## 3 Results and Discussion
### Master Curves
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**B**} & \multicolumn{4}{c}{**LS-B**} \\ \hline
**PAV** & \(\mathbf{M_{n}}\) **(g/mol)** & \(\mathbf{M_{w}}\) **(g/mol)** & **DI** & \(\mathbf{AI_{n}}\) & \(\mathbf{AI_{w}}\) & \(\mathbf{AI_{DI}}\) & \(\mathbf{M_{n}}\) **(g/mol)** & \(\mathbf{M_{w}}\) **(g/mol)** & **DI** & \(\mathbf{AI_{n}}\) & \(\mathbf{AI_{w}}\) & \(\mathbf{AI_{DI}}\) \\ \hline
0 & 743 & 784 & 1.06 & 1.00 & 1.00 & 1.00 & 794 & 836 & 1.05 & 1.00 & 1.00 & 1.00 \\
25 & 942 & 1013 & 1.08 & 1.27 & 1.29 & 1.02 & 923 & 986 & 1.07 & 1.16 & 1.18 & 1.02 \\
40 & 1002 & 1079 & 1.08 & 1.35 & 1.38 & 1.02 & 962 & 1029 & 1.07 & 1.21 & 1.23 & 1.02 \\
65 & 1167 & 1279 & 1.10 & 1.57 & 1.63 & 1.04 & 1050 & 1135 & 1.08 & 1.32 & 1.36 & 1.03 \\
90 & 1265 & 1394 & 1.10 & 1.70 & 1.78 & 1.04 & 1090 & 1180 & 1.08 & 1.37 & 1.41 & 1.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average molecular weights, dispersion, and aging indexes for B and LS-B. Figure 8: AMWD comparison of the unaged, 25, and 90 h PAV aged samples. All indexes confirm the anti-aging effect of the clay and the most sensitive index seems to be \(AI_{\text{w}}\). One of the disadvantages of the indexes defined in Equation (19) is that they refer to a single data point. The first and second give an idea of the shift of the curve toward higher MW. The third one is related to the variance of the curve, but it has not a clear physical meaning when the curve has a complex shape, such as the AMWD, after aging. As it was for the master curves, we need something that may take into account the changes in the whole curve. One parameter that may help is the Aging Molecular Distribution Shift (AMDS) proposed by [PERSON] et al. [39]:  
\[AMDS=\int_{0}^{\infty}\lvert f_{a}-f_{u}\rvert dlogMW \tag{20}\]  
where \(f_{a}\) and \(f_{u}\) are the weight fractions in the AMWD. In other words, the AMDS gives the area of the absolute value of the difference between the distributions obtained before and after aging. Both horizontal and vertical shifts as well as variations in shape affect this parameter. Figure 9 shows that AMDS is always higher for B and the difference with respect to LS-B increases with aging. Another interesting aspect of the AMWD is that with increasing aging, the main peaks of the distribution separate one from each other. This suggests analysing the peaks individually, by means of a simple deconvolution procedure. As proposed by [PERSON] et al. [40], the AMWD were fitted with four Gaussian functions associated with populations with different molecular weights. As an example, Figure 10 shows the four populations (named P1 to P4) for the B25 binder. Figure 9: AMDS for the B and LS-B binders at different levels of aging. All peaks shift toward higher molecular weights, this being more accentuated for the P3 and P4 peaks. With respect to the relative quantities, only P3 registers an increase due to aging while the other ones diminish more or less evidently. Moreover, the most significant variations usually appear in the first aging step. However, due to peaks overlapping, it is difficult to evaluate aging from the analysis of the individual populations. Therefore, the populations were grouped in light (P1 + P2) and heavy (P3 + P4) weight fractions and the following aging index (included in Table 5) was defined:  
\[AI_{P}=\frac{\left[\frac{(P3+P4)}{(P1+P2)}\right]_{q}}{\left[\frac{(P3+P4)}{( P1+P2)}\right]_{u}} \tag{21}\]  
\(AI_{P}\) takes into account the relative quantities of the high and low MW populations and gives a further confirmation of the positive effect of clay as an anti-aging additive. Figure 10: Deconvolution in four Gaussian peaks of the AMWD for B25 binder.