Diffusion Coefficient Calculator
Calculate diffusion coefficients using Einstein-Stokes relation for various particle shapes
Calculate Diffusion Coefficient
Absolute temperature of the system
Dynamic viscosity in Pa·s (water at 25°C ≈ 0.001)
Particle radius in nanometers
Diffusion Coefficient Results
Einstein-Stokes Relation: D = kBT / ξ
Formula: D = (1.381 × 10⁻²³ × 298.1) / (18.850 × 10⁻¹²)
Analysis: Medium-sized proteins, drugs, or small polymers
Common Particle Examples
Water Molecule
H₂O at 25°C
Radius: 0.14 nm
Glucose
C₆H₁₂O₆ in water
Radius: 0.37 nm
Hemoglobin
Human hemoglobin at 37°C
Radius: 2.8 nm
Gold Nanoparticle
20 nm diameter Au NP
Radius: 10 nm
DNA (Linear)
Linear DNA fragment
Axes: 50×1 nm
Diffusion Coefficient Range
Gas Molecules
10⁻⁵ to 10⁻⁴ m²/s
Very fast diffusion in air
Small Molecules in Water
10⁻⁹ to 10⁻⁸ m²/s
Ions, simple organics
Proteins in Water
10⁻¹¹ to 10⁻¹⁰ m²/s
Biological macromolecules
Nanoparticles
10⁻¹³ to 10⁻¹¹ m²/s
Colloids, large aggregates
Friction Coefficient Formulas
Where: η = viscosity, a = radius/semi-major axis, b = semi-minor axis
Common Solvent Viscosities
Understanding Diffusion Coefficients
What is a Diffusion Coefficient?
The diffusion coefficient (D) is a parameter that quantifies the ease with which particles move through a medium due to concentration gradients. It relates the flux of particles to the concentration gradient through Fick's first law of diffusion.
Physical Significance
- •Higher D means faster particle movement
- •Depends on temperature, viscosity, and particle size
- •Fundamental to mass transport processes
- •Critical for drug delivery and biochemical processes
Einstein-Stokes Relation
D = kBT / ξ
ξ = 6πηa (sphere)
- D: Diffusion coefficient (m²/s)
- kB: Boltzmann constant (1.381 × 10⁻²³ J/K)
- T: Absolute temperature (K)
- ξ: Friction coefficient (s/kg)
- η: Dynamic viscosity (Pa·s)
- a: Particle radius (m)
Note: This relation assumes spherical particles in low Reynolds number flow (Stokes regime)
Applications and Importance
Drug Delivery
Designing drug particles with optimal diffusion rates for targeted delivery and bioavailability.
Protein Studies
Characterizing protein size, shape, and interactions in biological systems and drug development.
Nanotechnology
Predicting nanoparticle behavior in biological systems and designing delivery systems.