Electric Double Layer — Gouy-Chapman-Stern Theory (2D)

This 2D companion to the 3D supercapacitor cycling simulator solves the actual electrostatics behind the double-layer capacitance instead of just cycling it: the nonlinear Poisson-Boltzmann equation for a flat charged electrode in contact with a symmetric electrolyte, using the classical Gouy-Chapman analytic solution. The top strip shows cations and anions sampled directly from their Boltzmann concentration profiles near the surface; the middle plot traces how the electric potential decays with distance over the Debye screening length; and the bottom plot traces the differential capacitance against applied potential, showing the characteristic Gouy-Chapman rise capped by a fixed Stern (compact) layer capacitance in series — the same rise-then-saturate curve measured on real electrochemical double layers. Adjust electrolyte concentration, applied surface potential and compact-layer thickness to see how each reshapes the potential profile, the ion clouds and the capacitance curve.