  In this work we theoretically study the differential capacitance of an
aqueous electrolyte in contact with a planar electrode, using classical Density
Functional Theory, and show how this measurable quantity can be used as a probe
to better understand the structure and composition of the electric double layer
at play. Specifically, we show how small trace amounts of divalent ions can
influence the differential capacitance greatly, and also how small ions
dominate its behaviour for high electrode potentials. In this study, we
consider primitive model electrolytes, and not only use the standard definition
of the differential capacitance, but also derive a new expression from
mechanical equilibrium in a planar geometry. This expression reveals explicitly
that the first layer of ions near the charged surface is key to its
understanding. Our insights might be used as a guide in experiments to better
understand the electrolyte-electrode interface as well as the (composition of
the) bulk electrolyte.

Soft Condensed Matter