## 2 Materials and Methods
### Stability Analysis and Regeneration Studies of La-EPRC Particles  
#### 2.4.1 Material Adsorption Stability  
The adsorption stability of the material was assessed by experimentally determining the desorption of adsorbed phosphorus elements from La-EPRC particles in room temperature water, high-temperature hot water, and sulfuric acid solution.  
1. Room Temperature Water Desorption  
The following amounts of 1 g P/L phosphorus standard reserve solution were taken: 1.25 mL, 2.5 mL, 5 mL, 12.5 mL, 25 mL, 37.5 mL, and 50 mL. These were diluted with deionized water to 250 mL, creating concentrations of 5 mg P/L, 10 mg P/L, 20 mg P/L, 50 mg P/L, 100 mg P/L, 150 mg P/L, 200 mg P/L. A total of 3 g of La-EPRC particles was weighed into each conical flask and placed in a shaker (25 \(\pm\) 1 \({}^{\circ}\)C, 150 \(\pm\) 5 r/min). After 48 h of continuous shaking, the samples were taken and filtered through a 0.45 \(\upmu\)m filter, and absorbance was measured using ammonium molybdate spectrophotometry to calculate residual phosphorus concentration and the adsorption amount of the adsorbent.  
After adsorption, La-EPRC particles were washed 3-5 times with water and air-dried. The dried particles were placed in seven 250 mL conical flasks sequentially, with 250 mL of deionized water added simultaneously. The particles were subjected to constant shaking in a shaker (25 \(\pm\) 1 \({}^{\circ}\)C, 150 \(\pm\) 5 r/min) for 48 h to desorb the material. After the reaction was halted, samples were collected, and after filtration for absorbance determination, the desorbed material amount and desorption rate were calculated.  
Description in High-Temperature Water  
The following amounts of 1 g P/L phosphorus standard reserve solution were taken: 1.25 mL, 2.5 mL, 5 mL, 12.5 mL, 25 mL, 37.5 mL, and 50 mL. These were diluted with deionized water to 250 mL, creating concentrations of 5 mg P/L, 10 mg P/L, 20 mg P/L, 50 mg P/L, 100 mg P/L, 150 mg P/L, and 200 mg P/L. A total of 3 g of La-EPRC particles was weighed for each flask, placed in a shaker (25 \(\pm\) 1 \({}^{\circ}\)C, 150 \(\pm\) 5 r/min), and sampled after the adsorption reaction reached equilibrium at 48 h. The samples were filtered, absorbance was measured, and phosphorus concentration and the adsorption amount of the adsorbent were calculated.  
After adsorption, La-EPRC particles were rinsed 3-5 times with water and dried naturally indoors. The dried particles were placed into 7 sets of 250 mL conical flasks, adding 250 mL of deionized water simultaneously. The particles were placed in a shaker with constant shaking (25 \(\pm\) 1 \({}^{\circ}\)C, 150 \(\pm\) 5 r/min), desorption was conducted for 48 h, the reaction was stopped, the supernatant was sampled, the samples were filtered, absorbance was determined, and the material desorption amount and desorption rate were calculated.  
Description in Sulfuric Acid Solution  
A total of 5 mL of 1 g P/L phosphorus standard reserve solution was taken and distributed into five conical flasks. Each flask was diluted to 250 mL with deionized water to create a 20 mg P/L dilute solution. A total of 3 g of La-EPRC particles was weighed into each flask, placed in a shaker with constant shaking (25 \(\pm\) 1 \({}^{\circ}\)C, 150 \(\pm\) 5 r/min), and sampled after the 48 h adsorption reaction reached equilibrium. The samples were filtered, absorbance was measured, and phosphorus concentration and the adsorption amount of the adsorbent were calculated.  
After adsorption, La-EPRC particles were rinsed 3-5 times with water and dried naturally indoors. Sulfuric acid solutions with concentrations of 0.01 mol/L, 0.1 mol/L, 0.5 mol/L, and 1.0 mol/L were prepared. The dried particles were sequentially placed into five 250 mL conical flasks and desorbed in a shaker for 48 h. The reaction was stopped, sampled, absorbance after filtration was measured, and the amount of material desorbed and desorption rate were calculated.