*3.3. Analysis of Particle Size by the Laser Di*ff*raction Method*

Figure 6 shows the evolution of the talc's particle size upon grinding, as measured by the laser diffraction particle size analysis.

The as-received talc shows a single distribution with a mean particle size of approximately 12 μm. With an increase in grinding time, the particle size generally decreased. However, the minimum particle size and reduction rate varied according to the ball size. When 2 mm and 1 mm balls were used, the particle size rapidly decreased to less than 1 μm for the first 60 min of grinding and did not change much after 120 min. However, when 0.1 mm balls were used, the particle size gradually decreases until 360 min of grinding, but the changes are relatively insignificant compared with the changes when using 1 mm and 2 mm balls.

The distribution pattern of particle sizes also varies upon grinding. The particle size of as-received talc shows a monomodal distribution ranging from ~3 to ~50 μm with a center at ~10 μm. As the grinding proceeds, an increase in submicron particles appeared in addition to the existing predominately micron-sized particles of approximately ~10 μm, which forms a bimodal distribution. In this case, we refer to the two distribution groups as a microscale group and a sub-microscale group. When using 1 mm and 2 mm balls, the sub-microscale group appears even after 10 min of grinding and its population gradually increases until 120 min of grinding at the expense of the microscale group. The mean particle size of the microscale group gradually decreases from ~10 to ~2 μm as the grinding proceeds for up to 60 min. The microscale group is not observed after 120 min of grinding, which indicates that talc powders are fully pulverized into sub-microscale after 120 min of grinding. However,

re-aggregation occurred in some samples, and, thus, small amounts of ~4 and ~20 μm particles were observed after 120 min of grinding. When using 0.1 mm balls, the population of the microscale group does not show a significant reduction even after 360 min of grinding and the population of the sub-microscale group is relatively insignificant when compared to the results when using 1 mm and 2 mm balls. We note that dispersion of the ground talc may be incomplete in aqueous solution and the sizes of the aggregated particles can be measured by the laser diffraction method.

**Figure 6.** Changes in particle size of talc upon grinding, measured using laser diffraction particle size analysis. The ball size for high-energy ball milling is (**a**) 2 mm, (**b**) 1 mm, and (**c**) 0.1 mm.

Figure 7 shows the change in the D50, which corresponds to 50% of the cumulative volume of the particle size distribution, upon grinding, according to the ball size.

**Figure 7.** Change of particle size (D50) of talc upon grinding.

When 2 mm balls were used, D50 decreased sharply to approximately 0.5 μm after 60 min of grinding, but did not show significant changes until 360 min. Similarly, when 1 mm balls were used, D50 decreased to approximately 0.7 μm in the first 30 min of grinding, but it did not change significantly after that. These results show that the particle size rarely decrease after approximately 60 min of grinding, which indicates that it reached the grinding limit under the grinding condition employed in this study. Until 60 min of grinding, the grinding efficiency of the 2 mm balls was slightly lower than that of the 1 mm balls. However, beyond this time frame, the D50 was smaller and the particle size distribution was narrower. In contrast, when 0.1 mm balls were used, the particle size steadily decreased until 360 min from the beginning of grinding. The final D50 was approximately 7.9 μm, which is approximately 7 μm larger than that obtained using 2 mm or 1 mm balls. These results indicate that, when 0.1 mm balls are used, the pulverization rate is slow and showed a lower grinding efficiency compared with the 2 mm and 1 mm balls.
