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Electrode surface roughness significantly impacts the structure of electricdouble layer on a molecular scale. We derive analytical solutions fordifferential capacitance (DC) of electric double layer near rough electrodesurface, comparing them with a range of experimental and numerical studies. Twocauses of ions separation are considered: ion size asymmetry and electrodesurface roughness. The model has three scale parameters determining DCproperties: the Debye length, difference of ion penetration depths, and surfaceroughness parameter. For the first time, DC profile with more than two peakswas obtained analytically due to account for ions reorientation effect. Themodel predicts DC curve transform from bell to camel and inverse induced byelectrode surface roughness. The behavior of DC-potential relation withtemperature and ion size ratio diverges depending on the type of ionsseparation. Additionally, we provide analytical solutions for zero chargepotential and demonstrate roughness effect on its value. Based on the results,we give recommendations for properties required to design effective electricdouble layer capacitors.

Molecular scale ion separation driven by surface roughness and ion size asymmetry: new analytical solutions for differential capacitance of EDL