## 3 Results and Discussion
### Characterization of Zr-EPRC
#### 3.2.4 Comparison with EPRC  
Table 6 presents the BET characterization results for Zr-EPRC particles before and after modification, alongside the previous findings for the EPRC particles. The specific surface area, pore volume, average pore diameter, and adsorption capacity are crucial parameters indicating the material's adsorption efficiency. By comparing the data, it becomes apparent that the modification with zirconium oxychloride octahydrate significantly enhances the Zr-EPRC particles' surface area and pore size. Specifically, the specific surface area of Zr-EPRC is 12.43 times greater than that of the original EPRC, and the average pore diameter was triple that of the original. The adsorption capacity of Zr-EPRC was 12.550 mg/g under the experimental conditions at 25 \({}^{\circ}\)C, which was four times higher than that of EPRC. These considerable improvements underscore the enhanced phosphorus adsorption capacity of Zr-EPRC particles, demonstrating their promising potential for practical applications in phosphate removal.  
Figure 11: Zr-EPRC adsorption–desorption isotherm curve.  
Figure 12: Zr-EPRC pore size distribution chart.  
As shown in Figures 13 and 14, the adsorption capacity of the Zr-EPRC particles gradually increased as the concentration of phosphate in the solution increased, ultimately reaching a stable value. Notably, temperature played a pivotal role in influencing the adsorption isotherm. At the same concentration, the adsorption capacity of the Zr-EPRC particles for phosphorus increased significantly with the rising temperature.  
The Langmuir model was applied to fit the isotherm data for the Zr-EPRC particles, and the fitting results are depicted in Figure 13. The correlation coefficients (R\({}^{2}\)) for the Langmuir model, as summarized in Table 7, were consistently higher than 0.990 at different temperatures. This indicates that the Langmuir adsorption model provides a more accurate description of the adsorption process of phosphate via Zr-EPRC particles. The application of [PERSON]'s formula to fit the isothermal adsorption data is illustrated in Figure 14. While the isothermal data can also be adequately fitted using the Freundlich model, the R\({}^{2}\) values for Freundlich (R\({}_{\text{F}}\)\({}^{2}\)) were slightly lower than the R\({}^{2}\) values for Langmuir (R\({}_{\text{L}}\)\({}^{2}\)), suggesting that the Langmuir isothermal adsorption model offers a more precise description of the adsorption process. Consequently, it can be inferred that the adsorption of phosphate via Zr-EPRC particles follows a monolayer adsorption mechanism dominated by chemisorption.  
Table 7 summarizes the values of Q\({}_{\text{m}}\) and K\({}_{\text{L}}\) at different temperatures, along with the corresponding values of K\({}_{\text{F}}\) and 1/n. It is evident that Q\({}_{\text{m}}\) increases significantly with the rising temperature, further confirming the positive impact of temperature on phosphate adsorption. This aligns with the observations made in the adsorption kinetics experiments. Moreover, the consistently observed 1/n values below 1 at all tested temperatures suggest the presence of a chemical affinity between the Zr-EPRC particles and phosphate, which is in accordance with previous findings.  
In summary, the Langmuir adsorption model accurately describes the monolayer adsorption behavior of phosphate via Zr-EPRC particles, with an increasing adsorption capacity at higher temperatures, suggesting chemisorption as the dominant mechanism.