## 2 Materials
### Nanomaterials  
The nanomaterials NT, NA, and NS exhibit distinct physical properties, making them invaluable in enhancing the performance of asphalt mixtures. NT is noted for its high purity and substantial specific surface area, NA is noted for its remarkable melting point, and NS is noted for its exceptional specific surface area and particle size range. The major physical properties of these nanomaterials are meticulously detailed in Table 4, providing a foundation for their selection and utilization in this research. A photograph showing these nanomaterials is presented in Figure 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Properties**} & \multicolumn{3}{c}{**Nanomaterial**} \\ \cline{2-4}  & **NT** & **NA** & **NS** \\ \hline Chemical formula & TiO\({}_{2}\) & Al\({}_{2}\)O\({}_{3}\) & SiO\({}_{2}\) \\ Molecule wt. (g/mol) & 85.42 & 101.96 & 60.08 \\ Appearance & White Powder & White Powder & White Powder \\ Average particle size (nm) & 20–30 & 10–20 & 25–35 \\ Purity (\%) & 99.9 & 99.9 & 99.8 \\ Specific surface area (m\({}^{2}\)/gm) & 120–160 & 120–160 & 190–250 \\ Meting point (\({}^{\circ}\)C) & 1860 & 2030 & 1730 \\ Bulk Density (g/mL) & 0.51 & 0.2 & 0.08 \\ Ph & 5.5–6.5 & 8.5–9.5 & 5–6.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Physical properties of nanomaterials. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Property**} & **Standard** & **Test Result** & **Specification Limit** \\ \hline Penetration at 25 \({}^{\circ}\)C, 100 gm, 5 s. (0.1 mm) & [42] & 49 & (40–50) \\ Ductility at 25 \({}^{\circ}\)C, 5 cm/min. (cm) & [43] & 110 & \(>\)100 \\ Flashpoint (Cleveland open cup) (\({}^{\circ}\)C) & [44] & 311 & Min. 232 \\ Softening point (\({}^{\circ}\)C) & [45] & 49.7 & - \\ Specific gravity at 25 \({}^{\circ}\)C & [46] & 1.04 & - \\ The residue from thin film oven test & [47] & - & \\ Retained penetration (\% of original) & [48] & 58 & \\ Ductility at 25 \({}^{\circ}\)C, 5 cm/min (cm) & [49] & 80 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The test results for the physical properties of asphalt cement. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Asphalt Cement**} & **Properties** & **Temperature** & **Measured** & **Specification** \\  & & \({}^{\circ}\)C & **Parameters** & **Requirements, [41]** \\ \hline \multirow{4}{*}{Original} & Flash point (\({}^{\circ}\)C) & - & 311 & 230 \({}^{\circ}\)C, min \\  & Viscosity at 135 \({}^{\circ}\)C (Pa-s) & - & 719.7 & 3000 m Pa-s, max \\  & 58 & 3.4515 & \\  & DSR, G/sin\(\delta\) at 10 rad/s (kPa) & 64 & 1.6623 & 1.00 kPa, min \\  & 70 & 0.8425 & \\ \hline \multirow{4}{*}{RTFO Aged} & Mass loss (\%) & - & 0.266 & 1\%, max \\  & 58 & 6.8651 & \\  & DSR, G/sin\(\delta\) at 10 rad/s (kPa) & 64 & 3.4578 & 2.2 kPa, min \\  & 70 & 1.7241 & \\ \hline \multirow{4}{*}{PAV Aged} & DSR, G.sin\(\delta\) at 10 rad/s (kPa) & 28 & 3485 & \\  & 25 & 5068 & 5000 kPa, max \\ \cline{1-1}  & BBR, creep stiffness (MPa) & \(-6\) & 183 & 300 MPa, max \\ \cline{1-1}  & Slope m-value & \(-6\) & 0.368 & 0.3, min \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Rheological properties of asphalt cement. Scinning Electron Microscope (SEM) images at 120,000\(\times\) magnification, as exhibited in Figure 2, provide a detailed portrayal of the nanostructured materials examined in this research. The SEM image of NT indicates a predominant cluster form of spherical particles, which has a fairly even size due to van der Waals forces or interfacial surface charge interactions. The uniformity and spherical nature of the particles suggest that NT could provide a consistent surface area to facilitate the mix with the asphalt binder, potentially leading to uniform dispersion within the mixture. The particle size, within the tens of nanometers range, aligns with the enhanced properties that are typically sought in nanomaterials, such as increased reactivity and strength when applied in a binder matrix.