What does the Debye length physically represent?

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.

How does concentration affect Debye length?

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.

What is the Debye length in blood?

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.

Why is Debye length important for colloidal stability?

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.

How does valence affect screening?

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.

What is the Bjerrum length?

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.

Debye Length Calculator

Calculate the Debye screening length for electrolytes, plasmas, and semiconductors. Determine electrostatic screening distances and ionic strength.

Medium

Temperature (K)

Dielectric Constant (εr)

Ion Concentration (mM)

Ion Valence (z)

Debye Length (λ_D)

0.971 nm

Characteristic screening distance for electrostatic interactions

Debye Length (m)

9.709e-10

In SI units

Screening Parameter (κ)

1.030e+9 m⁻¹

Inverse Debye length κ = 1/λ_D

Ionic Strength

0.1000 M

I = ½ Σ cᵢzᵢ² for all ion species

Thermal Voltage

25.68 mV

k_BT/e — characteristic energy scale at this temperature

Bjerrum Length

0.701 nm

Distance where Coulomb energy = thermal energy

Potential Screening

0.1 nm

90.2%

0.5 nm

59.8%

1 nm

35.7%

2 nm

12.7%

3 nm

4.6%

5 nm

0.6%

10 nm

0.0%

Concentration Dependence

Conc. (mM)	λ_D (nm)	κ (nm⁻¹)	Application
0.001	307.02	0.0033	Ultrapure water
0.01	97.09	0.0103	Lab solutions
0.1	30.70	0.0326	Lab solutions
1	9.71	0.1030	Physiological
10	3.07	0.3257	Physiological
100	0.97	1.0300	Physiological
500	0.43	2.3031	Concentrated
1000	0.31	3.2571	Concentrated

Planning notes, formulas, and examples

About the Debye Length Calculator

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.

When This Page Helps

The Debye length is a critical parameter in colloid science, biophysics, electrochemistry, and plasma physics. It gives results for any medium type and concentration, saving time in research and coursework where screening lengths must be evaluated.

How to Use the Inputs

Select the medium type: electrolyte solution, plasma, or semiconductor.
Enter the temperature in Kelvin (298 K for room temperature, 310 K for body temperature).
Input the dielectric constant of the medium (80 for water at 25°C).
For electrolytes, enter the ion concentration in millimolar and the ion valence.
For plasmas/semiconductors, enter the electron or carrier density.
Review the Debye length, screening parameter, and potential decay profile.

Formula used

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.

Example Calculation

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).

Tips & Best Practices

At physiological ionic strength (~150 mM), the Debye length is about 0.8 nm.
For multivalent electrolytes like CaCl₂, calculate the ionic strength using I = ½Σcᵢzᵢ².
The Debye length in pure water (~10 µm) is limited by autoionization (pH 7).
In semiconductors, use the carrier density from doping concentration.
The Debye–Hückel theory is accurate only for dilute solutions (< ~100 mM for 1:1 salts).

When To Use This Calculator

Calculate the Debye screening length for electrolytes, plasmas, and semiconductors. Determine electrostatic screening distances and ionic strength. Use it when you need a repeatable calculation in the physics / general category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

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.