirring time of 12 h). the quasi-primary kinetics. In comparison, the equilibrium adsorption capacity obtained by fitting the quasi-secondary kinetic model was 144.9593 mg/g, which is comparable with the actual adsorption capacity of 143.8667 mg/g, indicating that quasi-secondary kinetics can better describe the adsorption of Ni\({}^{2+}\) by composites and that the adsorption rate is mainly chemisorption [30; 31; 32; 33]. To gain a clearer understanding of the adsorption performance of nZVI@ATP, we compared its adsorption efficiency with that of other materials for Ni\({}^{2+}\). Table 4 presents a comparison of the adsorption performance of different materials on Ni\({}^{2+}\). The advantage of nZVI@ATP over other adsorbents in removing the Ni\({}^{2+}\) from solution suggests that nZVI@ATP has a greater potential for the removal of heavy metals. The data were fitted using the Weber-Morris model, and the fitting results and parameters are shown in Figure 8b and Table 4. It can be learned that the removal process of Ni\({}^{2+}\) by nZVI@ATP is divided into three stages. The surface diffusion process is from 0 to 1 h, which is the diffusion of Ni\({}^{2+}\) to the surface of the material through the thin film layer on the surface of the material. The intra-particle diffusion process is between 1 and 4 h, which is the diffusion of Ni\({}^{2+}\) to the interior of the material, at which point the rate of adsorption slows down and the majority of the active sites are on the outer surface of the nZVI@ATP. When the adsorption rate slows down and most of the active sites on the outer surface of the nZVI@ATP are occupied, the Ni\({}^{2+}\) gradually diffuses to the inner surface of the particles, occupying the active sites inside the particles. When it gradually occupies the adsorption active center in the pores of the nZVI@ATP, the adsorption rate in the pores tends to zero and reaches the state of adsorption equilibrium, i.e., the third stage. The surface diffusion rate constant R\({}_{1}\)\({}^{2}\) was 0.9918, which was significantly higher than that of R\({}_{2}\)\({}^{2}\) and R\({}_{3}\)\({}^{2}\). The results indicated that the surface diffusion process could remove Ni\({}^{2+}\) faster in the early stage of the reaction.