Director field n̂(r)
Nematic: long-range orientational order, no positional order.
Smectic-A: layers ⊥ n̂
Cholesteric: n̂ rotates helically.
Frederiks Transition
E > E_c = π/d·√(K/ε₀Δε)
director tilts above threshold
Defect charge: s=+½ or s=−½
(topological, cannot annihilate alone)
Nematic: long-range orientational order, no positional order.
Smectic-A: layers ⊥ n̂
Cholesteric: n̂ rotates helically.
Frederiks Transition
E > E_c = π/d·√(K/ε₀Δε)
director tilts above threshold
Defect charge: s=+½ or s=−½
(topological, cannot annihilate alone)