## 2 Materials and Methods
### AFM Image Processing  
Image analysis was conducted using NanoScope Analysis v3.0 software. Each coal sample underwent at least three scans at randomly selected locations. The average values and standard deviations of parameters were calculated from these repeated measurements. Initially, preprocessing of the raw data involved using NanoScope Analysis v3.0 to apply \"Flatten Order = 1\" to eliminate the tilted background. Subsequently, the surface morphology and pore structure of coal samples with different roughness were observed in tapping mode, and a comparative analysis of the three-dimensional morphology of the coal samples was performed. For particle analysis, Gwyddion v2.62 software was utilized with the \"Watershed Algorithm,\" configured with parameters set to Grain Boundary = 0.2 and Minimum Grain Size = 4 px (corresponding to pore diameters > 2 nm). This allowed for the derivation of nanopore parameters of the coal, including the statistical distribution of average pore diameter, pore count, and surface porosity. Among these, due to the often irregular shapes of pores, pore diameter was represented by equivalent circle diameter (the diameter of a circle with an area equal to the pore area). Since conventional parameters have limitations and cannot fully characterize the surface microstructure of coal, this study incorporated unconventional parameters to observe the surface structural characteristics of coal more comprehensively. The unconventional parameters are defined as follows:  
1. Surface Roughness Parameters  
R\({}_{a}\) is the most commonly used parameter to describe roughness. Average roughness (R\({}_{a}\)) is defined as the average absolute deviation from the mean line over a sampling length of the surface roughness, as described in (1) [25]:  
\[R_{a}=\frac{1}{N_{x}N_{y}}\sum_{i=1}^{N_{x}}\sum_{j=1}^{N_{y}}\lvert z(i,j)-z_{ mean}\rvert \tag{1}\]  
Similarly, root-mean-square roughness (R\({}_{a}\)) is defined as follows in (2):  
\[R_{q}=\sqrt{\frac{1}{N_{x}N_{y}}\sum_{i=1}^{N_{x}}\sum_{j=1}^{N_{y}}\left(z(i, j)-z_{mean}\right)^{2}} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sample Number**} & \multirow{2}{*}{**Origin**} & \multicolumn{3}{c}{**Proximate Analysis (wt\%)**} & \multicolumn{3}{c}{**Macerals (\%)**} \\ \cline{3-8}  & & **M\({}_{ad}\)** & **A\({}_{ad}\)** & **V\({}_{daf}\)** & **Vitrinite** & **Liptinite** & **Inertinite** \\ \hline AH-1 & Anhui Huainan & 2.3 & 11.9 & 33.17 & 86.54 & 7.83 & 5.63 \\ \hline HB-1 & Hebei Xingtai & 1.71 & 11.04 & 27.96 & 89.35 & 7.31 & 3.34 \\ \hline SX-1 & Shanxi Jincheng & 0.97 & 13.26 & 14.51 & 92.49 & 4.73 & 2.78 \\ \hline SX-2 & Shanxi Jincheng & 0.82 & 14.23 & 13.53 & 94.15 & 2.87 & 2.98 \\ \hline SX-3 & Shanxi Jincheng & 0.79 & 15.82 & 12.67 & 93.81 & 3.93 & 2.26 \\ \hline SX-4 & Shanxi Jincheng & 0.88 & 15.23 & 9.61 & 93.53 & 3.26 & 3.21 \\ \hline \hline \end{tabular} Note: M\({}_{ad}\) represents moisture on an air-dried basis; A\({}_{ad}\) represents ash on an air-dried basis; V\({}_{daf}\) represents volatile matter on a dry, ash-free basis.  
\end{table} 
Table 1: Basic Data of Coal Samples. \(z_{mean}\) in the above formulas is defined as follows in (3):  
\[z_{mean}=\frac{1}{N_{x}N_{y}}{\sum\limits_{i=1}^{N_{x}}{\sum\limits_{j=1}^{N_{y} }{z(i,j)}}} \tag{3}\]  
where N\({}_{x}\) and N\({}_{y}\) are the number of scan points on the \(x\)-axis and \(y\)-axis, respectively; z(i, j) is the height of point (i, j); and the average value of Z is the average height of all measured points. R\({}_{sk}\) is a dimensionless factor representing skewness, which characterizes the symmetry of image pixels around the average value. Its value is defined as shown in Formula (4):  
\[R_{sk}=\frac{1}{R_{q}^{3}}\frac{1}{N}{\sum\limits_{i=1}^{N}{Z_{i}^{3}}} \tag{4}\]  
R\({}_{ku}\) is a dimensionless factor used to assess the shape of the data distribution around the average value. Its value is defined as shown in Formula (5):  
\[R_{ku}=\frac{1}{R_{q}^{4}}\frac{1}{N}{\sum\limits_{i=1}^{N}{Z_{i}^{3}}} \tag{5}\]  
2.