## 3 Results and Discussion
### Performance Evaluation Results
Table 4 shows the measured properties of the original PMS xerogel and the hydrophobic CNF-PMS xerogel composite, and Figure 11 shows their measured normal-incidence  
Figure 10: SEM images of synthesized PMS xerogels: (**a**) original PMS xerogel; (**b**) original PMS xerogel; (**c**) hydrophobic CNF–PMS xerogel; (**d**) hydrophobic CNF–PMS xerogel. Figure 9: External appearance of synthesized PMS xerogels: (**a**) original PMS xerogel; (**b**) diluted PMS xerogel after aging; (**c**) CNF–PMS xerogel composite; and (**d**) hydrophobic CNF–PMS xerogel composite. sound absorption coefficients. The hydrophobic CNF-PMS xerogel composite exhibits an average sound absorption coefficient of 0.45 from 500 to 3150 Hz. This value is higher than that of the original PMS xerogel despite the smaller thickness of the hydrophobic composite; it is also approximately 1.7 times that of a porous sound-absorbing material commonly used in automobiles (3M Thusulate; Table 4). The Young's modulus of the hydrophobic CNF-PMS xerogel composite is 1/20 times that of the original PMS xerogel. The loss factor of the hydrophobic CNF-PMS xerogel composite is four times that of the original PMS xerogel. The raw material formulation and synthesis conditions of the polysiloxane network are equivalent, and the molecular structure and physical properties of the network are considered to be almost the same. Therefore, the difference in loss factor suggests that the hydrophobic CNF-PMS xerogel composite has a higher fraction of mechanically flexible sites, causing more enhanced sound dissipation at the flexible sites. From these results and Figure 10d, we infer that the hydrophobic CNF-PMS xerogel composite forms a structure similar to the rubber 4 model (Section 3.1), with rigid sites where the gel particles are covered with CNFs and flexible sites where the gel particles are exposed. \begin{table}
\begin{tabular}{c c c c} \hline  & **Original** & **Hydrophobic CNF** & **3 MTM** \\  & **PMS Xerogel** & **PMS Xerogel** & **ThinsulateTM (St. Paul, MN, USA)** \\ \hline Porosity [\%] & 89.5 & 93.2 & - \\ Pore size distribution & 8.1 & - & - \\ Peak size [\(\mu\)m] & 10 & 8 & 10 \\ Thickness [mm] & 1.35 \(\times\) 10\({}^{6}\) & \(5.54\times\) 10\({}^{5}\) & - \\ Bulk Density & 168.2 & 88.4 & - \\ [kg/m\({}^{3}\)] & 3.0 \(\times\) 10\({}^{4}\) & \(1.5\times\) 10\({}^{3}\) & - \\ Loss factor & 0.250 & 0.939 & - \\
500–3150 Hz & & & \\ Average & 0.39 & 0.45 & 0.27 \\ Sound absorption & & & \\ coefficient & & & \\
1000–5000 Hz & & & \\ Average & 0.43 & 0.62 & 0.49 \\ Sound absorption & & & \\ coefficient & & & \\ Thermal conductivity & 0.0371 & 0.0378 & 0.0536 \\
[W/(m-K)] & (0.0248) & (0.0252) & (0.0358) \\ \hline \end{tabular}
\end{table} 
Table 4: Properties of original PMS xerogel and hydrophobic CNF–PMS xerogel composite. Figure 11: Measured normal-incidence sound absorption coefficients of synthesized PMS xerogels. Moreover, as shown in the calculation model of rubber 4 in Section 3.1, the ligament of the hydrophobic specimen resonates more easily, which improves the sound absorption coefficient. The sound absorption coefficient of the hydrophobic CNF-PMS xerogel composite does not decrease at frequencies above 1000 Hz and remains high. The flow resistance per unit thickness is 1.35 \(\times\) 10\({}^{6}\) N\(\cdot\)s/m\({}^{4}\) for the original PMS xerogel and 5.54 \(\times\) 10\({}^{5}\) N\(\cdot\)s/m\({}^{4}\) for the hydrophobic CNF-PMS xerogel composite, suggesting that the hydrophobic specimen with higher porosity is penetrated by sound waves to a greater extent. This helps enhance the sound absorption coefficient in the high-frequency range. The peak diameter in the pore size distribution of the original PMS xerogel is 8.1 \(\upmu\)m, which is larger than the upper limit considered in the calculation model, namely, \(w\) = 10 \(\upmu\)m (the average pore size is approximately 5.2 \(\upmu\)m). In addition, the pore size may be measured smaller than the actual due to the deformation of this material during the measurement.