2D Gouy-Chapman-Stern Double Layer — Potential & Ion Density Profiles

Electrolyte

Valence z (z:z salt) 1

Bulk concentration 0.100 M

Electrode

Surface potential φ₀ 100 mV

Stern-layer thickness 0.30 nm

Readouts

Debye length λ_D

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Stern potential φ_S

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Surface charge σ₀

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C Stern

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C diffuse

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C total (series)

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Theory & equations

This solves the Gouy-Chapman-Stern model self-consistently: the compact Stern layer is a parallel-plate capacitor, the diffuse layer obeys the full nonlinear Poisson-Boltzmann (Grahame) relation, and the potential at the Stern/diffuse boundary φ_S is the value that makes both layers carry the same charge magnitude — solved here by bisection on every slider change.

C_Stern (φ0 − φ_S) = √(8 εr ε0 kT c NA) · sinh(zeφ_S / 2kT)
tanh(zeφ(x)/4kT) = tanh(zeφ_S/4kT) · exp(−κ(x−x_S))

Potential φ(x) Cation density Anion density Stern layer