Debye-Hückel Electrostatic Screening

Ion clouds screen charge in electrolytes — screening length sets the scale of electrostatic interactions.

Electrolyte

λ_D: — nm
κ: — nm⁻¹
Debye length: λ_D = √(ε₀ε_r k_B T / (2N_A e² z² c)), where c is ionic strength. For 1:1 electrolyte in water at 25°C: λ_D ≈ 0.304/√c nm (c in mol/L). The screened potential φ(r) = (Q/4πε₀ε_r) · e^(−r/λ_D)/r replaces the bare Coulomb 1/r. At high salt (large c), λ_D shrinks — DNA molecules, protein surfaces, and colloidal particles interact only at very short range. The potential map shows iso-contours of the screened Yukawa potential around an ion.