## 4 The Current Understanding of Dielectric Relaxation Processes
Dashed and dotted colored lines indicate the selected interatomic bond vibrations with the respectively involved bonds also highlighted: C-C stretching (red), C-O stretching (yellow), H-C-H bending (blue), and O-C-C-O torsion (green); the respectively colored arrows visualize the type of bond vibration, i.e., stretching (straight), bending or torsion (curved). The corresponding force fields are listed in Table 3.  
Figure 3: \(T_{g}\)-scaled temperature dependence of (**a**) the mean relaxation times and (**b**) the respective relaxation strength of the \(\alpha\)- and \(\beta\)-relaxation obtained from BDS measurements, as well as (**c**,**e**,**g**,**i**) the relative position and (**d**,**f**,**f**,**h**,**j**) area of select IR absorption bands of several polyalcohols as indicated: (**c**,**d**) stretching vibration of the C-C-O bond \(\
u\)(CCO); (**e**,**f**) scissoring vibration of the CH\({}_{2}\) bond \(\delta\)(CH\({}_{2}\)); (**g**,**h**) stretching vibration of the C-O bond \(\
u\)(CO); (**i**,**j**) stretching vibration of the O-H bond \(\
u\)(OH). Taken from [28] with permission. Figure 2: IR-spectra of (**a**) sorbitol and glycerol both at a temperature of 269 K in a wide spectral range, and close-ups of the spectral regions of (**b**,**e**) the \(\
u\)(C-O) stretching vibration, (**c**,**f**) the \(\
u\)(C-H) stretching vibration, and (**d**,**g**) the \(\
u\)(O-H) stretching vibration at their respective \(T_{g}\) and further temperatures as indicated for glycerol and sorbitol, respectively. The data are taken from [42]. It stands to reason that these different temperature dependencies are connected to different dynamics of the respective molecular moieties. Due to inherent (partial) charges, the timescale of certain molecular fluctuations can be deduced from their polarization in oscillating electrical fields. The classical theory of orientational polarization according to [PERSON] [2,3] assumes a single dipole with dipole moment \(\vec{\mu}\) interacting with an external electric field \(\vec{E}(\omega)\); using Boltzmann statistics, the averaged mean orientation counterbalanced with the thermal fluctuation of the dipolar system is determined. This yields the dielectric relaxation strength  
\[\Delta\epsilon=\frac{\mu^{2}}{3\epsilon_{o}k_{B}T}\frac{N}{V} \tag{1}\]  
where \(\mu=|\vec{\mu}|\) is the absolute value of the dipole moment, \(\epsilon_{o}=8.85\ldots\times 10^{-12}\frac{\Delta\epsilon}{\sqrt{\text{m}}}\) is the electrical field constant, \(k_{B}\) is the Boltzmann constant, \(T\) is the absolute temperature and \(\frac{N}{V}\) is the dipole concentration. Clearly, this approach can only hold for dilute systems; if the dipoles are more concentrated, their impact on each other and the surrounding field (inducing a so-called reaction field) changes the response of the system. Typically, \(\mu\) is replaced by an effective average dipole moment \(\langle\mu_{eff}\rangle\) that includes all these effects [23]. Consequently, \(\langle\mu_{eff}\rangle\) cannot be deduced from the structure of a single molecule. [PERSON] suggested to decompose the field which acts upon a molecule in a polarized dielectric into a cavity field \(G\) given by the shape of the molecule and a reaction field \(R\), which is proportional to the total electric moment [43]; its impact is described by the Onsager factor \(F=\frac{\epsilon_{o}(\epsilon_{o}+2)^{2}}{3(2\epsilon_{o}+\epsilon_{o})}\), where \(\epsilon_{o}\) and \(\epsilon_{s}\) are the limiting values of the permittivity at high and low frequencies, respectively.