# Novel Aromatic Estolide Esters from Biobased Resources by a Green Synthetic Approach
## 3 Results and Discussion
### Structural Characterization of the Estolide Ester Products
#### 3.3.5. Rheological Characterization  
Rheological characterization of the synthesized estolide ester products is helpful for the future formulation of cosmetic products that could include these oligoesters. The study was accomplished for the caffe acid ester of the RCA estolide. The rheological behavior of the icinoleic acid monomer was also studied, for comparison. The rheological properties are essential for understanding the flow properties necessary for different unit operations, as well as for blending with other constituents of possible cosmetic compositions. The kinematic viscosity and viscosity index values of the starting icinoleic acid and the obtained oligomerization product are presented in Table 2.  
It is observed that both samples fall into the category of oils with a medium viscosity index [43]. For ricinoleic acid, the relationships between shear stress \(\tau\) and shear rate \(\dot{\gamma}\) at three temperature values, shown in Figure S6, are linear. This behavior is characteristic of Newtonian fluids, which are fluids in which viscosity is independent of the shear rate [44]. The rheological equations obtained using the Table Curve 2D program are presented in Table 3. However, from the expression of these equations, it can be seen that the dependence \(\tau=\mathsf{f}(\dot{\gamma})\) is better represented by the Herschel-Bulkley model, where \(\tau_{0}\) is the yield stress below which there is no flow, \(\mathsf{k}\) is the consistency index and \(\mathsf{n}\) is the power index [45]. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Kinematic Viscosity, cSt**} & \multirow{2}{*}{**Viscosity Index**} \\  & **40 \({}^{\circ}\)C** & **100 \({}^{\circ}\)C** & \\ \hline RCA & 142.5 & 10.6 & 29 \\ Oligo(ricinoleyl)-caffeate & 200.6 & 14.7 & 61 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Rheological properties of the estolide ester product synthesized from ricinoleic acid and caffe acid, compared to the ricinoleic acid used as a raw material. Figure 8: DSC thermogram of the oligo (ricinoleyl)-caffeate product in an air atmosphere. It can be observed that increasing the temperature leads to a slight increase in the yield stress and a decrease in the consistency index without changing the nature of the rheological behavior. The values of power index, slightly higher than 1, suggest that the flow is shear thickening [45], which means that the apparent viscosity increases with the increase in shear rate, after the yield stress value has been exceeded. For ricinoleic acid, the variation in the apparent viscosity with the shear rate, at three temperature values, is depicted in Figure 9.  
It is found that the thickening effect is slightly more visible at lower temperatures (40 \({}^{\circ}\)C), and as the temperature increases, the apparent viscosity values remain approximately constant (Newtonian behavior, the power index n is very close to 1). The \(\tau=\mathrm{f}(\dot{\gamma})\) dependences, at 40 \({}^{\circ}\)C and 70 \({}^{\circ}\)C, for ricinoleic acid and the estolide ester synthesized with caffeic acid in toluene (RCN-CT) are shown in Figure 10.  
As results from Figure 9, in the case of estolides the dependencies are linear, and a small yield shear stress is present, which places them in the class of Herschel-Bulkley fluids. It can also be observed that, at the same temperature, the estolides synthesized in toluene  
Figure 10: The \(\tau=f(\dot{\gamma})\) dependence for ricinoleic acid and the estolide esters synthesized with caffeic acid. Figure 9: The \(\tau_{\mathrm{n}}=\mathrm{f}(\dot{\gamma})\) dependence for ricinoleic acid. have higher shear stress values compared to ricinoleic acid. This increase in viscosity is the result of the significant increase in molecular mass, along with the increase in the degree of oligomerization, as well as of structural changes due to the introduction of benzene rings in the structure of estolides.