## 3 Results and Discussion
### Master Curves
First, the low MW peaks decrease in intensity, while the high MW peaks increase; second, the overlapping of the peaks diminishes, introducing a shape shift from a unimodal to a multi-modal curve, according to aging time. The latter is a direct consequence of the increase in DI, which means a wider distribution. Again, a graph comparing the two binders helps understanding the effect of the clay (Figure 8). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sample** & **G\({}_{\rm 0}\) (Pa)** & **G\({}_{\rm so}\) (Pa)** & \(\alpha\) & \(\beta\) & \(\tau\) & **k** & **h** \\ \hline B & \(1.0\cdot 10^{-8}\) & \(5.82\cdot 10^{8}\) & 0.0350 & \(1.07\cdot 10^{4}\) & \(1.19\cdot 10^{-4}\) & 0.666 & 0.312 \\ B25 & \(1.0\cdot 10^{-8}\) & \(5.82\cdot 10^{8}\) & 0.0180 & \(1.58\cdot 10^{5}\) & \(3.48\cdot 10^{-4}\) & 0.633 & 0.305 \\ B40 & \(1.0\cdot 10^{-8}\) & \(5.82\cdot 10^{8}\) & 0.0191 & \(1.35\cdot 10^{5}\) & \(1.03\cdot 10^{-3}\) & 0.639 & 0.323 \\ B65 & \(1.0\cdot 10^{-8}\) & \(5.82\cdot 10^{8}\) & 0.0105 & \(2.32\cdot 10^{6}\) & \(7.50\cdot 10^{-4}\) & 0.595 & 0.292 \\ B90 & \(1.0\cdot 10^{-8}\) & \(5.82\cdot 10^{8}\) & 0.0084 & \(5.50\cdot 10^{6}\) & \(1.15\cdot 10^{-3}\) & 0.590 & 0.287 \\ LS-B & \(1.0\cdot 10^{-8}\) & \(5.82\cdot 10^{8}\) & 4.68 & \(6.05\cdot 10^{1}\) & \(5.53\cdot 10^{-2}\) & 0.338 & 0.680 \\ LS-B25 & \(1.0\cdot 10^{-8}\) & \(1.83\cdot 10^{8}\) & 6.13 & \(2.05\cdot 10^{2}\) & \(2.03\cdot 10^{-1}\) & 0.319 & 0.648 \\ LS-B40 & \(1.0\cdot 10^{-8}\) & \(5.82\cdot 10^{8}\) & 0.0253 & \(5.53\cdot 10^{4}\) & \(1.25\cdot 10^{-3}\) & 0.649 & 0.334 \\ LS-B65 & \(1.0\cdot 10^{-8}\) & \(5.82\cdot 10^{8}\) & 0.0153 & \(4.14\cdot 10^{5}\) & \(8.44\cdot 10^{-4}\) & 0.615 & 0.304 \\ LS-B90 & \(1.0\cdot 10^{-8}\) & \(3.70\cdot 10^{8}\) & 0.0114 & \(6.88\cdot 10^{5}\) & \(7.78\cdot 10^{-4}\) & 0.615 & 0.290 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The 2S2P1D model’s parameters. Figure 7: AMWD at different aging times for the LS-B binder. The AMWD is affected by both the molecular weight and the interactions that determine the aggregation of the molecules. In the unaged conditions, the B and LS-B curves are similar but not completely superposed, thus confirming the already observed influence of layered silicate on the bitumen structure [41; 42]. Nevertheless, the binders B and LS-B start from similar apparent distributions, which progressively diverge with increasing aging. At 25 PAV, the LS-B binder already shows a reduced dependence on aging with respect to the B binder. Then, at higher levels of aging, the B distribution clearly includes molecules or aggregates of higher dimensions. The shift toward higher \(M_{w}\) can be quantified by calculating the number (\(M_{n}\)) and weight (\(M_{w}\)) average molecular weights, and the dispersion index, which has a direct link with the square value of the variance (\(\sigma^{2}\)) of the distribution:  
\[DI=\frac{M_{w}}{M_{n}}=\frac{\sigma^{2}}{M_{n}^{2}}+1 \tag{18}\]  
Based on these quantities, we can define the following aging indexes:  
\[AI_{n}=\frac{M_{n,a}}{M_{n,u}}\;AI_{w}=\frac{M_{w,a}}{M_{w,u}}\;AI_{DI}=\frac{ DI_{a}}{DI_{u}} \tag{19}\]  
The numerical values for the two binders are reported in Table 4.