## 4 Discussion
For example, PEPA (19.63 \({}^{\circ}\)C) has a lower melting point than MEPA (26.25 \({}^{\circ}\)C) by 6.62 \({}^{\circ}\)C, and PEBE (42.38 \({}^{\circ}\)C) is lower than MEBE (47.91 \({}^{\circ}\)C) by 5.53 \({}^{\circ}\)C. Such behavior could be attributed to an \"odd-even\" effect which had also been observed by [PERSON] et al. [26] in polymers. Here, the authors formulated the theory that odd-numbered chains formed less symmetrical structures due to their arrangement. In fact, at the end of odd CH\({}_{2}\) sequences, the bonds to the ester groups are inclined at an angle of 112\({}^{\circ}\), whereas at the end of even sequences they are parallel. Methyl esters are technically odd-numbered as well, but thought not to follow this behavior due to a more \"fixed\" structure, since the methyl ends have merely one possible orientation. As such, the odd-effect is only visible for CH\({}_{2}\) chains longer than two carbon atoms. The odd-even effect does not affect only the phase change temperatures of the materials, but seems to influence the enthalpies of fusion as well. In fact, similarly to what was observed for melting temperatures, pentyl esters presented the lowest enthalpies of fusion of the whole series. This is possibly to be attributed to the odd-even effect described above and to the shifting of the ester group towards the middle of the molecule, which makes the crystal lattice subjected to stronger vibrations and disruptions. As such, these two behaviors together cause pentyl esters to possess lower symmetrical crystal packing. The odd-even effect and the influence of the alcohol and carboxylic acid chain length on the final melting point can be observed in Figure 5.  
Figure 4: Barplot of all onset crystallization and melting temperatures of the esters reported in this study and in [PERSON] et al. [14] work. Melting temperatures are indicated in red, while crystallization temperatures in blue. The esters are grouped according to both growing carboxylic acid and alcohol chain length. As such, MEMY, PEMY and DEMY are listed first since they are all derived from the shortest carboxylic acid in the sequence (myristic acid, C\({}_{14}\)) and in order of growing alcohol chain length (methanol C\({}_{1}\), 1-pentanol C\({}_{5}\), 1-decanol C\({}_{10}\)). Figure 5: Scatter plot of the onset melting points of all esters reported in Table 4 for visual evaluation of the odd-even effect and the influence of the carboxylic acid chain length and the alcohol chain length on the phase change temperatures. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Carbon Number** & \(\mathbf{T_{c}}\) (**Onset, \({}^{\circ}\)C**) & \(\mathbf{T_{m}}\) (**Onset, \({}^{\circ}\)C**) \\ \hline \hline PEMY (C\({}_{5}\)-C\({}_{41}\)) & 19 & 4.17 \(\pm\) 1.22 & 9.90 \(\pm\) 0.51 \\ MEMY (C\({}_{5}\)-C\({}_{10}\)) & 15 & 13.58 \(\pm\) 0.84 & 15.15 \(\pm\) 1.50 \\ PEFA (C\({}_{5}\)-C\({}_{18}\)) & 21 & 15.24 \(\pm\) 0.47 & 19.63 \(\pm\) 0.48 \\ PEFA (C\({}_{5}\)-C\({}_{18}\)) & 23 & 17.83 \(\pm\) 0.98 & 25.17 \(\pm\) 0.79 \\ DEHY (C\({}_{10}\)-C\({}_{14}\)) & 24 & 22.89 \(\pm\) 0.16 & 25.16 \(\pm\) 0.44 \\ MEPA (C\({}_{1}\)-C\({}_{18}\)) & 17 & 24.38 \(\pm\) 0.24 & 26.25 \(\pm\) 0.06 \\ DEPA (C\({}_{10}\)-C\({}_{10}\)) & 26 & 28.92 \(\pm\) 1.24 & 29.03 \(\pm\) 1.87 \\ PEAR (C\({}_{10}\)-C\({}_{10}\)) & 25 & 35.75 \(\pm\) 0.28 & 35.45 \(\pm\) 0.21 \\ MESA (C\({}_{1}\)-C\({}_{18}\)) & 19 & 31.86 \(\pm\) 1.14 & 35.63 \(\pm\) 0.97 \\ DESA (C\({}_{10}\)-C\({}_{18}\)) & 28 & 33.83 \(\pm\) 1.29 & 36.22 \(\pm\) 0.79 \\ DEAR (C\({}_{10}\)-C\({}_{20}\)) & 30 & 40.83 \(\pm\) 0.17 & 40.89 \(\pm\) 0.45 \\ PEBE (C\({}_{5}\)-C\({}_{22}\)) & 27 & 43.02 \(\pm\) 0.20 & 42.38 \(\pm\) 0.59 \\ MEAR (C\({}_{1}\)-C\({}_{20}\)) & 21 & 41.75 \(\pm\) 1.06 & 44.05 \(\pm\) 0.35 \\ DEBE (C\({}_{10}\)-C\({}_{22}\)) & 32 & 44.71 \(\pm\) 0.63 & 44.79 \(\pm\) 0.68 \\ MEBE (C\({}_{1}\)-C\({}_{22}\)) & 23 & 41.47 \(\pm\) 1.03 & 47.91 \(\pm\) 0.71 \\ \hline \end{tabular}
\end{table} 
Table 4: Fatty esters tested in this work as well as by [PERSON] et al.