Colloidal Crystals
self-assembly · opal structure · photonic bandgap
Physics: Colloidal crystals: monodisperse spheres (100 nm–1 μm) self-assemble by sedimentation or evaporation into FCC/HCP packing (74% volume filling, Kepler conjecture proved 1998). Bragg reflection: λ = 2n_eff·d_{111}·sinθ where d_{111} = a/√3 for FCC. Structural color in opals: SiO₂ spheres ~200 nm give iridescent visible colors. Photonic bandgap: range of λ that cannot propagate through the crystal. Polydispersity > 5%: crystallization is suppressed. Hard sphere entropy-driven transition: fluid → crystal at φ > 0.494; melting at φ > 0.545. Inverse opals (air spheres in silica/TiO₂) have larger photonic bandgaps.