## 3 Results and Discussion
### Zeta Potential and Average Particle Size Analysis
This is attributed to the reduced electrophoretic mobility of the solution with higher abrasive concentrations, leading to a decrease in the zeta potential. Overall, the maximum zeta potential in this experiment was \(-16.950\) mV, indicating an unstable phase; therefore, PEG does not significantly enhance the dispersion stability of the alumina polishing solution. The impact of different abrasive concentrations and PEG concentrations on the average particle size in the polishing solution is shown in Figure 7b. From the graph, it can be observed that, with an increase in abrasive concentration, the average particle size in the polishing solution also increased. As the PEG concentration increased, the average particle size initially decreased, then fluctuated within a small range. The analysis indicates that, when PEG serves as a dispersant, the average particle size distribution is narrower, implying a relatively weak enhancement in the dispersibility of the abrasive particles. Figure 8a demonstrates the impact of phosphoric ester compounds and abrasive concentration on the zeta potential of the polishing solution. From the graph, it is evident that the absolute value of the zeta potential decreased with an increase in abrasive concentration and followed an initial increase and subsequent decrease trend with an increase in phosphoric ester compounds concentration. At an abrasive concentration of \(20\) g/dm\({}^{3}\) and a phosphoric ester compounds concentration of \(1.0\) wt%, the zeta potential reached \(-61.117\) mV; however, with an increase in phosphoric ester compounds concentration, the zeta potential decreased to \(-40.583\) mV. Based on the zeta potential analysis, it can be inferred that, at an abrasive concentration of \(20\) g/dm\({}^{3}\) and phosphoric ester compounds concentrations within the range of \(0.5\) wt% to \(3.0\) wt%, the polishing solution remained in a stable state, with the phosphoric ester compounds concentration of \(1.0\) wt% achieving excellent stability. At abrasive concentrations of \(60\) g/dm\({}^{3}\) and \(100\) g/dm\({}^{3}\), the zeta potential reached its maximum values of \(-45.133\) mV and \(-40.404\) mV, respectively, at phosphoric ester compounds concentrations of \(1.0\) wt% and \(1.5\) wt%, indicating a good stability. However, with an increase in phosphoric ester compounds concentration, the stability decreased, reaching a moderate stability at a concentration of \(3.0\) wt%. Overall, phosphoric ester compounds have a significant enhancing effect on the dispersion stability of the polishing solution. This is attributed to the multiple components in the mixture of phosphoric ester compounds, with their ionized ions adsorbing on the particle surface, strengthening the electrostatic repulsion between the particles. Additionally, the co-polymers formed after complete dissolution of phosphoric ester compounds adsorb onto the particle surface, providing strong steric hindrance, thus achieving good dispersion stability of the polishing solution. Figure 7: Zeta potential and average particle size of polishing solution samples when PEG was used as a dispersant: (**a**) zeta potential; (**b**) average particle size. Figure 8b illustrates the relationship between the phosphoric ester compounds concentration, abrasive concentration, and average particle size. After adding phosphoric ester compounds, the minimum average particle size value, at 4.179 nm, was achieved at an abrasive concentration of 20 g/dm\({}^{3}\) and a phosphoric ester compounds concentration of 1.0 wt%. As the abrasive concentration increased, the average particle size also increased, becoming nearly fifty times higher at an abrasive concentration of 100 g/dm\({}^{3}\) compared to 20 g/dm\({}^{3}\). Therefore, when phosphoric ester compounds are used as dispersants, the abrasive particles in the polishing solution exhibit better dispersibility at an abrasive concentration of 20 g/dm\({}^{3}\) and a dispersant concentration of 1.0 wt%.