Worm-Like Chain — Entropic Spring Polymer

Thermal fluctuations of a semi-flexible polymer chain with bending stiffness κ

⟨R²⟩ theory: ⟨R²⟩ measured: End-to-end:
About: The worm-like chain (WLC) model describes semi-flexible polymers like DNA. Each segment aligns with its neighbor due to bending stiffness κ, with thermal noise breaking alignment. The persistence length L_p = κ/k_BT sets the length scale of orientational memory. The WLC formula predicts ⟨R²⟩ = 2L_p·L[1 − (L_p/L)(1 − e^(−L/L_p))]. The right panel shows the force-extension curve.