## 3 Results and Discussion
### Odd-Even Effect and the Definition of Oligomers  
The definition of oligomer is generically associated to a small (\"oligo\") number of repeated organic molecules, and it is used in many fields. However, it is unclear from which number of repeated units and up to how many that nomenclature can be used. It also seems to be highly dependent on the field of application: proteins with thousands of Da can still be considered oligomers, while in the synthetic polymeric field, substances with similar MW would certainly be considered a polymer [27; 28]. Additionally, associated  
Figure 7: T\({}_{\text{m}}\) variation of PET and PBT cyclic oligomers.  
to the increase of the number of repeated units, changes in the physical properties are also expected, which will also have implications in the analytical methods used [29].  
The results presented in this work for the PET cyclic oligomers showed that the progression of ring length from the smaller to the longer oligomers exhibited a behavior like what has been reported in the literature for other molecules, the so called odd-even effect. This affected not only their physical properties (solubility and T\({}_{\rm m}\)'s), chemical behavior and intermolecular forces, but could also be observed with two analytical techniques (HR-MS and NMR). Such as the case for other molecules, these clear differences may be related with the spatial molecular structure of the oligomers (Figure 1). One theory states that the odd counterparts are more distorted from their equilibrium geometries, leading to a reduction of the O\(\cdots\)O repulsions and consequent lowering of their melting point [19,20]. In fact, the even cyclic oligomers have an almost symmetric conformation, based also on the number of repeating units (e.g., di-, tri-, tetra-, etc.), which can justify the difficulty in solubilization (Table 1), the higher observed T\({}_{\rm m}\) (Figure 7) and the MS fragmentation patterns (Figure 5). Especially, the different MS fragmentation for tetra- and hexa- (even number) which consists the formation of a new fragment (385.09058 Da) which presented at high intensity and it was confirmed to represent the dimer (even-numbered oligomer). It can be concluded that these even-numbered structures present a structural symmetry. The more disordered structures of an odd oligomer may facilitate its solubilization and a smaller need of energy (temperature) for its melting. This phenomenon also aligns with what has been observed for the PBT cyclic oligomers. However, in the latter case, only cyclic oligomers up to the pentamer were available. Previous works of the authors include additional information on solubility, chemical behavior, analytical data, and physical-chemical properties of PBT cyclic oligomers [11,17,18].  
Another interesting observation is related with the T\({}_{\rm m}\)'s of the longer PET cyclic oligomers, the hexamer and the heptamer. With MW higher than 1000 Da, these two oligomers not only had roughly the same T\({}_{\rm m}\)'s, but respective T\({}_{\rm m}\)'s were very close to the polymer itself, PET. Also, the solubility properties were very close, as can be seen in Table 1. We can therefore hypothesize that the hexamer, for this type of oligomer, could be the upper limit in which an oligomer starts behaving and showing the physical properties of the polymer. Therefore, a potential definition for an oligomer in the synthetic polymeric field aligned with our observations could be _\"oligomers are chemical substances that have a varying number of the same repeating unit up to a point in which their melting point reaches the melting point of the polymer itself\"_.