Order parameter, defects, and Frank elastic energy
Defects: 0 | Order parameter S: 1.00
Nematics are liquid crystals with orientational order but no positional order. The director field n̂(r) describes local molecular alignment, with n̂ ≡ −n̂ (headless). Frank elastic energy: F = ½∫[K₁(∇·n̂)² + K₃(n̂×∇×n̂)²]dV penalizes splay and bend distortions. Topological defects have half-integer winding numbers (±½) — impossible in ordinary vector fields but allowed because n̂≡−n̂. Defect pairs annihilate, driving order. Click the canvas to add a defect.