Titanium dioxide (TiO₂) scattering calculator

About 270 nm in a binder of refractive index 1.5: that size scatters the most visible light per gram of pigment (table above), close to the 200–300 nm used for commercial white pigments. Smaller particles scatter too little (scattering falls as the sixth power of the size); larger ones put more mass into each particle than the extra scattering is worth.

Its refractive index (about 2.5–2.7) is far higher than that of the binder or air, and it absorbs no visible light. Particles of a few hundred nanometres therefore scatter all visible colours strongly and almost equally, which the eye sees as brilliant white.

Particles of 20–40 nm scatter almost no visible light (a 20 nm particle gives about 0.2 % of the optimum per volume), so the cream looks clear, yet they still absorb ultraviolet strongly: TiO₂ absorbs above its band gap, below about 400 nm, and at 350 nm most of a small particle's extinction is absorption (83 % at 20 nm).

Particles much smaller than the wavelength scatter as Rayleigh scatterers, about 1/λ⁴, so they scatter blue more than red: a thin layer looks bluish in reflection and yellowish in transmission. See Rayleigh scattering.

Scattering depends on the contrast between the particle and its surroundings. In air (dry films, voids) the contrast is higher and the best size shifts smaller; in high-index resins it falls and scattering weakens. Change the medium in the calculator to see it.

Rutile has the higher refractive index (about 2.7 versus 2.5 in the visible), so it scatters more and is preferred for pigments; anatase is the more photocatalytic form. Enter a custom refractive index in the calculator to compare them.

Yes: titanium dioxide nanospheres and core–shell nanoparticles (add a shell) are available in every calculator, from spectra to optical properties: near-field enhancement maps, dimers and hot spots, nanoparticle arrays and lattice resonances, particles on a substrate, emitters and the Purcell factor, nanorods and laser heating.