Effect of solvent on electric double layer capacitance and over screening inside spherical cavity by density functional theory

In this article, the solvent primitive model (SPM) and the restricted primitive model (RPM) in the framework of modified fundamental measure theory are compared for the prediction of the electric double layer (EDL) at the contact surface of the concave wall of a charged spherical cavity. The structure of EDL, EDL capacitance, Stern and diffuse contributions, zeta potential, and over screening phenomenon are predicted and compared with the two models. Our results show that considering the solvent molecules as hard spheres according to SPM leads to an appearance of layering structure and oscillatory behavior of density profiles inside the cavity. Also, the amount of ion adsorption in SPM is greater than that of RPM at the same condition. As a result of more counterion adsorption in comparison to co-ion adsorption, the total net charge inside the cavity increases. That way, the predicted amount of EDL capacitance and its diffuse contribution by SPM are greater than the corresponding values by RPM. Note that the Stern contribution to the capacitance has the same value in both models at fixed and equal sizes of ions and solvent molecules. Finally, the mean electrostatic potential (MEP) in the cavity, which is strongly affected by more counter-ion adsorption in SPM, shows evidence of an over screening phenomenon in the stern region at a lower concentration in comparison to RPM. Also, the slope of MEP is higher for SPM (in the Stern region), which leads to lower absolute values for its zeta potential.