## 4 Results and Discussion
### Complex Viscosity and Loss Factor (Tan \(\delta\)) Results  
The results from the frequency sweep tests evaluating complex viscosity (\(\eta^{\star}\)) and the loss factor (tan \(\delta\)) at two temperatures, 15 \({}^{\circ}\)C and 25 \({}^{\circ}\)C, provide valuable insight into the viscoelastic behavior of both unmodified and modified bitumen samples (Tables 7-10). Across all samples, as the angular frequency increases, the complex viscosity (\(\eta^{\star}\)) decreases, which is a typical rheological behavior indicating the shear-thinning nature of bitumen. This decrease in viscosity with frequency signifies that the materials exhibit more fluid-like behavior at higher frequencies, which could translate to better deformation resistance under traffic loading. However, the rate of this decreases and the absolute values of \(\eta^{\star}\) vary considerably between the modified and unmodified samples, influenced by the nature and percentage of additives. Tables 7 and 8 illustrate the relationship between complex viscosity (\(\eta^{\star}\)) and angular frequency for unmodified bitumen at two different temperatures: 15 \({}^{\circ}\)C and 25 \({}^{\circ}\)C. At both temperatures, the complex viscosity decreases as the angular frequency increases, showing the typical shear-thinning behavior of bitumen. This means that at higher frequencies, the bitumen becomes less viscous and more prone to flow, which is expected under dynamic loading conditions. At 15 \({}^{\circ}\)C, the complex viscosity is higher than at 25 \({}^{\circ}\)C, indicating that the bitumen is more resistant to deformation and behaves more like a solid at lower temperatures, making it more prone to cracking. At 25 \({}^{\circ}\)C, the bitumen has a lower complex viscosity, reflecting that it is more fluid-like and can flow more easily, which reduces its susceptibility to block cracking. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Bitumen Type** & **Unmodified** & **4\% SBS** & **5\% SBS** & **4\% AB** & **5\% AB** & **6\% AB** & **3\% WCO** & **4\% WCO** & **5\% WCO** \\ \hline
**Angular Frequency** & & & & & & & & & \\
**[rad/s]** & & & & & & & & & \\ \hline
100 & \(  
The loss factor (tan \(\delta\)), which represents the ratio of the loss modulus (G\({}^{\prime\prime}\)) to the storage modulus (G\({}^{\prime}\)), provides insight into the balance between viscous and elastic behavior. A higher tan \(\delta\) value indicates more viscous behavior, while a lower value suggests more elastic (solid-like) behavior. At 15 \({}^{\circ}\)C (Table 9), the tan \(\delta\) values are lower across the frequency range, suggesting that the bitumen behaves more elastically and has higher stiffness at this temperature. In contrast, at 25 \({}^{\circ}\)C (Table 10), the tan \(\delta\) values are higher, indicating that the bitumen exhibits more viscous behavior and increased flexibility, which helps prevent cracking. For the 4% SBS-modified samples (Tables 7-10), the complex viscosity decreases as the angular frequency increases, demonstrating shear-thinning behavior typical for viscoelastic materials. At 15 \({}^{\circ}\)C, the viscosity is higher than at 25 \({}^{\circ}\)C, showing that the material is more resistant to flow and stiffer at lower temperatures. The loss factor (tan \(\delta\)) is lower at 15 \({}^{\circ}\)C, indicating that the material behaves more elastically and has less energy dissipation compared to its behavior at 25 \({}^{\circ}\)C, where it exhibits more viscous (fluid-like) properties. In the 5% SBS-modified samples (Tables 7-10), a similar trend is observed, with the complex viscosity decreasing as the angular frequency increases. However, the 5% SBS sample exhibits slightly lower viscosity values compared to the 4% SBS sample, particularly at 25 \({}^{\circ}\)C, suggesting that the higher SBS content enhances the material's flexibility, reducing stiffness.