Random Walk Polymer Chain

A freely-jointed chain of N monomers performs a random walk in 2D. The end-to-end distance grows as R ~ N^0.5 — a signature of Gaussian chain statistics.

Monomers N 100

Bond Length b 5

Ensemble size 10

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Mean ⟨R⟩

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⟨R²⟩

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b√N (theory)

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⟨R⟩ / b√N

Key Relations

End-to-end: ⟨R²⟩ = N·b² → ⟨R⟩ ≈ b√N

Distribution: P(R) = (3/2πNb²)^(3/2) exp(−3R²/2Nb²)

Radius of gyration: Rg² = Nb²/6

Fractal dimension: df = 2 (Gaussian chain)