## 5 Results and Discussion  
The results of the particle size analysis are shown in Figure 3 and Table 5. The particle sizes of three samples (dispersion times of 60 minutes, 120 minutes, and 180 minutes) were measured over a period of 60 minutes. In the case of magnetic stirring, the mean diameter of the particles was 299 nm for 60 minutes, 277 nm for 120 minutes, and 267 nm for 180 minutes. The average diameter decreased with the increase in the dispersion time. In addition, the deviation from the mean decreased by approximately 20% for a dispersion time of 180 minutes, and the distribution was also close to the average value. Thus, a dispersion time of 180 minutes was considered to be optimal. Figure 2: Underlying principle of high-pressure dispersion (adapted from Ilshin Autoclave Co., Ltd.). Transmission electron microscopy (TEM) imaging indicated that the CNCs were bar-shaped and had formed clusters. Based on these results, we concluded that CNC dispersion using magnetic stirring is not suitable, as the dispersion time that is needed is very high, even though it results in a high degree of dispersion with the diameter of the CNC clusters decreasing with time. Based on the results of this experiment, the authors will evaluate the dispersibility according to the time and energy usage through comparison with the direct energy dispersion method: ultrasonic dispersion. The zeta potential can be used as a measure of dispersibility, with a higher absolute value indicating higher dispersibility. In general, when the zeta potential is measured, it is seen that particles have a positive charge in the case of acidic solutions, exhibit an isoelectric point at a pH of 9, and have a negative charge in alkaline solutions. The lowest average particle size is observed in the pH region where the absolute value of the zeta potential is high, with the dispersibility of the particles improving owing to the electrostatic repulsive force experienced by them. On the other hand, near the isoelectric point, the particles form agglomerates, resulting in a higher average particle size, and the system becomes unstable (Otsuka Electronics Co. Ltd., Seongnam, Korea). Figure 4 shows the zeta potentials  
Figure 3: CNC particle size during magnetic stirring. Size distributions with average diameters are shown for dispersion times of (**a**) 60 min, (**b**) 120 min, and (**c**) 180 min. (**d**) TEM image of particles dispersed for 180 min. \begin{table}
\begin{tabular}{c c c c} \hline
**Sample** & **Deviation (nm)** & **Diameter (nm)** & **Average Diameter (nm)** \\ \hline M-60 min & 31.5 & 300 & \\ M-120 min & 30.7 & 277.4 & 281.6 \(\pm\) 30 nm \\ M-180 min & 24.4 & 267.5 & \\ \hline \end{tabular}
\end{table} 
Table 5: Analysis of CNCs dispersed by magnetic stirring for different dispersion times. of alumina particles dispersed using the same equipment. In the case of the CNC samples, the highest zeta potential value was \(-48.83\) mV, which was observed for a dispersion time of 180 minutes; this was approximately 19% higher than that of the sample dispersed for 120 minutes (see Figure 5). Figure 6 shows the particle size distributions for the different numbers of dispersion passes at \(345\times 10^{5}\) Pa. It can be seen that under these conditions, the range of the particle diameters is 69-102 nm, and the spread of the diameters is not significant. However, the mean diameter was the lowest after three passes (79 nm). Further, while there was a decrease in the particle size after the second pass, the average diameter did not change significantly b  
Figure 4: Dependence of particle size and zeta potential of alumina particles on pH (adapted from Otsuka Electronics Korea Co. Ltd.). Figure 5: Zeta potential of CNC samples as a function of the magnetic dispersion time. As shown in Figure 7, the particle size distribution at 1035 \(\times\) 10\({}^{5}\) Pa became wider after the second pass; however, the average diameter was not significantly different from the overall average.