## 3 Results & Discussion
### X-ray Crystallography
#### 3.2.2 Degree of Crystallinity and Thickness of Lamellar Structure Evaluated by SAXS  
Figure 6 showed the SAXS profile of VPE and shear-treated HDPE at 0-100/s. The peak position (\(q_{max}\)) of VPE was 0.257 nm\({}^{-1}\). However, at the high shear treatment rates (50-100/s), the peak position shifted to high values at 0.262 nm\({}^{-1}\) of 100/s. This implies a decreasing of the long period (\(L_{0}\)) of the 50-100/s samples, which can be determined from the peak position of the SAXS profile. Figure 5: XRD profile and degree of crystallinity of VPE and shear-treated samples. Figure 6: SAXS profiles of VPE and shear-treated samples. The results of \(q_{max}\) and the long period calculated from the SAXS profile (Figure 6) are summarized in Table 2. The shifting of the peak position of 100/s related to the decreasing of long period which was the combination between the thicknesses of the crystalline, amorphous, and intermediate layers, suggesting that the shear treatment rate affected the changes of thickness of the lamellar structure of the shear-treated HDPE. The degree of crystallinity and thickness of lamellar structure of the VPE and shear-treated samples were characterized by SAXS, and also analyzed by the electron density correlation function method. The results are tabulated in Table 3. The degrees of crystallinity of shear-treated HDPE with low shear rates (0-50/s) were similar to VPE. At the high shear rate of 100/s, the degree of crystallinity was reduced around 10% from VPE. It can be found that the degree of crystallinity calculated by SAXS (Table 3) showed a similar trend with the calculation by XRD (Figure 5), even though the values are slightly different from the distinction of the instruments and the calculation methods. For the comparison of the long period, which is the combination of the total crystalline layer and total amorphous layer, the long period of shear-treated samples was slightly decreased from VPE. This reduction of the long period was related to the decreased thickness of core-crystalline layer, especially at the high shear treatment rate. The enlargement of the core-amorphous layer and the reduction of the core-crystalline layer were also associated with the decreasing degree of crystallinity of the shear-treated HDPE at 100/s. For the thickness of the intermediate layer, which is the interface area between the crystalline and amorphous regions, it was also shortened with the increasing of the shear treatment rate. From these calculations, it can be confirmed that shear treatment rate affected the changes to the degrees of crystallinity and thickness of lamellar structure of the HDPE. Especially at 100/s, the degree of crystallinity, long period, core-crystalline layer, and intermediate layer were decreased; however, the core-amorphous layer was slightly increased as compared to VPE. The relationship between mechanical properties and lamellar structure was studied by correlating between each thickness with the elongation at break which was the most important property of the HDPE film grades. Figure 7a shows the correlation between the thickness of core-amorphous layer (\(d_{a}\)) and elongation at break. A negative correlation can be detected. At the low shear rates (0-50/s), the elongation at break was higher \begin{table}
\begin{tabular}{c c c} \hline
**Sample** & **\(q_{max}\) [nm\({}^{-1}\)]** & **Long Period (\(L_{0}\)) [nm]** \\ \hline VPE & 0.257 & 24.4 \\
0/s & 0.257 & 24.4 \\
25/s & 0.257 & 24.4 \\
50/s & 0.270 & 23.3 \\
100/s & 0.262 & 23.9 \\ \hline \end{tabular}
\end{table} 
Table 2: Peak position (\(q_{max}\)) of the SAXS scattering curves and the calculated long period (\(L_{0}\)) of VPE and shear-treated samples.