# A Simple Method to Convert Cellular Polymers into Auxetic Metamaterials
## 3 Results and Discussion  
### Properties of the LDPE  
The initial foams were analyzed in terms of their pore diameters, foam density, foam porosity and OCP, which are summarized in Table 1. The initial foam densities were determined as 15.5 (D26), 20.9 (D21), 29.7 (D30) and 35.5 kg/m\({}^{3}\) (D36). The average cell sizes (diameters) were 752, 1107, 1209 and 694 \(\upmu\)m, respectively, leading to a decreasing porosity (between 98.4% and 96.2%) and leading to a higher foam density. Sample D21 had the highest OCP (12.3%), while values of 7.3, 8.3 and 6.3% were measured for D16, D30 and D36, respectively. These results implied that the samples were of a closed-cell structure. Finally, D21 had a higher OCP and larger pore sizes. This had a direct effect on the processing (conversion to auxetic foam). The nomenclature for the samples reported in Table 1 starts with \"PE\" for the foam (LDPE), where Dx is the initial foam density (kg/m\({}^{3}\)) and Px is the mechanical pressure (kPa). Based on our preliminary work [5], the treatment (vacuum) time was fixed at 3 h for all the samples. The temperature was fixed at 100 \({}^{\circ}\)C except for the two samples prepared at 105 \({}^{\circ}\)C for comparison. Hence, the sample PE-D16-P1.2 represents a foam with an original density of 16 kg/m\({}^{3}\) treated with a mechanical pressure of 1.2 kPa at 100 \({}^{\circ}\)C and the maximum vacuum (\(-\)0.88 bar) for 3 h, while PE-D16-O is the initial LDPE foam (neat sample) with an original density of 16 kg/m\({}^{3}\). The densities of the auxetic foams PE-D16-P1.5, PE-D21-P1.6, PE-D30-P1.5 and PE-D36-P1.5 were 120, 98.9, 87.3 and 90.3 kg/m\({}^{3}\), respectively, so the density increased by 7.5, 4.2, 3.8 and 2.5 kg/m\({}^{3}\) compared to the original D16, D21, D30 and D36 foams. This led to a decreased porosity and an increased percentage of open cells, especially for the samples based on D16, from 7.3% to 43.8%. This also indicated that the conversion broke several cell walls to produce a re-entrant structure, which had an influence on the mechanical properties, as described later. Figure 2 shows the DSC thermograms for the original LDPE foams. Each sample presented a melting point of 107-112 \({}^{\circ}\)C, which is typical for LDPE. Nevertheless, the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Foam** & **Initial Foam** & **Cell** & **Porosity** & **OCP** & **Auxetic** & **Density** & **Porosity** & **OCP** \\
**Code** & **Density** & **Diameter** & **Powosity** & **OCP** & **Auxetic** & **Rg/m\({}^{3}\)** & **\%** & **\%** \\ \hline - & kg/m\({}^{3}\) & \(\upmu\)m & \% & \% & - & kg/m\({}^{3}\) & \% & \% \\ \hline D16 & 15.5 \(\pm\) 0.4 & 752 \(\pm\) 204 & 98.4 & 7.3 & PE-D16-P1.5 & 120.0 & 86.9 & 43.8 \\ \hline D21 & 20.9 \(\pm\) 0.3 & 1107 \(\pm\) 238 & 97.8 & 12.3 & PE-D21-P1.6 & 98.9 & 89.2 & 19.8 \\ \hline D30 & 29.7 \(\pm\) 0.3 & 1209 \(\pm\) 279 & 96.8 & 8.3 & PE-D30-P1.5 & 116.0 & 87.3 & 22.2 \\ \hline D36 & 35.6 \(\pm\) 0.4 & 694 \(\pm\) 203 & 96.2 & 6.3 & PE-D36-P1.5 & 89.6 & 90.3 & 10.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of the initial LDPE and auxetic foams. crystallinity was different; it decreased with increasing the foam density. The crystallinity (\(Xc\)) was obtained via:  
\[Xc=\frac{\triangle H_{m}}{\triangle H_{100}}\ (100\%) \tag{11}\]  
where \(\Delta H_{m}\) is the sample enthalpy (heat step), and \(\Delta H_{100}\) is the theoretical value for 100% crystalline LDPE (293 J / g) [30]. The four types of auxetic foam were analyzed by DSC, and the results were compared to the original foams, as shown in Table 2. The crystallinities of D16 and D30 were the lowest, while that of D36 was the highest. The analysis of the DSC heating curves shown in Figure 2 showed that D16, D21 and D30 had an additional peak around 72 \({}^{\circ}\)C, while D16 and D21 had another peak around 126-133 \({}^{\circ}\)C. The presence of additional peaks implied the presence of other polyethylene resins and/or additives.