## 3 Results and Discussion
### Zeta Potential and Average Particle Size Analysis  
The dispersion mechanism of Na(PO3)6 arises from the anions produced by hydrolysis attaching to the particle surfaces, forming an electric double layer and inducing repulsion between particles. As shown in Figure 6a, the absolute value of the zeta potential exhibited a negative correlation with an abrasive concentration at the same Na(PO3)6 concentration. Figure 4: Sedimentation conditions of polishing solution at different abrasive and PEG concentrations. Figure 5: Sedimentation conditions of polishing solution at different abrasive and phosphoric ester compounds concentrations. This suggests a decrease in electrostatic repulsion between the particles as the abrasive concentration rises. Moreover, at a specific abrasive concentration, the absolute value of the zeta potential initially increased and then decreased with the rise in the Na(PO3)6 concentration. This phenomenon indicates that, when the Na(PO3)6 concentration reaches a certain threshold, hydrolyzed anions effectively cover the particle surface, enhancing the electrostatic repulsion between particles. However, surpassing this threshold may cause excessive anions to compress the electric double layer, diminishing electrostatic repulsion and hindering stable dispersion. It is noteworthy that, at an abrasive concentration of 100 g/dm3, the zeta potential fluctuated between \(-1.773\) mV and \(-14.463\) mV with varying Na(PO3)6 concentration, indicating an incipient instability state with poor dispersion stability and significant flocculation or agglomeration. When the Na(PO3)6 concentration was 0.5 wt% and the abrasive concentration was 20 g/dm3, the zeta potential reached \(-50.313\) mV, ensuring good dispersion stability in the polishing solution. Therefore, maintaining a balance between the Na(PO3)6 concentration and the abrasive concentration is crucial for a stable dispersion state. Figure 6b illustrates that, with a Na(PO3)6 concentration of 0, the average particle size increased with the rise in the abrasive concentration. However, upon the addition of Na(PO3)6, there was a slight decrease in the average particle size. Under a constant abrasive concentration, when the Na(PO3)6 concentration was 0.5 wt%, the average particle size reached its minimum for that abrasive concentration. Nevertheless, with a further increase in the Na(PO3)6 concentration, the average particle size exhibited an upward trend. The average particle size was positively correlated with the abrasive concentration at any Na(PO3)6 concentration. This suggests that both a high abrasive concentration and a high Na(PO3)6 concentration may lead to the formation of large particle clusters, thereby reducing dispersibility. Figure 7a illustrates the impact of the abrasive concentration and PEG concentration on the zeta potential. It can be observed from the graph that, at three different abrasive concentrations, there is no apparent linear relationship between the zeta potential of the polishing solution and the PEG concentration. This is because PEG, being a nonionic polymer, did not ionize in the solution, resulting in no correlation between the PEG concentration and the zeta potential at a certain abrasive concentration. When the abrasive concentration was 20 g/dm3, the zeta potential fluctuated between \(-14.817\) mV and \(-16.950\) mV, indicating that the polishing solution was in an incipient instability state. However, as the abrasive concentration increased to 100 g/dm3, the zeta potential fluctuated between \(-0.937\) mV and \(-1.773\) mV, indicating that the polishing solution was in the rapid coagulation or flocculation stage, suggesting poor dispersion stability. Additionally, it was observed that, under a constant PEG concentration, the absolute value of the zeta potential decreased  
Figure 6: Zeta potential and average particle size of polishing solution samples when Na(PO3)6 was used as a dispersant: (**a**) zeta potential; (**b**) average particle size. with an increase in abrasive concentration.