## 4 Results and Discussion
### Intensity-Dependent Photomechanical Measurements
#### 4.2.2 Separating Photothermal Heating and Angular Hole Burning Using the Tensor Response  
\(R^{(re)}(I_{0})\), the ratio of the orientational response to the heating response for light polarized along the axis between the clamps, is given by Equation (14), which is expressed in terms of the intensity-dependent photomechanical constants \(\kappa^{(1)}_{f}(I_{0})\) and \(\kappa^{(1)}_{\perp}(I_{0})\). Equation (36) relates the intensity-dependent photomechanical constants to the linear and quadratic photomechanical constants. These, in turn, are the fit parameters determined from a plot of the photomechanical stress response as a function of intensity, and determined for the polymers studied here from the data in Figure 11. The zero-intensity limit, \(R^{(re)}(0)\), is the value we observe in most experiments since the sample is typically not illuminated before the pump light is turned on to actuate a photomechanical response in the material. Table 6 summarizes the zero-intensity results for the DR1-doped PMMA fibers of varying CTA volume fraction. The fractional contribution to molecular reorientation \(R^{(re)}(0)\) is small and consistent with zero within experimental uncertainty, showing that heating is the dominant mechanism. \(\kappa^{(heat)}\) is positive, indicating that thermal expansion elongates the fiber sample along its long axis. The magnitudes of \(\kappa^{(re)}_{f}(I)\) and \(\kappa^{(re)}_{\perp}(I)\) are also within experimental uncertainty of vanishing, aside from the medium-chain-length sample. Figure 19: Figure of merit as a function of temperature for fibers with different CTA concentrations. The result is derived using \(\kappa^{(1)}(T)\) and \(E(T)\) as shown in Equation (40). The negative sign of \(\kappa_{//}^{(re)}(I)\) in all measurements, particularly in the medium-chain-length polymer, is marginally statistically significant. The results are consistent with molecular reorientation, which decreases the length of the samples along the polarization axis of the light, and the positive sign of \(\kappa_{\perp}^{(re)}(I)\) shows an increase in the samples' length along its long axis when excited by light perpendicular to it. The fact that all of the measured reorientational contributions are consistently of the correct sign suggests that the uncertainties determined from fits to the data might be overestimated. We find that the effect of heating and molecular reorientation are independent of polymer chain length, since all the photomechanical constants are the same within their experimental uncertainties. Figure 20 shows a plot of the relative reorientational, \(R^{(re)}(I_{0})\), as a function of background illumination \(I_{0}\). Such experiments are not common, but, as with temperature, they provide the experimenter with an additional degree of freedom that can be varied to provide yet another perspective of the photomechanical response. The ratio \(R^{(re)}(I_{0})\) is observed to vary significantly over the intensity range measured. The medium-chain-length sample, for example, starts with a ratio of \(-0.06\) and crosses zero at the higher intensity range. The short chain polymer (highest CTA concentration) shows the most dramatic change, with the sign changing at low intensity and the ratio increasing by a factor of almost 4. This data shows the most dramatic effect as a function of chain length; the average slope becomes more positive as the chain length decreases. Decreased chain length results in greater mobility, which should lead to a larger reorientational contribution, hence a more