## 2 Materials and Methods
### Strain Sweeps  
Strain sweep tests were performed on each testing temperature ranging from \(-15\)\({}^{\circ}\)C to 95 \({}^{\circ}\)C in strain controlled mode. Parallel plates measuring 8 mm were used for \(-15\)\({}^{\circ}\)C to 35 \({}^{\circ}\)C testing temperatures while 25 mm parallel plate geometry was used for a high temperature range of 45 \({}^{\circ}\)C to 95 \({}^{\circ}\)C. Percent Strain value was swept from 0.1 to 80% at a fixed frequency of 10 rad/s and initial stress value of 3.295 Pa. Complex shear modulus (G*) for all binders were measured and the percent strain value at which G* was reduced to 95% of its initial value and was noted as a threshold for linear viscoelastic (LVE) region. Table 6 lists the target strain values selected for LVE region for frequency sweep testing. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Wavenumber Range (cm\({}^{-1}\))** & **Functional Group** &
\begin{tabular}{c} **Bond Vibration Type** \\ **(Stretching/Bending/Rocking)** \\ \end{tabular} \\ \hline
3100–3500 & N-H group & Stretching vibration \\
1550–1640 & N-H group & Bending vibration \\
2500–3300 & O-H & Stretching vibration, Strong Intensity \\
2927–2935 & -CH2 & Asymmetric or symmetric stretch \\  & C=O (1652 cm\({}^{-1}\)) & Stretching vibrations \\
1628–1650 & cis C=C (1654 cm\({}^{-1}\)) & Stretching vibrations \\
1735–1750 & C=O (ester) & Stretching vibrations, strong intensity \\
1800–1830 & C=O (anhydride) & Stretching vibrations, two bands \\
1435 & CH2 (1462 cm\({}^{-1}\)) & Bending vibrations \\
1417 & CH bonds & Rocking vibrations \\
1404 & CH bonds & Rocking vibrations \\
1346 & CH3 & Bending vibrations \\
1000–1300 & C-O group & Stretching vibration, two bands or more \\
1111 and 1097 & -CH -CH & Bending and Deformation Vibrations \\
1065–1068 & C-O & Stretching \\
400–1000 & “Fingerprint region” & – \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Functional groups with their respective range of occurrence in wavenumbers [20; 34; 35]. Frequency Sweeps  
Frequency sweep tests were performed on a temperature range of \(-15\)\({}^{\circ}\)C to 95 \({}^{\circ}\)C in stress controlled mode. Parallel plates measuring 8 mm were used for \(-15\)\({}^{\circ}\)C to 35 \({}^{\circ}\)C testing temperatures while 25 mm parallel plate geometry was used for a high temperature range of 45 \({}^{\circ}\)C to 95 \({}^{\circ}\)C. Target strain values were fixed as per Table 6, to establish LVE region of measurement. The testing procedure was followed as per AASHTO T315-10. Frequency was swept from 0.01 Hz to 30 Hz for each testing temperature and complex shear modulus (G\({}^{\star}\)) and phase angle (\(\delta\)) were obtained for each binder sample. Master Curve  
Master curves for the whole temperature range were developed using frequency sweep isotherms for an overall assessment of rejuvenating the asphalt binder with engine oil. It exhibited the impact of loadings on rheological performance of asphalt cement over a wide range of loading frequency or times. Isotherms obtained from frequency sweep tests were shifted to a reference temperature using the time-temperature superposition principle [36; 37]. Shift factor (\(\alpha\)T) for superpositioning of isotherms can be obtained by using William-Landel-Ferry (WLF) equation and Arrhenius function [38; 39] shown as Equations (1) and (2) respectively. \[\log(\alpha_{\rm T})=-\frac{c_{2}(\rm T-T_{R})}{c_{2}+\rm T-T_{R}} \tag{1}\]  
In Equation (1), c1 and c2 are coefficients, T is target temperature, T\({}_{\rm R}\) is reference temperature. Values of C\({}_{1}\) and C\({}_{2}\) are usually taken 19 and 92, respectively [40]. \[\log(\alpha_{\rm T})=-\frac{E_{\rm a}}{2.303\rm R}\left(\frac{1}{\rm T}-\frac {1}{T_{\rm ref}}\right) \tag{2}\]  
In Equation (2), \(\rm E\) is activation energy, T is target temperature and T\({}_{\rm ref}\) is reference temperature. The shifting of isotherms can also be done using a new dynamic modulus function know as Sigmoidal Model [41].