## 4 Results and Discussion
### Temperature-Dependent Measurements  
At the beginning, [PERSON]'s modulus (E) of unannealed and annealed PMMA and DR1/PMMA fibers is measured at room temperature. The results in Table 1 show that Young's modulus \(E\) in DR1/PMMA fibers is greater than in PMMA fibers and is lower in annealed fibers compared with the unannealed ones. [PERSON]'s modulus as a function of temperature determines the effect of heating and population changes on the stiffness of the samples. Samples are heated from 296.15 \({}^{\circ}\)K to 323.15 K in 3 K increments and their elasticity is measured. Figure 4 shows [PERSON]'s modulus as a function of temperature for unannealed and annealed plain PMMA and DR1/PMMA fibers. The graphs are fitted to the Equation (10), where \(E_{0}\), \(T\), \(T_{c}\), and \(n^{\prime}\) are [PERSON]'s modulus at \(T=0\), the oven temperature, the characteristic temperature, and the critical exponent, respectively. Table 2 summarizes the results of the parameters of the fitting function. Figure 4 shows that increasing temperature decreases the elasticity of the samples and DR1/PMMA fibers have larger elasticity than plain PMMA fibers. Moreover, annealed fibers show lower Young's modulus compared with the unannealed ones. The glass transition temperature \(T_{g}\) of the fiber material is measured using differential scanning calorimetry (DSC) with a scanning rate of 10 \({}^{\circ}\)C/min. The DSC unit is manufactured by Mettler Toledo and has a temperature accuracy of \(\pm\)0.2 K and precision of \(\pm\)0.02 K based on metal standards. The samples' masses are between 2 and 3 mg. The results show that adding DR1 decreases \(T_{g}\). Moreover, annealing the samples increases their \(T_{g}\). This is consistent with the results of the characteristic temperature \(T_{c}\) that is derived using the fitting function, which shows that \(T_{c}\) in annealed PMMA and DR1/PMMA is greater than in unannealed ones. However, \(T_{c}\) is unchanged between plain PMMA and DR1/PMMA fibers, implying that adding DR1 did not affect the characteristic temperature. \(T_{c}\) values of the unannealed fibers are the same within experimental uncertainties, as are the annealed ones. Figure 5 shows the derivative of the heating flow as determined from DSC measurements used to determine \(T_{g}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & \(A\) **(mm\({}^{2}\))** & \(E\) **(GPa)** \\ \hline PMMA-Unannealed & 0.25 \(\times\) 0.14 & 2.84 (\(\pm\)0.1) \\ PMMA-Annealed & 0.25 \(\times\) 0.15 & 2.34 (\(\pm\)0.06) \\ DR1/PMMA-Unannealed & 0.25 \(\times\) 0.13 & 3.23 (\(\pm\)0.1) \\ DR1/PMMA-Annealed & 0.25 \(\times\) 0.14 & 2.92 (\(\pm\)0.09) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensions and Young’s modulus at room temperature of unannealed and annealed PMMA and DR1/PMMA fibers. Table 3 shows the correlations between various combinations of samples using the data in Table 2. The first row shows that there is a significant difference between annealed and unannealed PMMA polymer, as determined from the parameter \(E_{0}\)--the low temperature limit of [PERSON]'s modulus, and \(T_{c}\)--the critical temperature parameter. The difference is not as dramatic for DR1/PMMA. However, adding dye to PMMA has a statistically significant effect on increasing the parameter \(E_{0}\). The effect of annealing and dye doping on critical temperature is less obvious, partially due to the fact that the uncertainties are large in the critical exponent \(n^{\prime}\), which affects the accuracy in the determination of \(T_{c}\). In summary, [PERSON]'s modulus at room temperature results  
\[E^{\text{Annealed PMMA}}<E^{\text{Unannealed PMMA}}\leq\] \[E^{\text{Annealed DR1}}<E^{\text{Unannealed DR1}}.\]  
The temperature-dependent Young's modulus of the unannealed fibers are given by  
\[E^{\text{Unannealed PMMA}}<E^{\text{Unannealed DR1}}\]