## 3 Results and Discussion  
To highlight the rheological properties of bituminous materials used in this study, viscosity (\(\eta\)) was measured as a function of temperature for both neat and RTFOT-aged as they are and mixed with filler. The first aim of this study is to understand the macroscopic behavior in terms of molecule-based physics, so it must be pointed out that viscosity is a synthetic indicator concisely yielding information on the total amount of energy that the system absorbs under shear conditions. It has the physical meaning of representing the resistance to flow.  
The temperature dependence of \(\eta\) is reported in Figure 2 as In \(\eta\) vs. 1000/\(T\) (Arrhenius plot). The choice of the Arrhenius plot does not follow the common habit to show the temperature dependence of a dynamical property. Arrhenius-like approach in fact, is simple and informative for a wide range of processes (viscosity, diffusion, conductivity, relaxation times etc.) [47; 48; 49; 50], but in our case it is the result of our approach based on the molecular interpretation of the macroscopic properties. The arguments are reported in a recent study [51] and will not be extensively presented here. Here instead, it is enough to notice that although the fluids under study cannot be considered as simple liquids and despite other methods being available [52; 53; 54], the linear trend in the Arrhenius plot suggests the effectiveness of the two-wells potential model, at least in the considered temperature range. This allows to safely extract both the activation energy (\(Ea\)) and the pre-exponential factor (In \(As\)) by fitting of the experimental data through the plot of \(\ln\eta\left(T\right)\) vs. 1000/\(T\) according to the Equation (1) (\(Ea/R\) is the slope of the fitting curve and \(\ln As\) is the intercept):  
\[\ln\eta(T)=\ln As+\frac{Ea}{R}\cdot\frac{1000}{T} \tag{1}\]  
where \(\eta\) is the viscosity and \(R\) is the gas constant (\(R=8.314\) J K\({}^{-1}\) mol\({}^{-1}\)).  
Figure 3 reports the \(Ea\) (abscissa) and \(\ln As\) (ordinates) for the various samples, a representation allowing to detect the correlation between the two quantities (dashed line). In the Arrhenius model framework, \(Ea\) and \(As\) have precise physical meanings. In fact, although the Arrhenius model has been derived from the reaction kinetics in the gas phase, a favored theoretical base for the interpretation of viscosity has been provided by the application of the transition-state-theory [55] (TST) by [PERSON] of Arrhenius chemical kinetics to transport phenomena [56]. TST basically explains the reaction rates of elementary chemical reactions assuming a chemical quasi-equilibrium between reactants and an activated transition state complex.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Neat Bitumen Mix** & \
\begin{tabular}{c} **RTFOT-Aged** \\ **Bitumen Mix** \\ \end{tabular} &
\begin{tabular}{c} **Acceptance** \\ **Thresholds**[45] \\ \end{tabular} \\ \hline bulk density (g/cm\({}^{3}\)) & 2.481 \(\pm\) 0.005 & 2.465 \(\pm\) 0.005 & - \\ Marshall Stability (KN) & 11.9 \(\approx\)\(\pm\) 0.4 & 13.0 \(\pm\) 0.4 & \textgreater{}11 \\ Flow (mm) & 2.5 \(\pm\) 0.2 & 1.9 \(\pm\) 0.2 & - \\ Marshall Quotient (KN/mm) & 4.8 \(\pm\) 0.5 & 6.8 \(\pm\) 0.5 & \textgreater{}3 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Marshall Stability for asphalts concretes prepared with neat and RTFOT-Aged Bitumen (average of six independent samples). In parenthesis the standard deviation is reported.  
We will comment on _Ea_, In _As_ and their correlation separately in the following sections.