## 4 Discussion
This study aimed to investigate the impact of various variables in the nanoprecipitation method on particle size and size homogeneity (PDI) of nanoparticles formulated using preformed methacrylic acid-based polymers (Eudragit\({}^{\circledS}\)). Figure 2A (a) indicates that increasing the OP led to a reduction in particle S until a certain point, beyond which there is little or no effect on particle S. This can be attributed to a decrease in the concentration of polymer chains per droplet formed in more dilute solutions. However, the influence of this variable becomes negligible with a further increase in OP volume, resulting in a significant increase in particle size (\(p<0.05\)). This suggests that the droplet S increased due to a decline in the efficiency of OP diffusion into the AP. The ease of diffusion is affected by the concentration gradient, which decreases with increasing OP concentration in the AP. Consequently, larger droplets may form, leading to larger particles. In Figure 2B (a), an increase in PDI can be observed with an increase in OP volume in three of the polymers tested. This could be due to hindered diffusion leading to increased turbulence in the system. Among the various precipitation techniques, nanoprecipitation by adding liquid and solvent is the most widely used. In this process, a solvent (such as acetone, ethanol, or MeOH), preferably a water-miscible solvent (in which the drug and the polymer have adequate solubility), is mixed with an antisolvent (usually water) [29] by applying mixing forces (sonication, agitation, and temperature), as it has been observed that the addition of some external factors (ultrasonic waves, high revolutions in mixing, or increases in temperature) usually results in a smaller particle size or a narrower particle size distribution [30; 31]. The smaller particle size obtained by these methods results from faster mixing, affecting the nucleation stage or stopping particle growth [30]. Thus, we assume that the decrease in size with increasing OP and for certain polymers, AP is given in the first place via sonication to dissolve the polymers in the corresponding solvent, but mainly by applying high mixing forces [31]. In Figure 2B (b), it can be observed that particle size decreased only in the initial increments of PA volume variation. Droplet size is directly related to particle size in emulsion-based or pseudo-emulsion-based methods such as nanoprecipitation [32]. Therefore, it is possible that an increase in AP volume resulted in a decrease in droplet size. This could be because diffusion is facilitated by a higher concentration gradient, which typically decreases as OP is incorporated into AP, leading to dilution of the OP in AP. However, for three of the tested polymers, the influence of this variable quickly ended for the volumes tested. This indicates that the volume portion of the diffusion zone, known as the Marangoni effect zone [27], possibly has a defined volume for each system and cannot be expanded further despite increasing AP volume. On the other hand, the effect of this variable on particle size homogeneity needs further clarification. As discussed above, a successful formulation of stable and efficient nanocarriers requires the preparation of homogeneous (monodisperse) populations of a given S; however, it is difficult to control the particle size distribution without considering the composition of the nanocarriers and the nature of the solvents and cosolvents used during their preparation [33]. Figure 2A (c) shows that, when the amount of polymer was evaluated, larger particles were formed as the PA increased; this phenomenon may be due to the degree of supersaturation in the system, which is the ratio of the concentration of the solute in that solution at that particular condition. Therefore, the solubility profile of the solute in different solvent/antisolvent combinations at different conditions such as different temperatures must be known in advance to calculate the degree of supersaturation [30]; in our study, it was at room temperature.