## 3 Results
### Dynamic Rheological Properties of the MDCR-Modified Asphalts  
In the investigation of the complex shear modulus (G*) behavior across the various asphalt formulations in response to temperature variations, as delineated in Figure 9a, a universal trend was observed, where G* diminished with an increase in temperature across all the examined asphalt types. This trend signifies a reduction in the materials' resistance to deformation as temperatures escalate [32; 33]. Compared with the DCR20A modified asphalt, the influence of temperature on the modulus of the MDCR20A modified asphalt notably diminished, indicating that MDCR can significantly reduce the temperature sensitivity of modified asphalt. This may be due to the addition of the MDCR, which enhanced the interfacial effect with the asphalt and increased the chain entanglement with light and colloidal components in the asphalt. Furthermore, with increasing concentrations of MDCR, this molecular entanglement intensified, successively bolstering the asphalt's deformation resistance. At the molecular level, the entanglement involves cross-links and interactions that can significantly restrict the mobility of polymer chains, thereby increasing the material's elasticity, effectively increasing its deformation resistance. Figure 8: Difference in softening point of the modified asphalt with different DCR and MDCR contents. Figure 9: The dynamic rheological curves of **(a)** complex modulus and **(b)** phase angle vs. frequency. It was found that the d value of the matrix asphalt and DCR20A increased with the increase in temperature, indicating that the viscosity of the asphalt increased and the deformation recovery ability decreased. This phenomenon can be attributed to the breakdown of sulfur-carbon (S-C) and carbon-carbon (C-C) bonds within the crosslinked macromolecules, a process accelerated by the thermal energy accumulated during stirring and shearing. Such degradation reduced the mass of the rubber macromolecules, leading to diminished elasticity and recovery properties [34]. However, when the proportion of MDCR in the asphalt was between 20% and 50%, the parameter d showed a decrease above 70 \({}^{\circ}\)C, signifying a notable improvement in the elastic efficiency. It can be seen that the viscoelastic properties of the MDCR-modified asphalt have very complex influences, and more elastic components appeared in the MDCR-modified asphalt, which is further speculated to be related to a certain degree of chain entanglement in the asphalt colloid system. It is noted that the high-temperature performance of asphalt binders was improved after the addition of the MDCR. Figure 10 gives the cumulative strain curve of the modified asphalt sample at 58 \({}^{\circ}\)C. The cumulative strain of the asphalt substrate increased obviously with the extension of the loading time. The matrix asphalt is mainly viscous, and high temperatures or overload lead to more serious permanent deformation of the matrix asphalt [35]. The cumulative strain of the DCR-modified asphalt was smaller than that of the matrix asphalt at each strain level, indicating that the DCR had a complementary effect on the elasticity of the asphalt and improved the elastic recovery ability. At a low strain level, the cumulative strain change rate was small, but at a high strain level, the cumulative strain increased significantly. This shows that the elastic recovery ability of the DCR-modified asphalt under overload conditions was insufficient. In contrast, the MDCR-modified asphalt had excellent elastic resilience. MDCR can form a more stable elastic network structure in asphalt, such that the asphalt is still in a viscoelastic state under high-temperature and high-strain conditions, which has a positive effect on improving the deformation recovery ability of modified asphalt.