Sub-Nanometer Pore Ion Sieving in Supercapacitors

Electrolyte Ion

Pore Geometry & Drive

Slit pore width d 0.90 nm

Applied voltage 1.5 V

Animation speed 1.0×

Pore Access

Desolvated entry

Live Readouts

Areal capacitance

— µF/cm²

Effective d_eff

— nm

Pore utilization

— %

How it works

In carbon supercapacitor electrodes, ions from the electrolyte pack into pores to form an electric double layer. Each ion normally carries a shell of solvent molecules around it, so its solvated diameter is what determines whether it can enter a pore at all.

Pore access test (slit width d):
  d ≥ solvated diameter   → ion enters fully solvated
  bare diameter ≤ d < solvated diameter
                           → ion must shed part/all of its
                             solvation shell to fit (desolvation)
  d < bare diameter       → ion cannot enter; only the pore's
                             outer face contributes capacitance

This simulator uses a simplified parallel-plate (Helmholtz) model for the areal capacitance contributed by the pore wall:

C = ε₀·ε_r,eff / d_eff        (F/m², here shown in µF/cm²)

where d_eff is the distance from the ion's charge centre to the wall — the solvated radius when the ion keeps its shell, or the much smaller bare ionic radius once it desolvates. Because C scales as 1/d_eff, forcing desolvation by shrinking the pore below the solvated diameter produces a real, experimentally measured anomalous increase in capacitance as pores drop below ~1 nm (Chmiola et al., Science 2006, on carbide-derived carbons) — the opposite of what a naive "smaller pore, less room, less charge" intuition predicts. A fixed effective permittivity ε_r,eff is used here for clarity; real confined-electrolyte permittivity and ion packing (e.g. the "superionic" states studied by Kondrat & Kornyshev) are more intricate and not modelled directly.

Ion — sets the solvated and bare (crystallographic) radii used in the access test.
Pore width d — the slit gap between the two electrode walls; the geometry updates live and ions visibly shed their shell (or bounce back) at the pore mouth.
Voltage — drives how fast ions are drawn toward the pore mouth; it does not change the geometric capacitance in this Helmholtz model, matching the real physics that C is set by structure, not by V, to first order.

Solvation shell Bare (desolvated) ion Electrode wall

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