Onsager Hard Rods — Isotropic-Nematic

Entropy-driven orientational ordering: excluded volume selects alignment

S = 0.00 — Isotropic
3.00
8.0
60
4
Onsager (1949): hard rods undergo an isotropic→nematic transition driven purely by entropy at c·L²·D ≈ 3.3. Aligned rods lose orientational entropy but gain translational entropy (less excluded volume overlap). Order parameter S = ⟨(3cos²θ−1)/2⟩. Transition is first-order with coexistence between phases.