## 3 Results and Discussion  
### Master Curves  
Figure 2 shows the phase-angle master curves derived for the base binder by application of the TTSP. The master curves at all levels of aging have the typical behaviour of bitumen, which in a relatively short frequency range changes from a low-viscosity Newtonian liquid to a glassy, brittle solid. In the intermediate frequency range, bitumen has viscoelastic properties directly related to its colloidal structure, determined by the composition and relative amount of maltenes and asphaltenes (3,4). It is in this range that even small variations in the composition caused by the oxidative aging may have a significant effect on the rheological behaviour. This is clearly visible by observing the changes induced by multiple PAV cycles. From a qualitative point of view, the increase in bitumen stiffness is reflected by a reduction in the values of the phase angle (at a fixed reduced frequency) that determines a shift of the whole curve toward lower reduced frequencies. A qualitatively similar behaviour can be observed for the master curves of the LS-B binders and it is interesting to compare the master curves with and without clay, reported  
Figure 2: Phase-angle master curves for neat binder B before and after different levels of aging. Reference temperature 0 \({}^{\circ}\)C.  
in Figure 3 for some of the aging levels. Undoubtedly, LS has a remarkable impact on the aging behaviour. The unaged binders have similar values of the phase angle, the LS-B binder being a little bit stiffer due to the presence of the solid modifier. The relative position of the curves reverses after 25 h of PAV aging and the distance between the curves increases significantly at very high levels of aging. Considering the logarithmic scale of the \(x\)-axis, it is clear that for intermediate values of \(\delta\), the reduced frequency may vary even by one order of magnitude while comparing the two binders. This is the first indication of an anti-aging effect of the clay. The master curves of the magnitude of complex modulus (Figure 4) confirm the described trend. The \(|\)G*\(|\) value increases with aging and its variation is much higher without clay. Before aging, the curve of B has a lower magnitude of the modulus with respect to LS-B; after 25 h of PAV the curves are almost superposed, while an inversion is observed after further PAV treatments. Figure 4: Magnitude of complex modulus for the same samples reported in Figure 3. Reference temperature 0 \({}^{\circ}\)C.  
Figure 3: Phase-angle master curves for binders B and LS-B before and after different levels of aging. Reference temperature 0 \({}^{\circ}\)C.  
A quantitative evaluation of the aging can be performed in several ways, depending on the used aging index. Usually, the aging indexes are calculated as the ratio between a property before and after aging. This property can be chosen among the classical ones for bituminous binders (e.g., softening point, Brookfield viscosity, or penetration) or can be related to the chemical composition by evaluating the degree of oxidation (i.e., C=O groups quantified by infra-red spectra) [31]. Otherwise, it can derive from rheological data and this opens the debated question about the most representative indexes [3,4]. One reason why the choice is not easy, is that rheological data usually derive from frequency, temperature, stress, or strain sweeps, and thus cover a wide range of operating conditions. Evaluating the aging index on a single point of a long curve, such as the master curves of Figures 2-4, may not be fully representative. In contrast, deriving an \"aging master curve\" by considering all experimental data may be as much useless or dispersive and difficult to interpret. A possible solution is the use of parameters that somehow describe the curve shape, such as those derived from the Christensen-Andersen model [32].