## 4 Results and Discussion
### Intensity-Dependent Photomechanical Measurements
#### 4.2.1 Photothermal Heating
heating and molecular reorientational contributions determined from the polarization-dependent measurements. The solid curves, which show the fit functions to the measured values, and the dashed curves, which show the heating contribution determined from the polarization-dependent measurements, fall on top of each other. The polarization-dependent measurement shows that the degree of molecular reorientation is negligible. Aside from the polymer prepared with \(2.66\times 10^{-3}\) CTA volume per MMA volume, the pure heating model is consistent with the theoretical results. However, the trend of the heating model's prediction and the data are opposite to each other, but on average, they agree. This is not surprising, given that the model has no adjustable parameters and relies only on the temperature-dependent stress measurement and time constant measurement, both of which may be biased by systematic errors. We have found the temperature-dependent stress measurement of the polymer prepared with \(2.66\times 10^{-3}\) CTA volume per MMA volume to vary significantly between measurements, perhaps because of the high sensitivity of the material's properties to temperature variations due to its lower glass transition temperature. This lack of reproducibility for the heating model in this polymer is consistent with the heating theory being off by a factor of two, from the experimentally determined values. Figure 17: The vertical and horizontal lines (representing the pump polarization relative to the vertical) show the predicted heating contribution to the photomechanical response as a function of intensity using the theory (Equation (7)) and the parameters determined from the fits in Figure 9 of the temperature-induced stress. The smooth lines show the experimentally determined intensity-dependent photomechanical constant determined by the fit of the data to a quadratic function in the intensity, as shown in Figure 11, and identical to the results shown in Figure 12, but, here the points are connected to make smooth curves. \(\kappa^{(heat)}(I)\), \(\kappa^{(re)}_{f}(I)\), and \(\kappa^{(re)}_{\perp}(I)\) are also plotted and determined from the tensor properties of the polarization-dependent response using Equations (19)–(21). The figure of merit is typically defined by the linear photomechanical response and Young's modulus \(E\) to be given by \(\left(\kappa_{\sigma}^{(1)}\right)^{2}/E\). The intensity-dependent figure of merit is a generalization of the figure of merit for an illuminated sample, providing another degree of freedom that can be controlled. It depends on the intensity-dependent photomechanical response \(\kappa^{(1)}(I_{0})\) and the intensity-dependent [PERSON]'s modulus \(E(I_{0})\), which are determined using Equation (32), where \(T(I_{0})\) is the slope of the plots in Figures 15 and 16 at intensity \(I_{0}\), yielding  
\[E=\frac{E_{0}}{(1+(\frac{a+bI_{0}}{T_{c}})^{n})}, \tag{38}\]  
where \(a\) and \(b\) are the intercept and slope of the graphs in Figures 15 and 16. So  
\[FOM(I_{0})=\frac{(\kappa^{(1)}(I_{0}))^{2}}{E(I_{0})}=\frac{(\kappa^{(1)}+2 \kappa^{(2)}I_{0})^{2}}{\frac{E_{0}}{(1+(\frac{a+bI_{0}}{T_{c}})^{n})}}, \tag{39}\]  
Figure 18 shows a plot of the intensity-dependent figure of merit as a function of intensity as determined from fits to the data to get the appropriate parameters. The intensity-dependent figure of merit is observed to decrease as a function of intensity. While the decrease in Young's modulus with increased intensity works to improve the figure of merit, the decrease in the intensity-dependent photomechanical response wins out, resulting in a decreased figure of merit. As such, the best figure of merit is for a dark sample. Finally, we determine the temperature-dependent figure of merit due to the heating mechanism for the three polymers to determine if heating the material might improve it.