A statistical mechanics study on relationship between nanopore size and energy storage in supercapacitors

Abstract

By applying classical density functional theory approach, one study is done on the impacts of the relative size (compared to that of the salt ions) of the cylindrical pore electrode on the curves of differential electrical capacitance Cd vs surface charge strength |σ| and energy storage density E vs applied voltage U, main conclusions are summarized as follows. (i) Solvent granularity always tries to facilitate a change of the Cd - σ curve from bell-shaped to camel shape; given that the cylindrical pore is shallow with reduced radius such as R∗=1.5 and in the presence of symmetrical and higher valence ion the Cd - σ curve always assumes camel shape, whatever the electrolyte bulk concentration is. (ii) For sufficiently small cylindrical pore such as R∗=1.5, symmetrical high valence electrolyte induces one extremely high peak of the camel-shaped Cd - σ curve at both sides of zero surface charge. (iii) Symmetrical high valence (2:2 and 3:3) electrolytes help in raising the E value, which is almost independent on the electrolyte bulk concentration, whatever the cylindrical pore radius is. (iv) Influence of the pore size on the single pore E value becomes observable only when the applied voltage exceeds some lower limit voltage, which is positively correlated with the ion valence. After exceeding the lower limit voltage, the curve of E versus U display saturation trend only for smaller pore such as R∗=1.5; whereas for larger pore, increase rate of E with U becomes faster and faster. The deep reason for the small pore saturation phenomena is that the co-ion adsorption capacities go to zero when the σ value exceeds some critical value after which the surface potential increases steeply with the σ value.