## 2 Materials and Methods
### Characterization  
#### 2.3.1 Physical Properties  
In accordance with the standard ASTM D792 [23], the density of the vulcanized NR samples was measured by Archimedes' principle. The tests were performed at ambient temperature and employing a Mettler kit ME-3340 (Mettler Toledo, Columbus, OH, USA). The specimens were weighed in air and submerged in methanol. The density was calculated using Equation (1):  
\[\rho=\frac{a}{a-b}\times P \tag{1}\]  
where a is the weight of the sample in air, b is the weight of the material submerged in methanol, and P is the density of methanol at the testing temperature (0.791 g/cm \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **SMR 10** & **Sulfur** & **ZnO** & **Stearic Acid** & **ZDBC** \\  & **(phr)** & **(phr)** & **(phr)** & **(phr)** & **(phr)** \\ \hline NR\_1.5S & 100 & 1.5 & 5.0 & 2.0 & 0.7 \\ NR\_2.5S & 100 & 2.5 & 5.0 & 2.0 & 0.7 \\ NR\_3.5S & 100 & 3.5 & 5.0 & 2.0 & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The nominal composition of the produced samples (phr = parts per hundred rubber, i.e., grams of component every 100 g of rubber polymer). \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Stage**} & **Process/Ingredients** & **Time** \\ \hline I & Mastication of NR & 5 \\ II & ZnO & 1 \\ III & Stearic Acid & 1 \\ IV & ZDBC & 1 \\ V & Sulfur & 1 \\ VI & Mixing for homogenization & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Procedure used for mixing natural rubber compounds. determined by using the Mettler kit ME-33340 (Mettler Toledo, Columbus, OH, USA)). For each NR formulation, three specimens were tested. In accordance with the standard ASTM D6814 [24], the determination of the crosslinking density (\(\mathrm{v}\)) of the NR samples was conducted through equilibrium swelling measurements in toluene. NR specimens, weighing approximately 0.10 g each, were first immersed in acetone for three days to remove the acetone-soluble fraction. The rubbers were then dried for 24 h in a ventilated oven and cooled to room temperature. After that, the specimens were immersed in toluene for 4 days until an equilibrium state was achieved. Subsequently, the specimens were taken out, the swollen masses were weighted (\(\mathrm{w_{s}}\)) and subjected to drying to eliminate excess solvent in a ventilated oven at 60 \({}^{\circ}\)C until constant weight (i.e., approx. 24 h). Finally, the dried masses were recorded (\(\mathrm{w_{d}}\)). Then, the crosslinked density (\(\mathrm{v}\)) was determined through Equation (2), developed by [PERSON] [24]:  
\[v=\frac{-\ln(1-V_{r})+V_{r}+XxV_{r}^{2}}{V_{1}x(V_{r}^{\frac{1}{2}}-V_{r})/2} \tag{2}\]  
where X is the polymer-solvent interaction parameter, V\({}_{1}\) is the molecular volume of solvent, and V\({}_{r}\) is volume fraction of polymer in a swollen network in equilibrium with pure solvent, calculated according to ASTM D6814 standard, as reported in Equation (3):  
\[V_{r}=\frac{\frac{w_{d}}{\rho_{d}}}{\frac{w_{d}}{\rho_{d}}+\frac{w_{\mathrm{oa }}}{\rho_{s}}} \tag{3}\]  
where \(\mathrm{w_{d}}\) is the weight of dry rubber, \(\mathrm{\rho_{d}}\) is the density of dry rubber, \(\mathrm{w_{so}}\) is the solvent absorbed by the sample evaluated as difference between \(\mathrm{w_{s}}\) and \(\mathrm{w_{d}}\), and \(\mathrm{\rho_{s}}\) is the density of the solvent. The values used for the molar volume of toluene (V\({}_{1}\)), the Flory-Huggins interaction parameter (X) and the toluene density were 106.288 cm\({}^{3}\) mol\({}^{-1}\), 0.391 and 0.867 g/cm\({}^{3}\), respectively [24]. The density of dry natural rubber was determined by Archimedes' principle in methanol according to Equation (1). For each NR formulation, six specimens were tested. Shore A hardness measurements were conducted using a Hilderbrand Durometer (Pruf-und Mestechnik GmbH, Wendlingen am Neckar, Germany) in compliance with the ASTM D2240 standard [25].