New Insights on Infinite and Negative Values of Diffuse Capacitance and Correlations with Surface Phenomena

The electric double layer capacitance and its two contributions, the Stern and diffuse, in ionic liquid-based supercapacitors with porous electrodes containing spherical cavities have been investigated via modified fundamental measure theory. We observed that the negative values of diffuse capacitance convert to positive through passing infinity when zeta potential, ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ζ</mml:mi> </mml:math> ), becomes equal to potential of zero charge, ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic">PZC</mml:mi> </mml:math> ). Examination of the normalized integral charge density shows that at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ζ</mml:mi> <mml:mo>=</mml:mo> <mml:mi mathvariant="italic">PZC</mml:mi> </mml:math> the total net ion charge in the cavity is concentrated on the hypothetical plane parallel to the cavity wall, the Stern plane, instead of its spreading in the cavity. Hence, the electric double layer thickness reaches its minimum value, leading to equality of total capacitance with its Stern contribution. Thus, the capacitance is obtained via the system’s geometry. Also, the crowding and overscreening phenomena occurs respectively for potentials higher and lower than this specific potential. So, we introduced this specific potential as the transition potential from the overscreening phenomenon to the crowding one. Furthermore, we attributed the overscreening phenomenon to the negative values of diffuse capacitance, while crowding takes place when diffuse capacitance has positive values. The effect of cavity size and ionic size ratio on this specific potential was studied.