Semiflexible Polymer — WLC Buckling & Force-Extension

Worm-like chain (WLC) model: a semiflexible polymer with persistence length L_p under compressive/stretching force. The Euler-Bernoulli buckling transition and Marko-Siggia force-extension relation are shown alongside thermal fluctuation modes.

Parameters

Contour length L/L_p: 2.0 Applied force f·L_p/k_BT: 0.0 Thermal noise amplitude: 0.5

WLC: ⟨cos θ(s)⟩ = e^{-s/L_p} Marko-Siggia: f·L_p/kT = L/L_p - 1/4 + 1/4(1-x/L)^{-2} Buckling (Euler): f_c = π²EI/L² = π²kT/(4L·L_p) End-to-end: ⟨R²⟩ = 2L_p·L[1-L_p/L(1-e^{-L/L_p})]