Electric Double Layer Structure, Diffuse, and Zeta Potentials in Spherical Cationic and Anionic Liposomes: A Comparative Study of the Restricted Primitive Model and Solvent Restricted Primitive Model Using Classical Density Functional Theory

Modified fundamental measure theory (MFMT) has been used to model cationic and anionic liposomes into two frameworks: the restricted primitive model (RPM) and the solvent-restricted primitive model (SRPM). The liposomes were immersed in a mixture of symmetric and asymmetric electrolytes containing ions: A⁺, C²⁺, and B^-. In the case of SRPM, the solvent molecule has been considered as a hard sphere, <i>D</i>. The effect of concentration, liposome surface charge, cavity size, and liposomal membrane thickness on the structure and length of the electric double layer (EDL), mean electrostatic potential (MEP), diffuse (ψ_DP), and zeta potentials in both RPM and SRPM has been studied. Comparing the two models separates the role of solvent covolume from its role conducted by its dielectric constant in reducing the Coulomb interactions. For both models, increasing surface charge and concentration generally intensifies counterion adsorption and oscillatory density profiles and greatly reduces MEP, which in some cases leads to the charge inversion (CI) phenomenon. For all cases, the EDL structure in the liposome cavity was more compact with a smaller width in comparison to those at the convex, outer membrane wall of the liposome. Specifically, the studies on liposome cavity size showed that the smaller size amplifies the curvature effects, causing more ionic adsorption at the concave wall of the membrane compared to its convex wall. All of these effects amplify in the SRPM. In fact, the solvent, due to its high concentration, creates a regular and dense layered structure, which leads to the arrangement of the adsorbed ions into that structure. This causes more adsorption of ions as a result of the regular structure. Therefore, the SRPM induces a layering structure, resulting in a faster decay of MEP and leading to a CI phenomenon that is not observed with the RPM. The studies on the zeta and membrane potentials with surface charges show different behaviors depending on the concentration. Also, these results were remarkably different for the two models in both values and signs. These findings highlight the importance of considering solvent molecularity in theoretical models to better predict the EDL structure and optimize the stability and functional properties of liposomal drug delivery systems.