Colloidal Crystal Opal (2D): Structural Color From Self-Assembly

Opal Cross-Section

Sphere diameter D 260 nm

Viewing angle θ (from normal) 0°

Infiltrating Medium

Reflected Structural Color

— nm
Bragg peak, (111) planes

n_eff (Maxwell-Garnett)

1.32

Packing fraction φ

0.740

d₁₁₁ spacing

0 nm

Blue-shift vs θ=0

0 nm

How it works

This is a 2D cross-section through a close-packed FCC opal: monodisperse silica/PMMA nanospheres (150–400 nm) resting on the (111) close-packed plane, seen edge-on with the layer stack below. Every circle here is genuinely drawn at the packing geometry implied by the diameter slider — the same interplanar spacing d₁₁₁ that a real opal's (111) planes present to incoming light.

d_111 = D · √(2/3)                          (111)-plane spacing, D = sphere diameter
n_eff = √( φ·n_sphere² + (1−φ)·n_medium² )   Maxwell-Garnett effective index, φ = 0.74 (FCC)
λ = 2 · d_111 · √( n_eff² − sin²θ )           Bragg peak, θ = angle from surface normal

Sphere diameter D — sets d₁₁₁ directly, the dominant control on hue: ~200 nm gives blue, ~260 nm green, ~320 nm red-orange, matching real silica/PMMA opal photonic pigments.
Viewing angle θ — the sin²θ term inside the Bragg relation shrinks the effective index term, blue-shifting the reflected wavelength as you tilt away from normal incidence — the same angle-dependent iridescence seen in natural opal gemstones and butterfly wing scales. The chart below plots λ(θ) live for the current diameter and medium.
Infiltrating medium — swapping air for water or ethanol raises n_eff and red-shifts λ; this is the working principle of opal-based colorimetric vapor and humidity sensors.

Real-world relevance: this is the same Bragg-diffraction mechanism used to fabricate structural-color pigments, tunable photonic-crystal sensors, and templates for inverse-opal catalysts and battery electrodes.

Colloidal sphere, (111) cross-section