Dynamic Light Scattering — Nanoparticle Sizing Lab (2D)

Sample & Optics

Particle radius 30 nm

Temperature 298 K

Solvent viscosity 0.89 cP

Detector angle θ 90°

Live Readouts

Diffusion coeff. D

— µm²/s

Scattering vector q

— µm⁻¹

Real τ_c (formula)

— µs

Sim. half-life (measured)

— s

How it works

Suspended nanoparticles never sit still — thermal collisions with solvent molecules drive them in a random walk (Brownian motion) whose diffusion coefficient depends on their size through the Stokes–Einstein relation:

D = k_B·T / (6πη r)

A laser beam scatters off every particle in the illuminated plane. At a detector placed at angle θ, the scattered field is the sum of one wavelet per particle, each carrying a phase set by its position along the beam axis:

E(t) = Σᵢ exp(i q·xᵢ(t)),   I(t) = |E(t)|²
q = (4πn/λ) sin(θ/2)   — the scattering vector

As the particles diffuse, their relative phases scramble and the speckle intensity I(t) fluctuates. A DLS instrument never looks at I(t) directly — it computes the intensity autocorrelation function, which decays exponentially at a rate set by exactly the same D and q:

g₂(τ) = 1 + β·|g₁(τ)|²,   g₁(τ) = exp(−D q² τ)
τ_c = ln2 / (2 D q²)   (half-life)

That decay time is the entire measurement: plug the known q, viscosity and temperature into Stokes–Einstein and the instrument reports back a particle size — with no imaging, no microscope, just statistics of scattered light. The chart on the right computes g₂(τ) live from this simulation's own animated particles (their motion is slowed down for visibility, so its decay time doesn't match the "real τ_c" box — that one is the true instrument reading, computed directly from the formula at your current settings). Increase the radius and watch both the jiggling slow down and the correlation curve stretch out — exactly the relationship real DLS exploits.

Radius slider — bigger particles diffuse slower (D ∝ 1/r), so their scattered speckle pattern decorrelates more slowly.
Temperature — higher T means more energetic collisions, faster diffusion, faster decay.
Viscosity — a thicker solvent drags on the particles, slowing diffusion (D ∝ 1/η).
Detector angle θ — sets the scattering vector magnitude q; larger q probes smaller displacements and decays faster for the same D.
Drag / scroll on the cuvette — pan and zoom the view; the physics keeps running underneath exactly as before.

Nanoparticles Incident laser Detector at θ

drag to pan · scroll to zoom

Scattered intensity I(t)1.00

Intensity autocorrelation g₂(τ)2.00