## 3 Results
### Dmpc  
In Figure 2, the far-IR spectra of DMPC/H\({}_{2}\)O samples at five distinct hydration degrees (dry, RH = 11%, 43%, 64%, 75%) are shown with the corresponding fitting curve and the Gaussian components for the dry and mostly hydrated samples. We clearly observed that absorbance increases as the hydration level increases, as hypothesized (Figure 2a). We performed the curve fitting of the spectra as a linear combination of individual Gaussian component bands following the procedure described in detail in Section 2.3. We found that eight components are needed to reproduce each spectrum independently of the hydration level and the phase state of the lipid multilayers. The frequencies of the vibrations in the DMPC sample with the highest hydration (75%) are: 50, 70, 90, 119, 154, 186, 219, and 259 cm\({}^{-1}\) (named in the following A, B, C, D, E, F, G, and H). The frequencies in the dry DMPC sample are reported in Table 1. They coincide with those of the wet sample, except for bands D and E, which are shifted to lower frequencies in the wet sample (110 and 145 cm\({}^{-1}\)). Thus, the frequencies of the vibrational modes were almost unaffected by the hydration, while significant changes amongst the DMPC samples at different hydration degrees were observed in the width and the area of all of the bands, as will be detailed in the following. The experimental data and the data analysis reproduced our previous findings [6], with slight differences attributable to the different solvent (H\({}_{2}\)O was used in this work; D\({}_{2}\)O was used in the previous one). Additionally, while in the current work we carried out measurements under controlled hydration and in an equilibrated condition, in our previous work data were acquired in an out of equilibrium phase--i.e., as a function of the dehydration time by dehydrating under vacuum. Thus, it was not possible to obtain precise information on the hydration status of the samples. Differences between the two sets of measurements were also attributable to the different experimental modalities used. In Table 1, the number of water molecules per lipid, \(n_{\text{W}}\), are reported (see Section 2.1 for details concerning the determination of \(n_{\text{W}}\)). Therefore, we fully confirm the results of [6] and the assignment previously proposed for the revealed bands. The A, B, C, and E bands were assigned to vibrations of different lipids interacting through their intermolecular van der Waals forces. The D band was assigned to an unspecified motion of the terminal methyl carbons of the phospholipid chains C\(-\)CH\({}_{3}\)[14]. The F and H bands were attributed to the torsion modes of the hydrocarbon chains and the terminal methyl groups, respectively. The assignments of the observed excitations are reported in Table 2.  
Figure 2: Far-infrared spectra of the DMPC/H\({}_{2}\)O samples. **(a)** Spectra of pure water (dashed black line) and of the samples at five distinct hydration degrees: dry (black full line), RH = 11% (red), RH = 43% (green), RH = 64% (magenta), and RH = 75% (blue); **(b)** The spectra of the dry sample and of a wet sample (RH = 75%) are shown separately with the corresponding fitting curve (solid black line) obtained as the sum of the individual Gaussian peaks (dashed black lines). Returning to the observed frequency shift to lower values observed for the D and E bands in the wet DMPC sample, this signifies that the corresponding vibrational motions of the lipid molecular groups are influenced, even indirectly, by the presence of the solvent. We interpret the blue shift in the dry sample as a strengthening of the interactions within the compact structure in the absence of a solvent. For all of the components, we observed a decrease in the full-width half-maximum (fwhm) as the hydration level decreased (data not shown). This can be interpreted as being due to both decreased motional rates and a smaller number of explored conformations going towards the more ordered solid gel phase at extreme or complete dehydration.