# A Simple Method to Convert Cellular Polymers into Auxetic Metamaterials
## 3 Results and Discussion
### Auxetic Foams
#### 3.2.2 Poisson's Ratio  
To maximize the NPR, optimization of the processing conditions was explored. The first parameter examined was the level of vacuum. Figure 4 presents the Poisson ratio of D16 with respect to the tensile strain at three different vacuum pressures: \(-0.3\), \(-0.6\) and \(-0.88\) bar. The Poisson ratio did not significantly change between the original foam and the \(-0.3\)-bar (red triangles) samples. They both showed a constant positive Poisson's ratio (0.36-0.38). However, negative Poisson's ratios were obtained when stronger vacuum levels were applied, i.e., at least \(-0.6\) bar. NPR was achieved when the strain was less than 0.5 for PE-D16-P0.5-V0.6 (green inverted triangles), and for all strains, values up to 100% were achieved for PE-D16-P0.5-Vm (blue squares). In all cases, the Poisson ratios increased with increasing the engineering strain, as reported in the literature. Based on these results, the maximum vacuum (\(-0.88\) bar) was used for all the following experiments. The Poisson ratio of a material defines the ratio of between the transverse strain (X direction) and the axial strain (Y direction). The strain is defined as the ratio between the deformation and the initial size. The deformation in the Y direction (stretching direction) had a fixed rate (imposed by the machine), while in the X direction (thickness direction) it increased to 0.2-0.3 (depending on the sample) before decreasing with increasing strain. Therefore, the slope of the curve changed when the tensile engineering strain was around 0.2-0.3. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \(\mathbf{T_{m}}\) & \(\mathbf{\Delta H_{m}}\) & \(\mathbf{Xc}\) & **Auxetic** & \(\mathbf{T_{m}}\) & \(\mathbf{\Delta H_{m}}\) & \(\mathbf{Xc}\) \\  & (°C) & (J/g) & (\%) & **Foams** & (°C) & (J/g) & (\%) \\ \hline D16 & 110.3 & 45.7 & 15.6 & PE-D16-P1.5 & 110.1 & 15.0 & 5.1 \\ \hline D21 & 107.3 & 64.8 & 21.8 & PE-D21-P1.6 & 107.9 & 12.6 & 4.3 \\ \hline D30 & 108.8 & 45.5 & 15.5 & PE-D30-P1.5 & 108.9 & 18.5 & 6.3 \\ \hline D36 & 112.0 & 94.8 & 32.4 & PE-D36-P1.5 & 112.2 & 15.4 & 5.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: DSC results (main peak) of the initial LDPE and auxetic foams. Figure 3: Typical images of the initial foams: (**A**) D16, (**B**) D21, (**C**) D30 and (**D**) D36; and the auxetic foams: (**E**) PE-D16-P1.5, (**F**) PE-D21-P1.9, (**G**) PE-D30-P2.0 and (**H**) D36. PE-D36-P1.5. All the properties of the foams are listed in Table 3. The volume compression ratio (D\({}_{\text{f}}\)/D\({}_{\text{o}}\)) is the ratio between the final and original densities for which the honeycomb structure was transformed into a re-entrant morphology. The minimum tensile NPR of the auxetic D16 foams decreased from \(-2.53\) to \(-2.89\), while the compression ratio increased from \(4.9\) to \(7.61\) and then increased to \(-0.89\) with a compression ratio of \(7.74\). The best NPR value (\(-2.89\)) was obtained for PE-D16-P1.5, but PE-D16-P1.3 and PE-D16-P1.0 were very close with values of \(-2.83\) and \(-2.55\), respectively.