## 2 Materials and Methods
### Methods
It is also interesting to mention that, as the binders were produced using a laboratory high shear mixer, for the reproduction of these materials in large quantities, with the same characteristics and aiming at the adequate dispersion of the modifiers, it would be necessary to use of an industrial high-shear mixer or another solution that provides the same results in terms of modifiers dispersion. After production, the modified binders were then characterized according to the following properties: penetration (ASTM D 5 [35]), softening point ASTM D 36 [36]), elastic recovery (ABNT NBR 15086 [38]), phase separation (ABTN NBR 15166 [40]), and apparent viscosity (ASTM D 4402 [37]). Stage 2 consisted of establishing the design binder contents of the asphalt mixtures, beginning the part of this study that aims to evaluate the influence of the modifiers when interacting in the asphalt mixtures. For this, the Superpave mix design method was applied, according to the standards AASHTO M 323 [41] and AASHTO R 35 [42], with the use of a gyratory compactor. Considering a maximum nominal size of the aggregate of 19 mm and a heavy volume of traffic, the binder contents of the design correspond to the following dosage criteria that were met simultaneously: (1) percentage of void volume in Ninitial (9 spins, Vv@Ninitial) \(>\) 11.0%; (2) percentage of void volume in Ndesign (125 spins, Vv@Ndesign) = 4.0%; (3) voids in mineral aggregate (VMA) \(\geq\) 13.0%; (4) voids filled with asphalt (VFA) between 65% and 75%; and (5) dust to effective binder ratio between 0.8 and 1.6. It is important to note that, during the design mix and the subsequent steps, the asphalt mixtures were produced and compacted at temperatures of which the binder viscosities corresponded respectively to 0.17 Pa.s and 0.28 Pa.s. In Stage 3, after the design binder content definition, for each mixture, three plates were molded with one having dimensions of \(60\times 40\times 9\) cm (for sawing and obtaining prismatic specimens for the complex modulus and fatigue tests) and two plates having dimensions of \(50\times 18\times 5\) cm (for the permanent deformation tests). This molding was carried out at the LCPC compacting table, following the recommendations of the French standard AFNOR NF P 98-250-2 [43] for a heavy traffic highway. Plates with dimensions \(60\times 40\times 9\) cm were then sawn, and five specimens with dimensions close to \(6.3\times 5.0\times 40.0\) cm were obtained from each plate. In Stage 4, the rheological behavior characterization of the different mixtures was evaluated. This characterization was based on complex module tests, carried out in a four-point bending test machine, following the recommendations of the European standard EN 12697-26 [44]. For each asphalt mixture, two specimens produced in the previous stage were tested. These tests were carried out under alternating bending with the application of sinusoidal loading keeping the deformation amplitude at 50 \(\mu\epsilon\). Temperatures of 0 \({}^{\circ}\)C, 5 \({}^{\circ}\)C, 10 \({}^{\circ}\)C, 15 \({}^{\circ}\)C, 20 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 30 \({}^{\circ}\)C with load frequencies of 0.1 Hz, 0.2 Hz, 0.5 Hz, 1 Hz, 2 Hz, 5 Hz, 10 Hz, and 20 Hz, were evaluated. For the interpretation of the results, master curves and black spaces were analyzed. The master curves were built in the reference temperature of 20 \({}^{\circ}\)C, based on the TTS principle (time-temperature superposition) and by applying the Williams-Landel-Ferry equation, of which the constants were calculated using the Viscoanalyse software (developed by the LCPC). In Stage 5, the resistance to permanent deformation of the four different mixtures was evaluated. In this stage, tests were performed in the French traffic simulator following the standard EN 12697-22+A1 [45]. These tests were carried out at 60 \({}^{\circ}\)C, with the application of a single axle with single wheel load, intensity of 5 kN, tire inflation pressure of 0.6 MPa, and frequency of 1 Hz.