A new regularity used to predict the camel-bell shape transition in the capacitance curve of electric double layer capacitors

Abstract

The concentration at which the camel-bell shape transition occurs in the capacitance curve of electric double layer capacitors is predicted via a new regularity stating that various plots of the integral capacitance, related to different surface charge densities, versus concentration (i.e., Cs-C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${C}_{s}-C$$\\end{document} curves) intersect at a specific concentration. Interestingly, the concentration at the intersection point is found to correspond to that of the concentration of camel-bell shape transition. The existence of such intersection reveals that integral capacitance increases (decreases) with surface charge density for concentrations smaller (or, larger) than that corresponding to the intersection point. Using the modified fundamental measure theory within the framework of the restricted primitive model, this study explores the effects of wall curvature and its convexity or concavity on this regularity and the characteristics of the intersection point. Results show that the intersection point for a convex wall occurs at concentrations larger than those observed for concave walls. The new regularity described is found valid for the capacitance of electric double layers at the interface with walls of different curvatures, including the convex wall of a charged spherical colloid particle and concave wall of a charged spherical cavity as well as planar and cylindrical pores. Furthermore, it is shown that the regularity in question can be used to predict the concentration at which the observed minimum in the asymmetric capacitance curve disappears in the case of asymmetric electrolytes.