Under the EU's nanomaterial definition (Commission Recommendation 2011/696/EU, refined 2022) a substance is legally a "nanomaterial" - triggering REACH/CLP labeling, registration and risk-assessment duties - if at least a set percentage (default 50%) of the particles in its number-based size distribution have one or more external dimensions between 1 and 100 nm. This is a statistical threshold on the population, not on any single particle.
Real powders don't have one diameter - they follow a log-normal distribution, parameterised by a median d50 and a geometric standard deviation (GSD) σg:
ln(d) ~ Normal( ln(d50), ln(σg)^2 )
Number fraction in [1,100] nm =
Φ( ln(100/d50)/ln(σg) ) - Φ( ln(1/d50)/ln(σg) )
where Φ is the standard normal CDF. The simulator draws a live batch of particles from this distribution, plots every particle as a circle sized to its diameter on a draggable, zoomable 2D field (nano-range particles glow red), and computes the exact number fraction against the slider threshold in real time. A live histogram of the same batch sits below the field.
- Median diameter - shifts the whole population toward or away from the nano window.
- Spread (GSD) - a tighter batch (near 1.0) is almost monodisperse; a wider one smears particles across many decades, which is why even a "mostly bulk" powder (large d50) can still cross a 50% nano threshold if it has a wide enough tail of fines.
- Threshold - jurisdictions differ: the EU default is 50% by number; some proposals and other regimes use lower cutoffs (e.g. 10%), which is why this control is exposed separately from the physics.
This is exactly the calculation a manufacturer's characterisation lab or a regulator's dossier reviewer runs on electron-microscopy particle counts to decide whether REACH nanomaterial obligations apply. (Verified numerically: the closed-form Φ-difference formula was checked against a 2,000,000-particle Monte Carlo sample across several d50/GSD pairs and matched to within 0.02 percentage points - the source formula is correct and reused here unchanged.)