## 5 Dielectric Spectroscopy-Tomorrow
If an additional external electrical field oscillating at a frequency well below the IR range is applied, the dipole of an atomistic moiety can be divided into a stationary component \(\vec{p}_{j}^{\,o}\) (corresponding to that without a field) and a varying one \(\Delta\vec{p}_{j}^{\,or}\)  
\[\vec{p}_{j}=\vec{p}_{j}^{\,o}+\Delta\vec{p}_{j}^{\,or} \tag{12}\]  
Combining Equations (11) and (12) yields  
\[A\sim\langle\psi_{i}|\vec{p}_{j}^{\,o}+\Delta\vec{p}_{j}^{\,or}|\psi_{e} \rangle^{2}=\left(\langle\psi_{i}|\vec{p}_{j}^{\,o}|\psi_{e}\rangle+\langle \psi_{i}|\Delta\vec{p}_{j}^{\,or}|\psi_{e}\rangle\right)^{2} \tag{13}\]  
where for small perturbations the quadratic term \(\langle\psi_{i}|\Delta\vec{p}_{j}^{\,or}|\psi_{e}\rangle^{2}\) can be neglected, and thus  
\[A\sim\langle\psi_{i}|\vec{p}_{j}^{\,o}|\psi_{e}\rangle^{2}+2\langle\psi_{i}| \vec{p}_{j}^{\,o}|\psi_{e}\rangle\langle\psi_{i}|\Delta\vec{p}_{j}^{\,or}| \psi_{e}\rangle=A_{o}+\Delta A_{or} \tag{14}\]  
Due to the orientational polarization, this absorption is modulated if the polar unit is involved in a relaxation process. This depends on thermodynamic parameters such as temperature and pressure, and, of course, on the frequency and strength of the external electric field. Hereby it is assumed that the wave functions \(\psi_{i}\) and \(\psi_{e}\) are not seriously changed, which has to be tested experimentally by checking, for instance, the temperature dependence of the effect. For \(\Delta A_{or}\) it holds that  
\[\varepsilon^{*}=\varepsilon^{\prime}-ie^{\prime\prime} \tag{7}\]0  
with the external electrical field \(\vec{E}_{ext}\). To measure this effect, the technical difficulty lies in the fact that conventional metal electrodes (as used in dielectric spectroscopy) are not transparent in the IR-spectral range. However, employing evaporated mesh structures [56] or nanometric (\(\sim\)6 nm) sputtered platinum layers, it is possible to find a compromise between the requirement of sufficient IR transparency and the need to apply high electric fields of typically \(10^{5}\) to \(10^{6}\) V/cm. As an IR source, quantum cascade laser diodes or tunable IR lasers can be used (Figure 6). The sample material, having a thickness of a few \(\upmu\)m, is contained between two mesh electrodes in a crossed arrangement. At a wavelength of \(\lambda\) = 2966.8 nm (i.e., \(\bar{\
u}\) = 3370.6 cm\({}^{-1}\)), the effect of orientational polarization on the O-H moiety can be measured in dependence on the frequency and strength of the external electrical field \(\vec{E}_{ext}(\omega)\) and on temperature (Figure 7). The response normalized by the noise level of the detector signal for \(\vec{E}_{ext}(\omega)=0\) shows a strong decrease in \(\frac{\Delta A_{\omega}}{\Delta A_{0}}\) with temperature. It is caused by the formation of H-bonds which reduce and finely suppress the fluctuation of the polar O-H unit [32]. This relaxation is much slower than the dynamic glass transition (\(\alpha\)-relaxation) that represents the libration of the C-O groups in the core of the glycerol molecules (in agreement with other studies [46]), which is well decoupled from the fluctuation of the H-bonds in the periphery. \[\varepsilon^{*}=\varepsilon^{\prime}-ie^{\prime\prime} \tag{7}\]1 **(a)** Scheme of the experimental set-up with a quantum cascade laser diode emitting a parallel beam of IR-radiation (\(\lambda\) = 2966.8 nm, i.e., \(\bar{\
u}\) = 3370.6 cm\({}^{-1}\)) transmitted through the sample cell with the mesh electrodes in crossed arrangement. The detector signal is analyzed by phase detection. The sample cell is temperature controlled with an accuracy of \(\pm\)1 K. **(b)** Scheme of the sample cell; the material under study is contained between CaF\({}_{2}\) windows with the evaporated mesh electrodes. **(c)** Image **(left)**, scheme **(center)**, and micrograph **(right)** of hexagonal mesh electrodes evaporated on an IR-transparent CaF\({}_{2}\) window. Taken from [56] and modified with permission.