Calculate the Debye screening length for electrolytes, plasmas, and semiconductors. Determine electrostatic screening distances and ionic strength.
The Debye length (λ_D) is the characteristic distance over which electrostatic potentials are screened by mobile charge carriers in a conducting medium. In an electrolyte solution, free ions rearrange themselves around a charged surface, creating a diffuse layer that exponentially attenuates the electric potential with distance. The Debye length measures how thick this screening cloud is.
In biological systems, the Debye length determines the range of electrostatic interactions between proteins, DNA, and cell membranes—typically 0.7–1 nm at physiological ionic strength. In plasma physics, the Debye length separates the scale where individual particle effects matter from the collective behavior of the plasma. In semiconductor physics, it determines the thickness of depletion layers at junctions.
This calculator computes the Debye length for electrolyte solutions, plasmas, and semiconductors. It shows how the screening distance depends on ion concentration, temperature, and dielectric constant, and provides visual screening profiles and concentration-dependence tables for quick reference.
The Debye length is a critical parameter in colloid science, biophysics, electrochemistry, and plasma physics. This calculator provides instant results for any medium type and concentration, saving time in research and coursework where screening lengths must be evaluated. The note above highlights common interpretation risks for this workflow. Use this guidance when comparing outputs across similar calculators. Keep this check aligned with your reporting standard.
Electrolyte Debye length: λ_D = √(ε_r × ε₀ × k_BT / (2 × n × z² × e²)) Plasma Debye length: λ_D = √(ε₀ × k_BT / (n_e × e²)) Ionic strength: I = ½ × Σ cᵢzᵢ² Screening parameter: κ = 1/λ_D Where n = ion number density, z = valence, e = elementary charge, k_B = Boltzmann constant.
Result: Debye length ≈ 0.96 nm
At 100 mM monovalent salt concentration in water at 25°C, the Debye length is approximately 0.96 nm. This means electrostatic interactions are effectively screened beyond about 3 nm (3 Debye lengths).
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It represents the distance over which the electrostatic potential of a charge is reduced by a factor of 1/e (≈37%) due to screening by mobile charges. Beyond a few Debye lengths, charges are effectively invisible.
Higher ion concentrations give shorter Debye lengths because more mobile ions are available for screening. λ_D scales as 1/√c. Doubling concentration reduces the Debye length by a factor of √2.
Blood has approximately 150 mM ionic strength, giving a Debye length of about 0.7–0.8 nm at body temperature (37°C). This very short screening length means electrostatic forces are extremely short-range in vivo.
In DLVO theory, the balance between van der Waals attraction and electrostatic repulsion determines colloidal stability. The Debye length sets the range of electrostatic repulsion—longer Debye lengths (lower salt) favor stability.
Multivalent ions are much more effective at screening. The Debye length scales as 1/z, so divalent ions (z=2) screen twice as effectively as monovalent ions at the same molar concentration.
The Bjerrum length is the distance at which the Coulomb interaction between two elementary charges equals the thermal energy k_BT. In water at 25°C, it is about 0.71 nm. It sets the scale for ion pairing and electrostatic correlations.