## 3 Experiment
### Apparatus  
Figure 2 diagrams the force measurement apparatus. This custom apparatus, similar in principle to the one demonstrated by [PERSON] and [PERSON] [44], was designed and built at Washington Sate University specifically to measure a variety of photorheological properties in materials ranging from stiff dye-doped polymer fibers and thin films to soft elastomers. An inexpensive version [45] of the apparatus was found to give the same results as the more sophisticated one [16]. The 3D translational stage both centers the fiber in the oven and is used to stretch the fiber. A software-controlled stepper motor actuates the translation stage. The sample is mounted between two custom clamps and the upper clamp is attached in series with a force sensor, which connects the translation stage to the clamp. The oven chamber, clamps, and supporting hardware were custom  
Figure 1: Chemical structures of Disperse Red 1 (DR1) (**a**) trans isomer and (**b**) cis isomer. made and machined from solid metal. The oven is heated with resistive heating rods and controlled with an Omega Engineering Model CN7800 programmable PID using a k-type thermocouple temperature sensor and interfaced with an Arduino for control and data collection. The stress load cells are inexpensive generic models obtained from Amazon, similar to the SaiDian 0-100 g Load Cell Sensor. The load cell is calibrated as described in the literature [16; 45]. Young's modulus is determined by translating the translation stage at a constant rate while recording the force sensor reading and the displacement with an Arduino interface as the sample is stretched. Stress versus strain determined from these data and the sample's geometry is fit to a polynomial. The linear part yields Young's modulus of the material, while the tangent gives the stress-dependent Young's modulus. An oven chamber placed around the sample controls the temperature to determine Young's modulus as a function of temperature. These data are fit to the function given by Equation (10). The temperature-induced stress at constant sample length is determined from the measured stress as a function of temperature while the translation stage is kept stationary. These data are fit to the function given by Equation (6). The parameters determined from these two experiments are inputs to Equation (8). The load cell measures the force exerted on its ends by the translation stage from above and the sample clamp below. By [PERSON]'s third law of action-reaction, each component that is attached in series with the force load cell experiences the same uniaxial force. As such, the stress on each component will result in a strain; so, the displacement of the translation stage will equal the sum of the displacement of all of the components that are in series with it. The translation stage and clamps are made of massive metal components, which deform negligibly compared with the sample. However, the force sensor is designed to bend, which stretches the electrical wires that are glued to its sides. As such, the deformation of the force sensor must be taken into account. The contribution of the force sensor's deformation to the displacement of the translation stage is taken into account by assigning it a spring constant \(K\), which is in series with the spring constant \(k\) of the sample. The experiment measures the force as a function of displacement, whose ratio yields an effective spring constant \(k_{\mathit{eff}}\) given by  
\[k_{\mathit{eff}}=\frac{kK}{k+K^{\prime}}, \tag{12}\]  
Figure 2: Force measurement chamber. which can be inverted to obtain the spring constant of the sample:  
\[k=\frac{k_{eff}}{1-\frac{k_{eff}}{K}}. \tag{13}\]  
Thus, we need to know the spring constant \(K\) of the force senor to determine the spring constant \(k\) of the fiber sample. The spring constant of the force sensor is measured by pushing together the upper and lower clamps in the absence of a sample.