## 6 Conclusions  
Based on experimental evaluations of asphalt binders modified with Nano-Titanium Dioxide (NT), Nano-Aluminum Oxide (NA), and Nano-Silica Oxide (NS) at various dosages ranging from 0% to 8%, the following conclusions are drawn:  
1. The SEM analysis highlights unique morphologies of the nanomaterials used. NT displays spherical clusters, suggesting efficient dispersion within asphalt. NA is characterized by irregular agglomerates, potentially influencing its interaction with the binder. NS reveals a dense arrangement of particles, indicative of a significant surface area, which is crucial for integrating with the asphalt binder. These morphological traits are fundamental in understanding the interaction of each nanomaterial with the asphalt matrix. 2. NS-modified asphalt demonstrated the best storage stability with a 225% increase in \(\Delta\)T at an 8% inclusion compared to a 400% increase for NT and a 300% increase for NA, highlighting NS's superior homogeneity. 3. All modified binders remained within acceptable viscosity limits after RTFO aging. NS had the highest average viscosity increase of 33% compared to neat asphalt, suggesting its significant impact on the binder's viscosity. 4. TiO\({}_{2}\) reduced mass loss by 12% at a 2% dosage, demonstrating potential anti-aging properties. In contrast, Al\({}_{2}\)O\({}_{3}\) and SiO\({}_{2}\) increased the mass loss by 55.64% and 109.77%, respectively, at an 8% inclusion, affecting thermal stability differently. 5. SiO\({}_{2}\) markedly improved the rutting resistance, showing the highest rutting factor, making it effective for high-temperature performance and heavy traffic conditions. 6. Nanomaterials increased the binder stiffness, with the G\({}^{*}\) sin \(\delta\) values indicating a slightly higher risk of fatigue cracking. However, the benefits in rutting resistance may offset this risk. 7. The optimal dosage for enhanced performance was identified as 6% for both NT and NA, while NS achieved the best balance of properties at a 4% inclusion rate. This suggests that a nuanced approach is required when selecting nanomaterial dosages to maximize the overall asphalt binder's performance. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & \multirow{2}{*}{**Parameter**} & \multicolumn{6}{c}{**NS Content, \%**} \\ \cline{3-6}  & & **0** & **2** & **4** & **6** & **8** \\ \hline Penetration, 1/10 mm & X\({}_{1}\)\({}^{(0)}\) & 49 & 47 & 43 & 37 & 29 \\  & X\({}_{1}\)\({}^{*}\) & 0.000 & 0.100 & 0.300 & 0.600 & 1.000 \\ Softening point, \({}^{\circ}\)C & X\({}_{2}\)\({}^{(0)}\) & 49.7 & 50.9 & 52.1 & 53.2 & 55.7 \\  & X\({}_{2}\)\({}^{*}\) & 0.000 & 0.200 & 0.400 & 0.583 & 1.000 \\ PI & X\({}_{3}\)\({}^{(0)}\) & \(-1.33\) & \(-1.12\) & \(-1.03\) & \(-1.1\) & \(-1.04\) \\  & X\({}_{3}\)\({}^{*}\) & 0.000 & 0.700 & 1.000 & 0.767 & 0.967 \\ Mass loss, \% & X\({}_{4}\)\({}^{(0)}\) & 0.266 & 0.282 & 0.321 & 0.432 & 0.558 \\  & X\({}_{4}\)\({}^{*}\) & 1.000 & 0.945 & 0.812 & 0.432 & 0.000 \\ Storage stability, \({}^{\circ}\)C & X\({}_{5}\)\({}^{(0)}\) & 0.4 & 0.6 & 0.7 & 0.9 & 1.3 \\  & X\({}_{5}\)\({}^{*}\) & 1.000 & 0.778 & 0.667 & 0.444 & 0.000 \\ RV at 135 \({}^{\circ}\)C, mPa-s & X\({}_{6}\)\({}^{(0)}\) & 719.7 & 804.9 & 1129.3 & 1325.8 & 1770.8 \\  & X\({}_{6}\)\({}^{*}\) & 1.000 & 0.919 & 0.610 & 0.423 & 0.000 \\ Temp (\({}^{\circ}\)C) at rutting & X\({}_{7}\)\({}^{(0)}\) & 68.85 & 71.53 & 77.56 & 79.72 & 81 \\ index = 1 kPa & X\({}_{7}\)\({}^{*}\) & 0.000 & 0.221 & 0.717 & 0.895 & 1.000 \\ Temp (\({}^{\circ}\)C) at rutting & X\({}_{8}\)\({}^{(0)}\) & 68.35 & 70.71 & 74.61 & 77.3 & 80.87 \\ index = 2.2 kPa & X\({}_{8}\)\({}^{*}\) & 0.000 & 0.188 & 0.500 & 0.715 & 1.000 \\ Temp (\({}^{\circ}\)C) at fatigue & X\({}_{9}\)\({}^{(0)}\) & 25.13 & 26.12 & 27.56 & 28.67 & 30.6 \\ index = 5000 kPa & X\({}_{9}\)\({}^{*}\) & 1.000 & 0.819 & 0.556 & 0.353 & 0.000 \\ \hline Overall Desirability (OD) & 0.000 & 0.409 & 0.584 & 0.554 & 0.000 \\ \hline \hline \end{tabular}
\end{table}