HPLC-grade cyclohexane, acetone, ethanol, and polyethylene glycol 6000 (PEG-6000) were acquired from Sigma-Aldrich (Saint Louis, USA). Anionic copolymers based on methacrylic acid and methyl methacrylate (1:1) (Eudragit L100) were sourced from Evonik Roehm, Darmstadt, Germany. Ultrapure water was generated using the Milli-Q filtration system (Millipore, Saint-Quentin-en Yvelines, France). We also utilized Acrodisc Syringe Filters with Nylon Membrane, provided by PALL life sciences (USA). All chemicals employed were of analytical grade.

The synthesis of nanoparticles was carried out through spontaneous nano-emulsification, a widely adopted low-energy method for nanoparticle synthesis. This process involves an abrupt shift of solvents such as acetone and ethanol to an aqueous phase, leading to the formation of nanoparticles [15] [16] [17] . Figures 1(a) and Figure 1(b) illustrate the size distribution of Eudragit® nanoparticles based on Eudragit/polyethylene glycol (PEG) combinations (1:1 and 1:6) and the evaluation of the nanoparticles’ hydrodynamic diameter as influenced by the Eudragit®/PEG ratio, respectively. Figure 1(c) represents the Polydispersity Index.

The nanoparticles were synthesized according to the Eudragit/PEG ratio used. According to Kırımlıoğlu et al. and Dillen et al. [18] [19] , one of the most significant physical characteristics of colloidal carriers is their particle size and distribution. The analysis depicted in Figure 1 illustrates that the Eudragit/PEG ratio

significantly influenced the hydrodynamic diameter and the polydispersity index. In fact, PEG serves as a stabilizer. We selected it because it shows promise for in vivo applications, being a polymer with a well-established safety profile in humans [20] [21] . W.-S. Cho and colleagues synthesized spherical gold nanoparticles (AuNPs) coated with PEG. The hydrodynamic sizes of the PEG-coated AuNPs were measured at 27.6 ± 6.6 nm. The authors attributed this size to the formation of protective PEG layers covalently bonded to the AuNPs’ surfaces. The presence of a PEG layer was confirmed through Fourier transform infrared (FTIR) analysis [22] .

We observed a decrease in the size of the Eudragit® nanoparticles as the quantity of PEG present in the aqueous phase was reduced. The hydrodynamic diameter of the nanoparticles expanded from 85.38 nm at an Eudragit®/PEG ratio of 0.16, to 44.94 nm when the ratio was 1. Ali and Lamprecht demonstrated in their study, titled “Polyethylene glycol as an alternative polymer solvent for nanoparticle preparation,” the significant role of PEG in determining the size of polymeric nanoparticles [23] .

This could be attributed to the fact that PEG reduces the negative charge on the surface of the anionic polymer. This is illustrated in Figure 2, where the zeta potential shifts from −46.62 mV for a Eudragit/PEG ratio of 1; to −8.94 for a

ratio of 0.16. Indeed, the decrease in surface charge leads to diminished electrostatic repulsion between the Eudragit® nanoparticles, thus facilitating their partial agglomeration. This process of partial agglomeration or flocculation results in an increase in the size of the nanoparticles, as depicted in Figure 1. Our previous study involving magnesium hydroxide nanoparticles demonstrated this phenomenon of partial agglomeration through zeta potential modification [7] .

This partial flocculation is explained by the increase in the polydispersity index from 0.089 to roughly 0.109 when the quantity of PEG is increased. Specifically, as nanoparticles partially agglomerate, some retain their original hydrodynamic diameter, whereas others form flocs. These flocs have a significantly higher polydispersity index.

When a new interface forms, it is initially empty, allowing each nanoparticle colliding with it to adsorb freely. At the onset of this process, there is no energy barrier between the interface and the interfacial sub-layer. This adsorption creates a concentration gradient, inducing the diffusion-controlled movement of nanoparticles from the mass towards the interfacial sub-layer, until its concentration matches that of the suspended mass. Thus, the kinetics of adsorption depends on several processes, such as diffusional transport, reorientation, and adsorption. In this work, we examined the surface dynamics of solid nanoparticles at the cyclohexane/water interface using the axisymmetric drop shape analysis method. Initially, we measured the surface tension of the interface without nanoparticles to confirm the absence of impurities. The tension values obtained ranged between 48 and 50 mN∙m⁻¹ (Figure 3). Figure 3 also presents a series of tensiometer measurements for Eudragit® nanoparticles (NPs) with diameters of 85, 74, 60, 53, and 44 nm.

By analyzing Figure 3, a sharp decrease in interfacial tension was observed for Eudragit® NPs. Thus, in the early stages of adsorption (t → 0), the interfacial tension decreases rapidly. Subsequently, the decrease in interfacial tension slows down and finally reaches a dynamic equilibrium where the maximum coverage of the interface with the nanoparticles is reached (t → ∞). γ t → ∞ was obtained by intercepting a curve of the variation of interfacial tension against (1/t)^1/2, as

suggested by Equation (S1). This equation has been successfully used to characterize the transient behavior of surface and interfacial tension in the presence of nonionic amphiphilic molecules or macromolecules in aqueous environments, as supported by references [24] [25] [26] [27] [28] .

We also noticed that this decrease was made with the increase of the size of nanoparticles. Indeed, as the size of the nanoparticles increased, the interfacial tension gradually decreased over time, eventually reaching an equilibrium value, Equation (S2), that diminishes with the increase in nanoparticle size. Specifically, with 85 nm nanoparticles, the interfacial tension decreased from 48 - 50 mN∙m⁻¹ to around 18 mN∙m⁻¹. Meanwhile, with 60 and 74 nm nanoparticles, it decreases to around 22 mN∙m⁻¹. For the smallest nanoparticles, measuring 53 and 44 nm, the interfacial tension was observed to be 26 and 28 mN∙m⁻¹ respectively, after 2 hours. Similar results were obtained by Kutuzov et al., who studied the effect of cadmium selenide nanoparticles’ adsorption at a water/oil interface [29] . Lin et al. also demonstrated that the self-assembly of particles at fluid interfaces, driven by a reduction in interfacial energy, is well established. However, for nanoscopic particles, thermal fluctuations compete with interfacial energy, leading to self-assembly that depends on the size of the particles [30] . However, it is essential to consider the hydrophilicity or hydrophobicity of nanoparticles, as these characteristics significantly impact the contact angle. Tiwari et al., in an experimental study investigating the effect of silica nanoparticles (NPs) on surface tension in the presence of Triton X-100 and Tween-20 surfactants, demonstrated the role of parameters such as size and hydrophobicity, and consequently, the contact angle, in reducing interfacial tension [31] .

From the results of physicochemical characterization, it is hypothesized that the zeta potential plays a significant role in the self-assembly of nanoparticles and, consequently, their adsorption at the oil/water interface. Notably, nanoparticles with the lowest zeta potential values (85 nm, −8.94) exhibited the most substantial decreases in interfacial tension. This could be attributed to their self-organization behavior. This organization plays a crucial role in the stability of Pickering emulsions by preventing coalescence between two emulsion droplets. This certainly accounts for the superior stability of Pickering emulsions in comparison to conventional emulsions. The reduction of interfacial tension properties is also vital in stabilizing Pickering emulsions. Consequently, these nanoparticles enable the production of innovative pharmaceutical forms. These forms are not only capable of encapsulating active ingredients but also releasing them according to the pH conditions of biological environments [7] [8] .