This is a 2D side-on slice through the same self-assembled film as the 3D version: cellulose nanocrystal (CNC) rods pack into thin layers, and each layer's average orientation is rotated a small fixed step relative to the layer below it. Stack enough of those steps and the director sweeps out a full 360° turn — a chiral nematic (cholesteric) helix, sometimes called a Bouligand stack after the arched "fingerprint" pattern it makes in a polarised-light cross-section, which is exactly the pattern drawn here: each horizontal band is one layer, and the short strokes show that layer's rod orientation.
Bragg (de Vries) condition: λ = n̄ · P · cos(θ)
n̄ = average refractive index of the film
P = helical pitch (twist period, one full 360°)
θ = angle of the incident/viewing light from the film normal
When P lands in the hundreds-of-nanometres range — comparable to a wavelength of visible light — the periodic stack behaves like a Bragg mirror and reflects one narrow band of colour with no pigment at all: structural colour, the same trick used by beetle shells and opal. Because the helix has a single handedness, it only reflects left-circularly-polarized light, which caps the peak reflectance near 50%; everything else passes straight through the film.
- Ionic strength — dissolved salt screens the electrostatic repulsion between the negatively charged CNC rods as the film dries, letting them pack into a tighter helix. More salt → shorter pitch P → the band drawn here compresses and the reflected colour blue-shifts.
- Refractive index n̄ — the film's average index (cellulose plus any residual water) scales λ directly through the Bragg law.
- Viewing angle θ — tilting the film (or your eye) shortens the effective optical path, so λ = n̄P·cosθ drops and the colour blue-shifts toward grazing angles — the same iridescent colour-shift you see tilting a mother-of-pearl shell or a nanocellulose coating in your hand. The incident/reflected arrows above the stack tip over with θ.
This is a real, exploited effect: evaporation-cast CNC films make pigment-free, biodegradable structural-colour coatings, anti-counterfeiting labels, and humidity/ionic-strength sensors whose colour reports the drying conditions directly. Drag the canvas to pan and scroll to zoom into individual layers.