Fig. 1

Enlargement of the capacitance of a microslit capacitor. a Schematic illustration of a continuum model of a microslit capacitor consisting of MXene Ti₂CT_x nanosheets. Ti (dark cyan), C (brown), surface termination group T (gray) atoms are shown. b Schematic illustration of a bilayer-capacitor model. c Experimental specific capacitance of MXene Ti₂CT_x with aqueous Li⁺, Na⁺, K⁺, Rb⁺, TMA⁺ (tetramethylammonium), TEA⁺ (tetraethylammonium), and TBA⁺ (tetrabutylammonium) electrolytes. Each capacitance is calculated from the CV curve at the scan rate of 0.5 mV s⁻¹. d Orders of bare-ion size, hydrated ion size, and observed capacitance. e Ion-MXene distance (b − a₀) dependence of the experimental specific capacitance. The black dotted line shows a calculated capacitance based on the continuum model (\(C = \frac{{\varepsilon _{\mathrm{r}}\varepsilon _0A}}{{b\, -\, a_0}}\) with constant ε_rε₀), whereas the blue line shows a calculated capacitance based on the bilayer-capacitor model with variable ε_rε₀ from the 3D-RISM calculation