The effect of electro-neutrality violation inside a charged spherical cavity on the capacitance curve shape in DFT approach and interpretation of mean electrostatic potential

Abstract

The effect of electro-neutrality deviation in small charged cavities on the shape of the capacitance curve is investigated in this study. The data required are obtained using the modified fundamental measure theory and two models; namely, the restricted primitive model (RPM) and the primitive model (PM). The results of RPM investigations show that the capacitance curve will take on a bell shape when electro-neutrality parameter decreases with increasing surface charge, but that it exhibits a camel shape when electro-neutrality parameter shows a maximum versus surface charge. This behavior is essentially governed by both curvature and bulk concentration as it is observed that electro-neutrality parameter declines at high enough bulk concentrations and large enough curvatures. The PM study results indicate that an increase in the ratio of anion size to that of cation gives rise to higher positive values of the electric potential at zero surface charge. Moreover, it is seen that an increase in counter ion size causes more deviations from the electro-neutral condition while an increase in co-ion size relative to that of counter ions leads to the minimum value of electro-neutrality parameter versus surface charge but to a maximum for larger counter ions. Finally, it is found that, at the saturation point, the value for electro-neutrality parameter and, thereby, that for capacitance both become dependent on the size of counter ions. Base on the concept of the work in the thermodynamics and definition of mean electrostatic potential we interpreted all the terms present in the mean electrostatic potential in spherical cavity.