Theory of the Differential Capacitance of the Double Layer in Unadsorbed Electrolytes

Abstract

A partly phenomenological, one‐dimensional theory is presented of the double layer formed at an ideal polarized electrode in uni‐univalent aqueous electrolytes showing no specific adsorption. The system analyzed consists of the metallic electrode with its surface charge density, a charge‐free layer next to the electrode, and a diffuse layer containing positive and negative charges in unequal concentration extending into the body of the electrolyte. The theory includes the effect of dielectric saturation in both layers due to the field produced by an applied negative bias potential, and compression of the charge‐free layer by this field is also taken into account. The theory is compared with experimental data of D. C. Grahame on 0.916 N to 0.001 N NaF, which shows little or no adsorption on negative polarization. Good agreement is found both for the dependence of the differential capacitance of the entire system on negative polarizing potential (measured from the electrocapillary maximum) and on concentration. Such agreement allows several constants of the charge‐free layer to be obtained relatively accurately. In particular, values for its initial thickness, modulus of linear compressibility, initial dielectric constant, and dielectric saturation constant are obtained. Comparison of these results with corresponding results for bulk water affords strong evidence that the charge‐free layer consists of a single molecule of water and thus that cations nearest the polarized electrode are hydrated.