## 3 Results  
### FAME Selection  
Table 2 reports the value of Hansen and Teas parameters for the FAME shown in Table 1. The increment in the CH\({}_{2}\) groups within the ester molecule directly associates with an increase in the dispersion solubility parameter (\(\delta\)D) due to heightened van der Waals intermolecular forces. Moreover, distinct structural features intrinsic to different fatty acid esters result in further disparities. Factors such as chain length, levels of unsaturation, and branching exert substantial influence over the overall properties of FAME. The CCOO group, constituting a minor fraction of the molecule, exhibits a limited dipole moment and minimal capacity to engage in hydrogen bond formation. Consequently, slight variations in the \(\delta\)P and \(\delta\)H values are observable, such as in the comparison between methyl caprylate and methyl linoleate. However, an exception arises with ricinoleate, which contains a hydroxyl group at C-12, resulting in notably higher \(\delta\)P and \(\delta\)H values compared to other esters. Figure 2: The step in the process of calculating the percentage of black present on the surface of canvases. Table 3 displays the relative energy difference (RED) of FAME shown in Table 2, calculated using white spirit as reference. As the affinity for the miscibility of the two substances decreases, RED numbers increase. RED = 0 signifies that solvent 1 can replace solvent 2; RED < 1 indicates compatibility between the two solvents; and RED > 1 suggests their incompatibility. Methyl Caproate and Methyl Ricinoleate are incompatible with ligroin and white spirit. Figure 3 plots the tested solvents on the Teas chart. On the same Teas' diagram, the area of solubility for different materials used in cultural heritage applications is reported. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Compound Name** & \multicolumn{3}{c}{**Hansen Parameters**} & \multicolumn{3}{c}{**Teas Parameters**} \\ \hline  & **\(\delta\)d** & **\(\delta\)p** & **\(\delta\)h** & **Fd** & **Fp** & **Fh** \\ \hline Methyl Canolate & 14.8 & 2.7 & 4.5 & 67.3 & 12.3 & 20.5 \\ \hline Methyl Caporate (Methyl decanoate) & 15.9 & 2.4 & 5.7 & 66.3 & 10.0 & 23.8 \\ \hline Methyl Caproate (Methyl hexanoate) & 16.0 & 4.3 & 5.8 & 61.1 & 16.6 & 22.3 \\ \hline Methyl Capylate (Octanoate) & 15.4 & 2.7 & 5.9 & 64.2 & 11.3 & 24.6 \\ \hline Methyl Cocinate & 16.0 & 1.8 & 4.7 & 71.1 & 8.0 & 20.9 \\ \hline Methyl Laurate (Methyl Dodecanoate) & 16.0 & 2.1 & 5.2 & 68.7 & 9.0 & 22.3 \\ \hline Methyl Linoleate & 16.2 & 1.6 & 3.9 & 74.7 & 7.4 & 18.0 \\ \hline Methyl Linolenate & 16.2 & 1.7 & 4.2 & 73.3 & 7.7 & 19.0 \\ \hline Methyl Myristate (Methyl tetradecanoate) & 16.0 & 1.9 & 4.2 & 72.4 & 8.6 & 19.0 \\ \hline Methyl Oleate (Methyl (Z)-9-Octadeceenoate) & 16.1 & 1.5 & 3.5 & 76.3 & 7.1 & 16.6 \\ \hline Methyl Palmitate & 16.0 & 1.6 & 3.6 & 75.5 & 7.5 & 17.0 \\ \hline Methyl Ricinoleate & 16.4 & 3.5 & 9.3 & 56.2 & 12.0 & 31.8 \\ \hline Methyl Searate & 15.9 & 1.4 & 3.2 & 77.6 & 6.8 & 15.6 \\ \hline Methyl Soyate & 16.1 & 1.6 & 3.8 & 74.9 & 7.4 & 17.7 \\ \hline Agnique\({}^{\text{\textregistered}}\) ME (mix methyl ester) & 16.4 & 3.3 & 4.7 & 67.2 & 13.5 & 19.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hansen parameters and the corresponding Teas parameters.