## 4 Results and Discussion  
### Morphology and Porosity Structure of Porous Materials  
#### 4.1.1 Morphology and Pore Size Distribution of Single-Fiber Porous Materials  
The morphology of the fiber porous material is shown in Figure 3a. Observations reveal that fine particles are attached to the fiber surfaces, giving them a rough texture (the detailed microscopic surface morphology images of the fibers are presented in Figure S3). The fibers are bonded to each other through potassium silicate (spot analyses by EDS revealed the presence of K in these particles; see Table S1 for details), forming interconnected pores. These pores act as transmission channels for sound waves to enter the material. When sound waves penetrate the porous material, they continuously collide with the fiber surfaces and undergo friction with the pore walls and air molecules. These interactions, combined with multiple reflections and refractions within the porous structure, lead to significant energy dissipation, thereby enhancing the material's sound absorption performance. For fibers with the same diameter, taking the fiber with a diameter of 7 \(\upmu\)m as an example, the pore size of the porous material decreases as the density increases, as shown in Figure 3c,d. Similarly, for a constant density, taking 80 kg/m\({}^{3}\) as an example, a reduction in fiber diameter also leads to smaller pore sizes, as shown in Figure 3e,f. It can be observed that decreasing the fiber diameter increases the number of fibers per unit area, resulting in tighter fiber overlaps. This increases the porosity and specific surface area of the porous material. Consequently, due to greater viscous losses and thermal losses [45], the dissipation of sound waves within the material becomes more significant. From the SEM image in Figure 3, it can be observed that the pore structures formed by fiber intersections are highly complex. To analyze the pore size distribution of the porous material, the diameters of inscribed circles within the polygonal pores created by fiber overlaps were used to represent pore sizes [46]. SEM images of fiber porous materials with a fiber diameter of 7 \(\upmu\)m at densities of 80 kg/m\({}^{3}\), 100 kg/m\({}^{3}\), and 120 kg/m\({}^{3}\) were imported into ImageJ software for analysis. Figure 4a-c shows the partial SEM top view of porous materials with 7 \(\upmu\)m fiber diameters under three densities, respectively. These images reveal a large number of pores with varying sizes. Figure 3: Microscopic morphology of fibrous porous materials: (**a**) Microscopic image of fiber interlocking, (**b**) EDS analysis, (**c**) 7 \(\upmu\)m diameter, 80 kg/m\({}^{3}\), (**d**) 7 \(\upmu\)m diameter, 100 kg/m\({}^{3}\), (**e**) 7 \(\upmu\)m diameter, 80 kg/m\({}^{3}\), (**f**) 5 \(\upmu\)m diameter, 80 kg/m\({}^{3}\). By measuring and statistically analyzing the diameters of the inscribed circles within the polygonal pores, the pore size distributions and median pore sizes of the fiber porous materials were obtained. The statistical results are shown in Figure 4d-f. It can be seen that as the density increases, the median pore size decreases progressively, which is consistent with the results of the SEM observation. The pore size distribution of porous sound-absorbing materials was further tested by the capillary pore size analysis technique. The test results are shown in Figure 4g,h, where it can be observed that the pore size distribution of the fiber porous materials follows an approximately normal distribution, consistent with the application rules of the three-parameter analytical model [33]. Additionally, Table 3 lists the specific porosity and median pore size of the porous sound-absorbing materials. The pore size of the porous sound-absorbing materials primarily falls within the macropore range [47] (50 nm < pore size < 100 \(\upmu\)m). As the density increases from 60 kg/m\({}^{3}\) to 140 kg/m\({}^{3}\), the median pore size of the materials gradually decreases, with a maximum reduction of 45.82%.