## 4 Discussion
### Relationship between Young's Modulus and Temperature
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Temperature**} & **[PERSON]’s** & **Linear** & \multirow{2}{*}{**R2**} & **[PERSON]’s** & **Linear** & \multirow{2}{*}{**R2**} \\  & **Modulus** & **Interval** & & & **Modulus** & **Interval** & \\ \hline \multicolumn{7}{c}{**Longitudinal Specimen**} & \multicolumn{4}{c}{**Transverse Specimen**} \\ \cline{2-7}  & **MPa** & **\%** & **—** & **MPa** & **\%** & **—** \\ \hline \(-40.0\) & 7960.55 & [0, 2.00] & 0.976 & 8014.67 & [0, 1.00] & 0.961 \\ \(-30.0\) & 5975.66 & [0, 2.50] & 0.973 & 5139.42 & [0, 2.50] & 0.979 \\ \(-25.0\) & 3896.48 & [0, 5.00] & 0.972 & 3877.39 & [0, 2.50] & 0.979 \\ \(-20.0\) & 3277.24 & [0, 5.00] & 0.975 & 3336.25 & [0, 5.00] & 0.987 \\ \(-15.0\) & 1990.38 & [0, 5.00] & 0.963 & 1912.44 & [0, 5.00] & 0.966 \\ \(-10.0\) & 469.66 & [0, 10.0] & 0.997 & 1366.01 & [0, 5.00] & 0.993 \\ \(-5.0\) & 391.12 & [0, 10.0] & 0.997 & 492.91 & [0, 5.00] & 0.972 \\ \(0.0\) & 267.47 & [0, 10.0] & 0.983 & 245.80 & [0, 20.0] & 0.998 \\ \(4.0\) & 262.70 & [0, 30.0] & 0.999 & 211.97 & [0, 20.0] & 0.994 \\ \(10.0\) & 154.58 & [0, 30.0] & 0.997 & 151.42 & [0, 20.0] & 0.999 \\ \(20.0\) & 129.87 & [0, 30.0] & 0.996 & 72.13 & [0, 20.0] & 0.999 \\ \(30.0\) & 74.26 & [0, 30.0] & 0.989 & 53.54 & [0, 20.0] & 0.999 \\ \(40.0\) & 55.11 & [0, 40.0] & 0.997 & 45.10 & [0, 40.0] & 0.997 \\ \(50.0\) & 38.60 & [0, 40.0] & 0.992 & 28.60 & [0, 40.0] & 1.000 \\ \(60.0\) & 28.54 & [0, 40.0] & 0.998 & 24.42 & [0, 40.0] & 0.998 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: [PERSON]’s modulus and linear interval at different ambient temperatures. \(-273.15\)\({}^{\circ}\)C, at which the calculated values of the [PERSON]'s modulus of the longitudinal and transverse specimen are 9109.85 and 8971.15 MPa, respectively, which are identical with the fitted values. \(E_{1}\) can be considered as the [PERSON]'s modulus at \(-273.15\)\({}^{\circ}\)C.  
Figure 8 shows that there is a change in the [PERSON]'s modulus with temperature: a faster rate in the early stage followed by a slower rate. An inflection point of [PERSON]'s modulus appears with increasing temperature for both longitudinal and transverse specimen, i.e., [PERSON]'s modulus changes greatly in the interval of [\(-40\), \(-9\pm 2\)\({}^{\circ}\)C], while flat in the interval of [\(-9\pm 2\), 60 \({}^{\circ}\)C]. The temperature-dependent polymer has typical glassy state, high elastic state and viscous state, and mechanical properties differ in each state. It can be inferred that PVC GEM is in glassy state and high elastic state in the test temperature range. To confirm the rationality of the inference, DSC was implemented to obtain the glass transition temperature. First, the specimen was melted in the molten state to reduce possible influencing factors; then, the temperature was reduced to \(-10\)\({}^{\circ}\)C, and finally heated to the molten state, and the DSC curve was obtained. The DSC curve of the specimen at the temperature varying from \(-10\)\({}^{\circ}\)C to \(10\)\({}^{\circ}\)C is given in Figure 9, from which the glass transition temperature of the PVC GEM is \(-7\pm 0.1\)\({}^{\circ}\)C.  
The glass transition temperature obtained from the test is close to the opposite number of transverse specimens \(Tr\) fitted by Boltzmann function. It can be inferred that the opposite number of \(Tr\) is the glass transition temperature of the PVC GEM, while in contrast, the fitted value of \(Tr\) for the longitudinal specimen is 10.14 \({}^{\circ}\)C, and its opposite number differs from the glass transition temperature by the DSC test. The reason is that the DSC test is obtained by heating the specimen to the fluid state to eliminate the longitudinal and transverse difference. Equation (7) can be modified to the following equation for a better physical meaning:  
\[E=E_{2}+\frac{E_{1}-E_{2}}{1+e^{(T_{0}-T)/T_{r}}} \tag{8}\]  
Figure 8: Relationship between [PERSON]’s modulus and temperature: (**a**) longitudinal specimen; (**b**) transverse specimen.