## 4 Discussion
Any condition that increases the concentration of the solute or drug in solution or reduces the solubility of the solute (via an increase in antisolvent or decrease in temperature) increases the degree of supersaturation. Thus, if the degree of supersaturation is low and reached slowly (in the case of poor mixing), the nucleation rate is slow, and the system takes longer, which favors particle growth over nucleation [30]. However, high supersaturation also increases the mass transfer gradient and can increase particle size [29]. Thus, the effect of supersaturation on final particle size depends solely on how supersaturation is achieved; this can be modified by altering some parameters of the antisolvent phase (volume and temperature) and/or solvent phase (volume and concentration) [34]. This behavior suggests that, during the turbulence caused by the diffusion of the OP in the AP in our system, the tiny droplets formed may contain a more significant number of polymer chains than the particles formed, leading to a larger size. On the other hand, Figure 2B (c) does not show a clear trend between an increase in the amount of polymer used and the homogeneity of size. This indicates that this variable did not have a significant influence that surpassed the combinations of implicit phenomena during the formation of the NP, which would have allowed for suggesting conditions to obtain a homogeneous S a priori. Instead, it suggests that the changes caused by increases in the amount of polymer mass (PA) are unique to each system and need to be studied on a case-by-case basis. In terms of the polymer used, two structurally related groups were examined, as illustrated in Figure 1. The first group consisted of E100 and EPO polymers, which share the same monomer and have molecular weights of approximately 47,000 g/mol. In contrast, the second group comprised the structurally similar L100 and L00-55 polymers, with molecular weights around 125,000 g/mol [8; 17]. The performance of these materials was similar within each group across the different variables tested. Regardless of the variable analyzed, the Eudragit(r) E100 and EPO polymers resulted in larger particles. This implies that molecular size was not the primary factor, as these polymers had lower molecular weights than L100 and L00-55 polymers. However, their polymeric chains had more extensive branching, resulting in a greater steric effect when compressed by aggregation during nanoparticle formation [35]. The key challenge of nanoprecipitation is identifying the critical parameters or variables for the system to establish a functional diffusion zone, typically referred to as the Ouzo region, where nanoparticles will form, as also noted by other authors [36]. However, the successful production of PNPs is limited to a narrow range within the Ouzo region, beyond which the formation of microparticles or polymer aggregates occurs [36]. Therefore, it was possible to develop PNPs with Eudragit polymers with homogeneous PDI, size, and round morphology, as shown in Figure 4, allowin the development of nanocapsules with quercetin (Qr). Qr is a natural flavonol widely studied to possess a wide range of physiological benefits in humans, including antioxidant, anticancer, antiamoeba, antiparasitic, and antiviral activities [37; 38; 39]; however, the clinical use of quercetin is limited due to its poor oral bioavailability nonaqueous solubility, as well as degradation in the physiological alkaline pH of the intestine. Thus, encapsulation has been used in several investigations [40; 41]. There are several articles where Qr is encapsulated, demonstrating the advantages of encapsulation in terms of chemical stability and against photodegradation under ultraviolet light irradiation, thus increasing its antioxidant capacity [42], which indicates that Qr in NPs may be useful for improving the bioavailability. The literature provides some instances where the fundamental parameters suffice for generating particles with the desired characteristics [43].