## 4 Results and Discussion
### Intensity-Dependent Photomechanical Measurements
#### 4.2.1 Photothermal Heating  
This section shows how the parameters in the photothermal heating model are determined from the experiment and how the tensor properties of the photomechanical response are used to isolate the heating contribution. These two independent approaches will be used to separate the photothermal response and hole burning/molecular reorientation. The degree of consistency between them will provide an estimate of the reliability of the measurements and their interpretation. Figures 15 and 16 show the semi-empirically determined temperature change as a function of intensity using Equation (4) and the measured time constant of the photomechanical response. The theory has no adjustable parameters, and depends only on known material parameters, such as the specific heat capacity \(c\) and the density \(\rho\), as well as on the sample's geometry, characterized by its width, \(w\). The values of \(\rho\), \(c\), and \(w\) that are used to find the temperature increase are listed in Table 5. The insets in the graphs in Figures 15 and 16 show the temperature change per unit of absorbed intensity as a function of CTA volume fraction. Figure 14: Time constant \(t_{2}\) (light off) as a function of intensity for different CTA volume fractions for a vertically and horizontally polarized pump. The insets show the time constants as a function of CTA volume fraction averaged over all intensities. Figure 15: Temperature change as a function of intensity calculated from Equation (4) using the time constants measured from the photomechanical response, the density, heat capacity, and the sample’s dimensions. The insets show the temperature change per unit of absorbed intensity as a function of CTA volume fraction averaged over all intensities. The plots use \(t_{1}\) to get \(\Delta T\) for vertically and horizontally polarized pumps. \begin{table}
\begin{tabular}{c c c c} \hline
**CTA Volume Fraction** & \(\rho\) **(kg/m\({}^{2}\))** & \(\epsilon\) **(J/kg\({}^{\circ}\)K)** & \(w\) **(mm)** \\ \hline \(1.33\times 10^{-3}\) & \(1.19\times 10^{3}\) & \(1.42\times 10^{3}\) & 0.12 \\ \hline \(2\times 10^{-3}\) & \(1.19\times 10^{3}\) & \(1.42\times 10^{3}\) & 0.12 \\ \hline \(2.66\times 10^{-3}\) & \(1.19\times 10^{3}\) & \(1.42\times 10^{3}\) & 0.15 \\ \hline \end{tabular}
\end{table} 
Table 5: Values of density \(\rho\), the specific heat \(c\), and thickness \(w\) of the fibers used to calculate the temperature increase. Figure 17 summarizes all the results obtained in this paper by providing plots of the intensity-dependent linear photomechanical response \(\kappa_{e^{\prime}}^{(1)}(I_{0})\), defined by Equation (36) as a function of intensity. Included are plots of the theory of the heating contribution that use the temperature change determined from Equation (3) in the heating model given by Equation (7), which draws from the parameters shown in Table 2. These parameters are determined from fits to the temperature-dependent stress shown in Figure 9 to the function given by Equation (6). The response along the two principle axes of the fiber sample are denoted by \"\(\mid\)\" and \"\(\mid\)\" for the pump polarization along and perpendicular to the long axis (mounted vertically) for three polymer chain lengths as controlled by the amount of chain transfer agent used during polymerization. Additionally included are plots of the experimentally determined values for the same quantities, which are represented by smooth lines that are determined from fits to the data. The dashed curves are the  
Figure 16: Temperature change as a function of intensity calculated from Equation (4) using the time constants measured from the photomechanical response, the density, heat capacity, and the sample’s dimensions. The insets show the temperature change per unit of absorbed intensity as a function of CTA volume fraction averaged over all intensities. The plots use \(t_{2}\) to get \(\Delta T\) for vertically and horizontally polarized pumps.