## 2 Materials and Methods
### Characterization of Dispersion Stability and Abrasive Particle Dispersibility  
To characterize the dispersion stability of the polishing solution and the dispersibility of the abrasive particles, a series of static sedimentation experiments were conducted on each formulated polishing solution sample. The effects of the dispersant type and concentration on the dispersion stability and abrasive particle dispersibility were analyzed by measuring the zeta potential and average particle size of the samples. Finally, SEM analyses were performed on the dispersants with the best dispersing effect to explore the effect of different concentrations of dispersants from a visual perspective.  
Initially, the prepared polishing solution samples underwent sequential static sedimentation experiments in reagent bottles. The dispersion stability was preliminarily assessed by observing whether the sample in the reagent bottle exhibited noticeable delamination after 30 min.  
A zeta potential/particle size analyzer (model: ZETASIZER NANO ZSP, produced by Malvern Instruments, Malvern, UK, capable of measuring sample concentrations ranging from 1 ppm to 40% \(w/v\)) was employed to measure the zeta potential and average particle size of the samples. The 1-cm\({}^{3}\) sample of thoroughly stirred polishing solution was dropped into the sample chamber, and its zeta potential was measured using the electrophoretic light scattering (ELS) method, while its particle size was measured using the dynamic light scattering (DLS) method at 25 \({}^{\circ}\)C. Each sample was measured three times, and the average value was taken as the final result. The dispersion stability of the polishing solution was categorized into the following five assessments based on the zeta potential values [21]: rapid coagulation or flocculation (0 to \(\pm\)5 mV), incipient instability (\(\pm\)10 mV to \(\pm\)30 mV), moderate stability (\(\pm\)30 mV to \(\pm\)40 mV), good stability (\(\pm\)40 mV to \(\pm\)60 mV), and excellent stability (\(\geq\pm\)60 mV). Therefore, the impact of the dispersants on the stability of the polishing solution samples can be determined by the zeta potential. A larger average particle size indicates poorer dispersibility, while a smaller average particle size suggests better dispersibility.  
The scanning electron microscope (model: EVO 10, produced by Zeiss, Oberkochen, Germany) was used to observe the microscopic morphology. The carrier stage was covered with aluminum foil fixed with conductive adhesive. A 1-cm\({}^{3}\) sample of the polishing solution was dropped onto the foil and dried using an infrared lamp. The sample was then gold-sprayed and observed under SEM.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Abrasive** & **Na(PO3)6** & **PEG Concentration** & **Phosphoric Ester** \\
**Concentration (g/dm\({}^{3}\))** & **Concentration (wt\%)** & **(wt\%)** & **Compounds** \\  & & & **Concentration (wt\%)** \\ \hline  & 0 & 0 & 0 \\  & 0.5 & 0.5 & 0.5 \\  & 1.0 & 1.0 & 1.0 \\
20 & 1.5 & 1.5 & 1.5 \\  & 2.0 & 2.0 & 2.0 \\  & \(\backslash\) & 3.0 & 3.0 \\  & 0 & 0 & 0 \\  & 0.5 & 0.5 & 0.5 \\  & 1.0 & 1.0 & 1.0 \\
60 & 1.5 & 1.5 & 1.5 \\  & 2.0 & 2.0 & 2.0 \\  & \(\backslash\) & 3.0 & 3.0 \\  & 0 & 0 & 0 \\  & 0.5 & 0.5 & 0.5 \\  & 1.0 & 1.0 & 1.0 \\  & 1.5 & 1.5 & 1.5 \\  & 2.0 & 2.0 & 2.0 \\  & \(\backslash\) & 3.0 & 3.0 \\  & & & \\ \end{tabular}
\end{table}
Table 1: The combinations of abrasive concentration and dispersant concentration of all polishing solution samples.