## 4 The Current Understanding of Dielectric Relaxation Processes  
A refined analysis of dielectric spectra requires, in addition to dielectric measurements in a wide frequency and temperature range, knowledge of vibrational dynamics as measured with IR or Raman spectroscopy, calorimetric data, and the temperature dependence of the density. Such combined information is often only available for a few molecular systems, e.g., the homologous series of polyalcohols glycerol, threitol, xylitol and sorbitol (Table 1) [32; 33; 34; 35]. Polyalcohols consist of several different polar moieties (Table 1) with different polarity (Table 2, Figure 1) which are interlinked by intra- and inter-molecular bonds with widely varying atomic potentials (Table 3), having quite different temperature dependencies. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Name** & **Sum** & **Structure** & \(M_{\textbf{W}}\) & \(\rho\) & \(T_{g}\) & \(V_{m}\) & \(V_{\textbf{COH}}\) \\  & & & **[g/mol]** & **[g/cm\({}^{3}\)]** & **[K]** & **[Å\({}^{3}\)]** & **[Å\({}^{3}\)]** \\ \hline glycerol & C\({}_{3}\)H\({}_{8}\)O\({}_{3}\) & OH & 92.09 & 1.259 * [36] & 192 [37] & 121 & 40.4 \\ \hline DL-threitol & C\({}_{4}\)H\({}_{10}\)O\({}_{4}\) & HO & OH & 122.1 & 1.386 **[38] & 226 [37] & 146 & 36.6 \\  & & OH & OH & & & & \\ \hline xylitol & C\({}_{5}\)H\({}_{12}\)O\({}_{5}\) & HO & OH & 152.2 & 1.402 *** [39] & 248 [37] & 180 & 36.0 \\  & & OH & & & & & \\ \hline D-sorbitol & C\({}_{6}\)H\({}_{14}\)O\({}_{6}\) & HO & OH & 182.2 & 1.449 * [40] & 268 [37] & 209 & 34.8 \\  & & OH & OH & & & & \\ \hline \hline \end{tabular}  
* At 292 K. ** At 293.15 K. ** At 300 K.  
\end{table} 
Table 1: Characteristics of several polyalcohols: chemical sum and structure, molecular mass \(M_{\textbf{W}}\), mass density \(\rho\), glass transition temperature \(T_{g}\) and—calculated from the latter two—the average volumes per molecule \(V_{m}\), as well as per COH unit \(V_{\textbf{COH}}\). IR spectroscopy enables one to trace in detail the evolution of the different vibrational bands with temperature far above and below the (calorimetrically determined) glass transition temperature \(T_{g}\) of the specific molecular system (Figure 2). u\)(O-H) stretching vibration for all four polyalcohols, a similar temperature dependence is observed, showing a pronounced blue-shift with increasing temperature (Figure 3i). It is caused by the weakening of the inter-molecular H-bonds with increasing temperature, and hence an increase in the strength of the \(\
u\)(O-H) [32]. At the calorimetric glass transition temperature for all polyalcohols, a kink in the spectral position and the oscillator strength is observed, indicating that at this temperature, the inter-molecular H-bonds change (Figure 3j). In contrast, for the intra-molecular C-O and C-C-O bonds, a red-shift is found without discontinuity at \(T_{g}\) (Figure 3c,g). This can be explained semi-quantitatively by the increase in the potential width caused by a decrease in density with increasing temperature [28]. However, also the rescaled oscillator strengths of the \(\
u\)(C-O) and \(\
u\)(C-C-O) stretching vibrations exhibit, in part, a kink at \(T_{g}\) (Figure 3d,h), which cannot be explained at the moment. In summary, it has been proven that the different polar groups in polyalcohols can be separated into two fractions, intra- and inter-molecular bonds, which vary quite differently with temperature. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bond Type** & **Bond Length** & \multicolumn{2}{c}{**Dipole Moment**} \\  & **[pm]** & **[10\({}^{-30}\) cm]** & **[Debye]** \\ \hline O-H & 96 & 15.1 & 4.5 \\ C-H & 110 & 2.4 & 0.72 \\ C-O & 143 & 17.5 & 5.3 \\ C-C & 150 & 0.65 & 0.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of different covalent bond types in glycerol taken from [41]: bond length and dipole moment. Figure 1: Calculated atomic charges of the glycerol molecule with permission (image taken from and modified after [41], see reference for details of the calculation).