Electrochemistry & Plasma Physics

Debye-Hückel Shielding

Simulate Peter Debye and Erich Hückel's 1923 electrostatic screening theory. Mobile counter-ions surround central ions to form a Debye screening cloud, damping the bare Coulomb potential $V(r) \propto 1/r$ into a screened Yukawa potential $\Phi(r) = \frac{q}{4\pi\varepsilon r} e^{-r/\lambda_D}$.

Debye Length λ_D 3.04 nm

Ionic Strength I 0.10 M

Screening Factor e^(-r/λ_D)

Electrolyte Setup

Concentration c 0.10 M

Electrolyte Valence

Visual Overlay

Show Counter-Ion Atmosphere Cloud

Show Screened Potential Curve Φ(r)

Show Debye Sphere Badges

Controls

Debye Screening Length & Screened Coulomb Potential

Debye Length: λ_D = √[ (ε_0 ε_r k_B T) / (2 N_A e² I) ]
Ionic Strength: I = ½ ∑ c_i z_i²
Screened Yukawa Potential: Φ(r) = [ q / (4π ε r) ] · exp(- r / λ_D)

Developer Reference

Core Algorithm & Standalone Script

// Debye-Huckel ionic screening & potential solver
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// Phi(r) = (q / (4 * pi * eps * r)) * exp(-r / lambda_D)