Debye-Hückel Electrostatic Screening

Ions in solution screen electric fields exponentially over the Debye length λ_D. The screened potential φ ∝ e^−r/λ_D/r decays much faster than bare Coulomb 1/r.

Ion concentration c (mM) 50 mM

Charge Z +1

Temperature T (K) 298 K

φ(r) = (Ze/4πε₀ε) · e^{−r/λ_D}/r
Debye length: λ_D = √(ε₀ε k_B T / 2 N_A e² I) where I = ionic strength. Gold curve = screened; grey dashed = bare Coulomb. Charge cloud density: ρ ∝ e^{−r/λ_D}.