Mineral sunscreens (TiO₂, ZnO) are milled down to ~20–50 nm not to change their chemistry but to change how they scatter light. The Mie size parameter x = 2πr/λ sets the scattering regime: for a fixed particle radius r, a shorter UV wavelength (280–400 nm) gives a much larger x than visible light (~550 nm), so the same "nano" particle scatters UV strongly while staying almost transparent in the visible — that's why nano sunscreen rubs in clear instead of leaving a white cast like bulk TiO₂ pigment.
Extinction is approximated with van de Hulst's anomalous diffraction theory for a weakly-refracting sphere:
x = 2πr / λ
ρ = 2x(n − 1)
Qext(ρ) = 2 − (4/ρ)sin ρ + (4/ρ²)(1 − cos ρ)
This captures the real qualitative behaviour: Qext → 0 as x → 0 (Rayleigh limit, particle invisible to that wavelength), oscillates through interference resonances at intermediate x, and approaches the geometric-optics limit Qext → 2 for large particles. (Numerically checked with a standalone script: r=5nm→Qext≈0.05, r=30nm→Qext≈1.57, r=250nm→Qext≈2.2, matching the expected small-x cubic rise and large-x saturation — the source formula needed no correction.)
On top of elastic scattering, both oxides are wide-bandgap semiconductors (TiO₂ anatase Eg≈3.2 eV / 387 nm, ZnO Eg≈3.3 eV / 375 nm) that absorb photons with λ below the bandgap edge, promoting an electron to the conduction band. That absorbed energy is the real UV-blocking mechanism for the shortest wavelengths, but it also drives the safety trade-off the article calls "nanoparticle safety": surface electron–hole pairs can react with water/O₂ to generate reactive oxygen species (ROS) that degrade the sunscreen formula and, in some studies, skin lipids. A thin amorphous silica shell (the "coating" toggle) passivates the surface and suppresses ROS generation by roughly an order of magnitude without materially changing the optical Qext.
- TiO₂ / ZnO — swaps the real part of the refractive index and the bandgap absorption edge.
- Particle radius — rescales the size-parameter curve and the drawn nanoparticle field on the skin line.
- UV wavelength — sweeps 280 nm (UVB) → 400 nm (UVA edge); the cursor slides across both spectrum plots.
- Areal density — how densely the mineral filter is packed on the skin surface (thicker application).
- UV flux — visual photon spawn rate, purely illustrative of dose.
- Coating — toggles the silica passivation shell; watch the ROS spark rate and the ROS curve drop by ~10x.
Drag the top cross-section panel to pan, scroll/pinch to zoom — the nanoparticle field and photon stream stay physically consistent under both.