Understanding the anatomy of capacitance at interfaces between two immiscible electrolytic solutions

Why does the Gouy-Chapman theory often predict the magnitude and behavior of capacitance curves at the interface between two immiscible electrolytic solutions, and sometimes fail? Why do experiments sometimes show an "unphysical" negative or zero Stern-layer contribution to the inverse capacitance? These questions motivated the construction of a model to encapsulate the anatomy of this easily experimentally accessible interfacial characteristic. The Verwey-Niessen theory is extended here to allow ionic penetration at the interface. This extension explains several features of experimental curves that arise when solutes vary, such as asymmetry and shifts of the capacitance minimum - features that are described by neither the Gouy-Chapman nor the Verwey-Niessen theories. Free energies of ion transfer are taken as model input parameters to describe ionic penetration into a mixed-solvent interfacial layer. With a single additional parameter that lies in a narrowly constrained range, the model successfully reproduces experimental data. It also shows why the Gouy-Chapman theory works and why the Verwey-Niessen theory rarely does, rationalizing how inner-layer contributions are hidden in the capacitance response.