# Characterization of Waves in the Roman Wall Paintings of the Herculaneum Site (Italy)
## 3 Results and Discussion
### Analyses of the Reference Wax Samples  
#### 3.1.1 FTIR and Raman Spectroscopies  
Waxes consist essentially of saturated and unsaturated long chain components (wax esters, free fatty acids, long chain alcohols, hydrocarbons, aromatic compounds): the most critical features for their identification are the CH\({}_{\text{X}}\) stretching vibration (\(\
u\)(CH\({}_{\text{X}}\)), with x = 1, 2, 3) around 3000 cm\({}^{-1}\) and the bending and rocking deformations of CH\({}_{\text{X}}\) at about 1400 cm\({}^{-1}\) (\(\delta\)(CH\({}_{\text{X}}\))) and 700 cm\({}^{-1}\) (\(\rho\)(CH\({}_{\text{X}}\))), respectively. In waxes of animal and vegetal origin, the carbonyl stretching vibration (\(\
u\)(C=O)) is an important feature. In Figure 1a,b are reported the FTIR spectra of all investigated waxes. The strong doublets at 2916 and 2848 cm\({}^{-1}\) and at 1472 and 1462 cm\({}^{-1}\), due to the asymmetric and symmetric stretching and in-plane bending vibrations of methylene groups (CH\({}_{2}\)), respectively, and the medium strong doublet at 730 and 718 cm\({}^{-1}\), due to the out-of-plane deformation of successive methylene groups (\(-\)(CH\({}_{2}\))_n_), with \(n\geq 4\)[42]), are characteristic of long aliphatic chains and suggest the presence in waxes of long-chain fatty acids, esters and alkanes [43,44]. In the 1350-1200 cm\({}^{-1}\) region, there are some sharp absorption bands assigned to C-C-C skeletal vibrational modes and to the wagging and twisting vibrations of methylene groups in the chain, one band for every two methylene groups [42, 43, 44, 45]. These features are characteristic of long-chain acids, such as palmitic or stearic acids. The strong band at 1737 cm\({}^{-1}\) due to carbonyl (C=O) and at 1170 cm\({}^{-1}\) assigned to C-O-C stretching vibrations are indicative of wax ester components [30,46,47]. Some differences in the features of the waves of different origin are clearly observable in Figure 1. Beeswax, lanolin, carnauba wax and candellilla wax (Figure 1a) show barely visible bands due to the OH stretching vibrations of alcohols, hydroxyl-esters and free fatty acids (marked by asterisks), absent in spermaceti was. In addition, in beeswax and carnauba wax, the \(\
u\)(C=O) vibrational bands at 1708 and 1693 cm\({}^{-1}\) associated with free fatty acids [43; 48] are also observed. In candellilla wax, the band at 1708 cm\({}^{-1}\) has almost equal intensity with that of the carbonyl band, which may be due to unionized carboxyl groups [30]. Medium-weak bands, only detectable in the FTIR spectrum of carnauba wax at 1634, 1607, 1515 and 834 cm\({}^{-1}\), are attributed to the skeletal ring breathing modes of aromatic groups [30; 47]. Artificial and mineral waxes (Figure 1b) are dominated by the strong CH\({}_{2}\) and CH\({}_{3}\) stretching, in-plane bending and out-of-plane bending vibrations. The formulated candellilla, which is a mixture of glyceryl stearate and lesser amounts of natural waxes, also exhibits the strong and wide bands associated with the OH stretching vibrations at 3296 and 3233 cm\({}^{-1}\) and the band due to the C-O stretching at 1046 cm\({}^{-1}\) belonging to glyceryl stearate. The Raman spectra of all waxes (Figure 2a,b) are dominated by the strong bands related to the CH\({}_{\rm x}\) stretching vibrations: the bands at 2879 cm\({}^{-1}\) and 2846 cm\({}^{-1}\) are attributed to the symmetric stretching vibrations of methyl and methylene groups, respectively, and the weak bands at 2957 and 2929 cm\({}^{-1}\) are assigned to the corresponding antisymmetric  
Figure 1: (**a**) FTIR spectra of natural waxes: beeswax (A), spermaceti (B), lanolin (C), carnauba (D) and candellilla (E). (**b**) FTIR spectra of artificial and mineral waxes: formulated candellilla (F), microcrystalline (G) and paraffin (H). modes. The medium-weak peak at 2720 cm\({}^{-1}\) is due to a combination of the stretching vibrational modes of methyl groups associated with CH\({}_{2}\)[49; 50].