3D random walk · end-to-end distribution · Gaussian chain approximation
The freely jointed chain (FJC) model treats a polymer as N rigid segments of length b, each pointing in a uniformly random direction — a 3D random walk. The end-to-end distance R has distribution:
P(R) ∝ R² · exp(−3R²/2Nb²) for large N (Gaussian limit)
Root-mean-square end-to-end distance: ⟨R²⟩^(1/2) = b√N. The polymer swells as a random walk, not a rod — this is the entropic elasticity underlying rubber and DNA mechanics.