## 3 Results and Discussion
### Results of Advanced Performance-Related Characterization Tests
#### 3.3.1 SAOS Tests
In general terms, it was observed that in both considered ageing states, polymer modification produced a reduction in \(C_{1}\) and \(C_{2}\). Such an outcome is consistent with findings reported in studies that indicate that the use of SBR and PBR can cause a significant change of the temperature dependency of base bitumen [9; 15; 18]. As expected, the addition of both polymers caused a hardening effect that was reflected by the progressive reduction of crossover frequency as a function of polymer dosage. In such a context, PBR polymers proved to be more effective, leading to lower values of \(\omega_{c}\) in comparison to those obtained for SBR-modified binders. In the case of PBR polymers, the abovementioned hardening was greater for the premium quality product, whereas such an effect was recorded for the SBR modifiers only for tests carried out on unaged samples. Both SBR and PBR polymers induced a remarkable increase in the rheological parameter R, thus indicating that the corresponding master curves were flattened out with a more gradual transition from the purely viscous to the glassy state. The effects caused by the two polymers were comparable. In the case of the SBR-modified binders, only slight differences were observed between polymers of different quality. Greater differences were recorded for PBR modified binders, with greater \(R\) values associated with the use of the waste product. Figure 6: Black diagrams of SBR-modified binders: (**a**) unaged binders; (**b**) RTFO-aged binders. Figure 7: Black diagrams of PBR-modified binders: (**a**) unaged binders; (**b**) RTFO-aged binders. The glassy modulus \(G_{g}\), extrapolated from the available data, in most cases, was found to decrease with polymer modification for unaged binders, whereas it increased for RTFO-aged samples. However, these findings would need to be validated by further low temperature tests. In order to assess the specific effects of ageing, reference was made to the \(AI\) index defined according to the following expression [40]:  
\[AI=\frac{(\omega_{c})_{A}}{(\omega_{c})_{U}}, \tag{6}\]  
where \((\omega_{c})_{A}\) and \((\omega_{c})_{U}\) are the crossover frequencies determined in aged and unaged conditions, respectively. Calculated values of \(AI\) are shown in Figure 8. It can be observed that the binders modified with SBR, w-SBR, and PBR exhibited an ageing level which was lower than that of base bitumen. This is proven by the higher values of \(AI\), that progressively increased with polymer dosage. Such an outcome is consistent with the findings of previous investigations, in which it was observed that SBR modification can reduce the rate of oxidation [6; 12]. On the contrary, use of the w-PBR polymer led to a reduction in the considered index, thus indicating that it was less effective in reducing the ageing which occurred during RTFO treatment. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ageing State** & **Binder Code** & **TR** & \begin{tabular}{c} **\(\mathbf{C_{1}}\)** \\ **[-]** \\ \end{tabular}  & \begin{tabular}{c} \(\mathbf{C_{2}}\)** \\ **[\({}^{\circ}\)C]** \\ \end{tabular}  & \begin{tabular}{c} \(\mathbf{G_{g}}\) \\ **[Pa]** \\ \end{tabular}  & \ \begin{tabular}{c} \(\mathbf{\omega_{c}}\) \\ **[rad/s]** \\ \end{tabular}  & \begin{tabular}{c} \(\mathbf{R}\) \\ **[kPa]** \\ \end{tabular}  \\ \hline Virgin & NB & 20 & 14.05 & 120.31 & \(4.98\times 10^{8}\) & 380.19 & 1.19 \\ RTFO & NB & 20 & 14.29 & 116.03 & \(3.38\times 10^{8}\) & 93.33 & 1.23 \\ \hline Virgin & SW3 & 20 & 11.67 & 95.41 & \(4.52\times 10^{8}\) & 279.12 & 1.31 \\  & SQ3 & 20 & 12.04 & 98.41 & \(4.51\times 10^{8}