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David C. Grahame developed a quantitative treatment of the electric double layer and electrocapillarity. His analysis combined the Poisson equation with the Boltzmann distribution and distinguished accumulated interfacial charge, integral capacitance, and differential capacitance.^[ref]

Electrocapillarity is the dependence of interfacial surface tension on an electrical potential difference. Charging an electrode–electrolyte interface changes its interfacial free energy.^[ref]

At fixed temperature, pressure and chemical potentials, the electrocapillary relation reduces towhere $\gamma$ is interfacial surface tension, $E$ the appropriately defined electrode potential and $\sigma$ the electrode's free surface charge density. Thus an experimental curve of $\gamma$ versus $E$ measures charge through its slope. If $C=d\sigma /dE>0$, then $d^2\gamma /d{E}^2=-C<0$; zero charge gives a local maximum under these conditions. Adsorption or changing solution composition adds chemical-potential terms, so a measured maximum is not an unconditional universal charge marker.