# Polysaccharides-Reinforced Bitumens: Specificities and Universality of Rheological Behavior
## 3 Results and Discussion
### Viscosity (\(\eta\)) as a Function of Temperature (T)--Arrhenius Model
It has been also observed that:  
1. this behavior is observed for all the investigated samples;
2. the same linear trend is observed also in a wider interval including lower temperatures;
3. the effect of network breakdown at higher temperatures (\(G^{\prime}\) drop at T = T*), which represents however a strong structural modification, does not exert its effects in the temperature range considered, preserving the linear trend in the Arrhenius plot. These observations suggest that the choice the Arrhenius model is the most adequate. There is no reason, in fact, to use the VTF equation since the temperatures considered are significantly higher than the Tg (in this case the VTS would reduce to the Arrhenius giving T\({}_{0}\) = 0) and since a polynomial expression would get rid of the physics behind the Arrhenius model (see later) to simply take into account for the numerical interpolation of experimental data. 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 [33] (TST) by [PERSON] of Arrhenius chemical kinetics to transport phenomena [34]. In this framework, \(\mathrm{E}\)a represents the activation energy to overcome for flowing to occur. It can be easily derived from the slope of the best fit line in the Arrhenius plot (as shown in the inset of Figure 1) according to the logarithmic form  
\[\ln\eta\star(T)=\ln As+\frac{Ea}{R}\cdot\frac{1}{T} \tag{3}\]  
where \(\eta^{\star}\) is the complex viscosity (Equation (2)), R is the gas constant, 8.314 J K\({}^{-1}\) mol\({}^{-1}\) and As is the pre-exponential (entropic) factor. In the same framework, the logarithm of pre-exponential factor (\(\ln As\)) can be derived as the intercept of the best fit linear regression of the experimental data. \(As\) has been generally dealt with a \"frequency factor\", representing the fraction of effective collisions which are able to turn into the flow process. In the context of TST, \(\ln As\) represents the entropic change when passing from the initial state to the transition state typically formed during the hopping between one potential well to the other in the shearing process. Let's now use these physical quantities to interpret the observed data (reported in Table 1). The \(\mathrm{E}\)a values are consistent with the value observed for other additivated bitumens [3] lying in the range 120-140 kJ/mol. In addition, while all additives cause a more or less marked increase in the \(G^{\prime}\)@50 \({}^{\circ}\)C, they do not uniquely affect \(\mathrm{E}\)a. Some additives in fact cause an increase in \(\mathrm{E}\)a, like carob seeds flour, xanthan gum, pectin and carboxymethylcellulose, whereas some other compounds affect the bitumen in the opposite way causing a decrease of \(\mathrm{E}\)a, like oranges skins and carragenines. This observation suggests prudence in interpreting the two parameters (rigidity--or \(G^{\prime}\)--and \(\mathrm{E}\)a) in the same terms. They should be treated, instead, as independent and sometimes different aspects of the phenomenon. Indeed, as shown in Figure 3, lack of correlation has been found between \(\mathrm{E}\)a and \(G^{\prime}\)@50 \({}^{\circ}\)C (or T*, given the correlation between T* and \(G^{\prime}\)@50 \({}^{\circ}\)C shown in Figure 2). Similar behavior has been found in other papers as, for example, the polyphosphoric acid-additivated bitumen in [31], which showed higher rigidity with respect to the neat bitumen but lower activation energy of the viscosity. As for the pre-exponential factor, it can be observed that In As is always negative, independently of the additive used. Remaining in the same theoretical model considering the formation of a transition state during flow (TST model), this would indicate a positive entropy of formation of the activated state during flow. This means that the mechanism of flowing is mediated by the formation of a _disaggregated_ transition state.