= Diffuse-layer differential capacitance
{title2=$C_D=\varepsilon\kappa_D\cosh[e\psi_0/(2k_BT)]$}
Differentiate the <Grahame equation> for a planar symmetric monovalent electrolyte with respect to surface potential at fixed reservoir <concentration> and <temperature>. The result is the displayed <capacitance> per unit <area>. It approaches $\varepsilon\kappa_D$ in the <Debye–Hückel approximation>. A compact surface layer can contribute a separate series <capacitance>; point-ion packing assumptions also fail at sufficiently high near-surface <concentration>.<The Electrical Double Layer and the Theory of Electrocapillarity by David C. Grahame>[section VI, equations (43)–(48), printed p. 474]{ref}
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