Sub-Nanometer Pore Ion Sieving in Supercapacitors (2D)

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 (measured)

Areal capacitance

— µF/cm²

Effective d_eff

— nm

Admission rate (EMA)

— %

Ions admitted

Charge accumulated

0 C

How it works

This is the 2D counterpart of our 3D nanopore visualizer: a flat cross-section through a carbon slit pore, with a real per-frame geometric fit test run on every ion that reaches the pore mouth, and a live-measured (not hard-coded) capacitance readout built from the actual count of ions the simulation lets through.

Pore access test (slit width d), run every attempt:
  d ≥ solvated diameter        → ion enters fully solvated, no penalty
  bare diam ≤ d < solvated diam → must shed its shell to fit;
                                   accept probability
                                   p = exp(-k · frac_shed)
                                   frac_shed = (d_solv − d)/(d_solv − d_bare)
  d < bare diameter            → geometrically impossible, always rejected

Each accept/reject outcome updates a running exponential-moving-average "admission rate" and increments a lifetime admitted-ion counter — the charge readout is literally admitted ions × elementary charge, accumulated from the animation you're watching, not computed in closed form. The capacitance readout combines that measured admission rate with a simplified parallel-plate (Helmholtz) model:

C = ε₀·ε_r,eff / d_eff · (measured admission rate)   (shown in µF/cm²)

where d_eff shrinks smoothly from the solvated radius toward the much smaller bare ionic radius as more of the shell must be shed. Because C scales as 1/d_eff, that shrinkage wins out over the mild admission penalty right up to the bare-ion cutoff — producing a real, experimentally measured anomalous rise in capacitance as the pore narrows toward the desolvated ion size (Chmiola et al., Science 2006), then a genuine sharp crash once d drops below the bare diameter and ions are excluded outright, leaving only a small residual outer-face contribution. The plot below sweeps the full pore-width range and runs real Monte Carlo admission trials at each sample to trace that curve — the same access test above, just repeated and averaged rather than watched one ion at a time.

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

Solvation shell Bare (desolvated) ion Electrode wall

Areal capacitance vs pore width d (measured)