## 2 Materials and Methods
### Testing Methods  
Fourier transform infrared spectroscopy (FT-IR) can identify the differences between the functional groups and characteristic absorption peaks in ESO/TATA and ESO and TETA and analyze the synthesis mechanism. FT-IR (Invenio-S, Bruker, WI, USA) was used to evaluate the changes in the functional groups during the reaction. The scanning wavenumber range was 4000-400 cm\({}^{-1}\), and the cumulative number of scans and scanning rate were 32 and 4 cm\({}^{-1}\), respectively.  
The nuclear magnetic resonance spectroscopy (NMR) analysis of the samples was conducted using a Bruker 600 MHz high-resolution NMR spectrophotometer (Bruker-electrospin 600 MHz Ultrashield, Bruker, WI, USA). \({}^{1}\)H-NMR spectra were used in the study of the ESO/TATA structure. The samples were prepared by dissolving 10 mg in deuterated CDCl\({}_{3}\), and the spectra were obtained at room temperature.  
The primary element types and contents of the DCR and MDCR were examined using EDS (Gemini SEM 360, ZEISS, Jena, Germany) at a voltage with 5 kV.  
The physical characteristics of each modified asphalt sample were tested following the JTG E20-2011 test specification for highway engineering asphalt and asphalt mixtures. The softening point was determined using the ball-and-ring method with a fully automatic asphalt softening point tester (SYD-2806G, Changji Geological Instrument Co., Ltd., Shanghai, China). The penetration was determined using an automatic penetration tester (SYD-2801H, Changji Geological Instrument Co., Ltd., Shanghai, China). The ductility and elastic recovery were determined using a ductility tester (SYD-4508G, Changji Geological Instrument Co., Ltd., Shanghai, China).  
Segregation testing was performed to measure the degree of separation between the rubber and asphalt binder. At first, the samples were heated to 163 \({}^{\circ}\)C to allow them to pour easily into aluminum tubes. Then, they were placed in an upright position in a holder rack. Then, the tube tops were sealed and placed inside an oven at 163 \({}^{\circ}\)C for a continuous 48 h. After that, the rack was taken out and kept in a refrigerator for 4 h at \(-2\) \({}^{\circ}\)C. After the asphalt solidified, one-third of the upper and lower parts were taken, put into a beaker, and melted in the oven. To evaluate the storage stability of the composite modified asphalt, the difference between the softening point of the top sample and the bottom sample was determined according to ASTM D5892 [24]; if the difference was less than \(2.2\) \({}^{\circ}\)C, the sample was considered stable in terms of storage.  
A dynamic shear rheometer (DSR) was used to assess the high-temperature rheological performance of the asphalt binder using a dynamic rheometer (ARES-G2, TA Instruments Company, New Castle, DE, USA). Samples were prepared by placing them between two parallel plates, each with a diameter of 25 mm, and a sample thickness of 1 mm was maintained. DSR temperature sweep tests were performed. The asphalt binder was under the linear viscoelastic range when the tests were conducted. The temperature sweeps were operated with test temperatures changing from 52 \({}^{\circ}\)C to 82 \({}^{\circ}\)C at a certain frequency of 10 rad/s.  
For the assessment of the recovery and putting characteristics, the multiple stress creep recovery (MSCR) test was conducted using a rheometer (DHR, TA Instruments Company, New Castle, DE, USA). The oscillation rate was set to 10 rad/s, as this typically represents a traffic speed of 90 km/h. For the test, a set of 10 cycles of repetitive loading and unloading were measured by the instrument, with a loading time of 1 s and a relaxation time of 9 s. The measurements were taken for both stresses of 0.1 kPa and 3.2 kPa. The data were then utilized to calculate the percentage recoverable strain in the specimens. In addition, the rutting performance of the binder was assessed using the MSCR test, as outlined in the standards (ASTM-D7405, 2015).