Fractal Fract. 2025 , 9 , 123
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Based on these findings, FD can be used as a complementary parameter to evaluate surface characteristics. Its ability to capture unique surface information, independent of conventional roughness and friction metrics [30–33], highlights its potential for providing a more comprehensive understanding of surface properties. 3.5. Application of Fractal Geometry to Surface Characterization A comparison of surface parameters between the P&W11 (uncoated) and P&W12 (coated) paper samples highlights the effects of coating on surface properties (Table 5). The surface roughness and friction profiles of these samples are shown in Figure 13. In general, for coated paper to meet print quality requirements, the paper surface must be filled with a suitable pigment-rich composition to enhance smoothness. The coating also improves gloss, slickness, color, printing detail, and brightness. Therefore, coating pigments such as clay, CaCO 3, and TiO 2 are used with binders or adhesives [8] to produce plastic-like surfaces. The RMAD and FMAD values decreased by 16.7% and 16.2%, respectively, in the coated sample, indicating improved surface uniformity and reduced friction variability after coating. Conversely, the MIU value increased by 23%, suggesting that the coating enhanced the surface friction, probably due to the increased contact area.
Table5. Effect of coating on surface characteristics.
Sample P&W11 P&W12 Change
RMAD , μ m
MIU 0.203 0.250
FMAD
FD
0.42 0.35
0.037 0.031
1.19 1.25
− 16.7%
23%
− 16.2%
5%
Figure13. Effects of coating on surface roughness ( a ) and friction profiles ( b ).
The FD increased by 5% in the coated sample, reflecting greater surface complexity introduced by the coating (Figure 14). Unlike RMAD and FMAD , which focus on variability, FD provides insights into the geometric intricacies of surfaces. This result shows that coating not only smooths the surface but also adds finer-scale features, highlighting the complementary role of FD in surface characterization. Overall, although RMAD and FMAD capture surface variability and MIU re- flects friction, FD provides a unique measure of surface complexity. Together, these parameters provide a comprehensive understanding of the impact of coating on sur- face properties.
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