## 3 Measurement Techniques of the Electro-Optic Coefficient
### Isothermal Relaxation Measurements  
A more reliable and useful measurement technique to probe stability of the EO properties is the series of isothermal relaxation measurements. In this technique, the sample must be poled, as usual, at the poling temperature \(\mathrm{T_{p}}\) for a time interval \(\mathrm{\Delta t_{p}}\) with an applied poling voltage \(\mathrm{V_{p}}\), then the sample is cooled down to the measurement temperature \(\mathrm{T_{m}}\) maintaining the applied poling field. As soon as the \(\mathrm{T_{m}}\) is reached, the poling field is switched off and the EO coefficient is continuously monitored by using either fast TMT or fast SHG measurements. In this case, the value of \(\mathrm{r_{33}}\) is evaluated as a function of time for the given temperature \(\mathrm{T_{m}}\). As an example, Figure 6 reports the isothermal measurements at 90 \({}^{\circ}\)C, 110 \({}^{\circ}\)C, 130 \({}^{\circ}\)C (in log scale in this example) performed on HFIP-DR1 AF [62]. Aligning the behaviour of the EO coefficient with the Kohlrausch-Williams-Watts (KWW) stretched exponential law Equation (20), it is possible to obtain the value of the time constant \(\tau\), of the  
Figure 5: Temperature scanning measurement on HFIP-DR1 AF. Reprinted with permission from [62]. Copyright 2005, American Institute of Physics. Figure 6: Isothermal relaxation measurements on HFIP-DR1 AF. Reprinted with permission from [62].Copyright 2005, American Institute of Physics. stretching constant \(\beta\) and, from Equation (21), the value of the average time constant \(<\)\(<\)\(>\) at a given temperature. By comparing the curves for different temperatures, it is possible to retrieve the dependence of \(\beta\) and \(<\)\(>\) as a function of temperature. The \(\beta\) dependence is usually described by the Equation (24), while \(<\)\(>\) is well described by the Equation (22) for temperatures close or greater than T\({}_{0}\), and by the Equation (23) for temperatures below T\({}_{0}\). In Figure 7, we report the \(<\)\(>\) values obtained in the previous measurements in logarithmic scale as a function of the reciprocal of the absolute temperature (multiplied by 1,000), as is usually done when describing temperature activated processes [62]. For temperatures below T\({}_{0}\)\(\approx\) 110 \({}^{\circ}\)C, (1/T \(\times\) 1,000 \(>\) 2.6 K\({}^{-1}\)), the average time constant follows an Arrhenius behaviour Equation (23). The Arrhenius behavior is described by a straight line in such type of plot. an activation energy \(E_{a}\) = 58 kcal/mol is then obtained by fitting the measurements below 110 \({}^{\circ}\)C with the Equation (23). For temperatures above 110 \({}^{\circ}\)C the relaxation is faster than that predicted by the Arrhenius model and follows the Vogel-Fulcher-Tamann-Hesse (VFTH) behavior (or Williams-Landel-Ferry (WLF)) described in the Equation (22). The activation energy is a parameter that represents the stability of the chromophores orientation in a more complete way than the depolarization temperature reported in the previous paragraph. Moreover, the activation energy can be recovered by performing measurements at relatively high temperatures, and can be used to extrapolate time constants at a lower temperature (room temperature) that cannot easily be measured (because it would take years). We point out that, for this purpose, it is necessary to be sure that the measurements are performed in the Arrhenius regime and not in the VFTH regime. This last observation shows that it is not possible to perform relaxation measurements at high temperatures, near \(T_{g}\), (appealing for their convenience, as they are rather quick measurements) in order to extrapolate the relaxation time constants at a low temperature (e.g., 50 \({}^{\circ}\)C) by using an Arrhenius type model.