## 4 Results and Discussion  
### Temperature Dependent Measurements  
Each sample is mounted between the clamps with initial length \(L_{0}\), and [PERSON]'s modulus is measured at room temperature and elevated temperatures. Figure 7 shows [PERSON]'s modulus at room temperature as a function of CTA volume fraction. [PERSON]'s modulus is observed to decrease with decreased average chain length.  
Figure 8 shows [PERSON]'s modulus as a function of temperature from 293.15 \({}^{\circ}\)K to 323.15 \({}^{\circ}\)K in 3 \({}^{\circ}\)K increments. The samples soak for 15 min at each temperature to assure they have reached equilibrium before taking a measurement. [PERSON]'s modulus is observed to decrease as a function of increasing temperature, where all samples show similar behavior. The decrease of [PERSON]'s modulus with increased temperature and increased CTA volume fraction is consistent with the increased degree of chain mobility as the temperature in increased nearer to \(T_{g}\) and the decrease of chain length with the addition of CTA during polymerization, which is associated with a decrease in \(T_{g}\) as chain length decreases.  
We propose a model for [PERSON]'s modulus that takes the form  
\[E=\frac{E_{0}}{(1+(\frac{T}{T_{c}})^{n})}, \tag{32}\]  
where \(E_{0}\) is [PERSON]'s modulus in the \(T=0\) limit, \(T\) the oven/sample temperature, \(T_{c}\) a characteristic temperature where the Young's modulus is half the zero-temperature value,  
Figure 7: Measured [PERSON]’s modulus as a function of CTA volume fraction at room temperature.  
and \(n\) is a critical exponent. We chose this function because it fits the data well with a minimal number of parameters. Equation (32) provides a convenient analytical function that can be fit to the data from which one can determine material parameters, such as \(dE/dT(T)\).  
Table 1 shows the parameters obtained from fitting the data in Figure 8 to Equation (32). \(E_{0}\) decreases as a function of CTA volume fraction, as we would expect from shorter chain length. The characteristic temperature and the critical exponent are the same within experimental uncertainties for 1.33 \(\times\) 10\({}^{-3}\) and 2 \(\times\) 10\({}^{-3}\) CTA volume fraction but the exponent for 2.66 \(\times\) 10\({}^{-3}\) CTA volume fraction is much larger, as we would expect for the increased mobility of shorter chain length.  
Figure 9 shows a plot of the temperature-dependent stress of the clamped fibers for the three different chain lengths. The temperature is increased from 294 \({}^{\circ}\)K to 313 \({}^{\circ}\)K in 3 min and modeled with the function given by Equation (6) because it fits the data well and the analytical form determined from a fit to the data can be used to determine \(d\sigma/dT\), which is used to model the photothermal mechanism, as described in Section 2.1. Table 2 summarizes the parameters of the stress fitting function.  
\begin{table}
\begin{tabular}{c c c c} \hline
**CTA Volume Fraction** & \(E_{0}\) (GPa) & \(T_{c}\) (\({}^{\circ}\)K) & **n** \\ \hline \(1.33\times 10^{-3}\) & 3.18 (\(\pm 0.05\)) & 342.5 (\(\pm 2.4\)) & 22.0 (\(\pm 3.2\)) \\ \hline \(2\times 10^{-3}\) & 3.05 (\(\pm 0.05\)) & 341.6 (\(\pm 2.5\)) & 23.9 (\(\pm 3.6\)) \\ \hline \(2.66\times 10^{-3}\) & 2.83 (\(\pm 0.01\)) & 332.50 (\(\pm 0.60\)) & 42.4 (\(\pm 2.4\)) \\ \hline \end{tabular}
\end{table}
Table 1: Parameters determined from fitting the Young’s modulus data to Equation (32) for the three CTA volume fractions.  
Figure 8: Measured Young’s modulus as a function of temperature for three CTA volume fractions (points with error bars) and fits to the model given by Equation (32).