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Polymer Physics: Chain Models
Freely-jointed chain · Worm-like chain · Gaussian chain · DNA stretching
Chain Configuration
FJC
WLC
Gaussian
New Config
N (segments)
50
Segment length l (nm)
1.0
Persistence length Lp (nm)
50
⟨R²⟩^½
—
Rg
—
R/Rmax
—
Force-Extension Curve
Applied Force F (pN)
0.0
WLC (DNA)
FJC
WLC: F·Lp/kT = ¼(1-x/L)⁻² - ¼ + x/L
(Marko-Siggia 1995)
DNA: Lp≈50nm, L_contour≈λ-DNA 16.5μm
Extension x/L
—
F·Lp/kT
—
End-to-End Distribution P(R)
FJC/Gaussian: P(R) ∝ R² exp(-3R²/2Nl²)
Flory exponent ν≈0.588 in 3D (self-avoiding)
ν=½ (ideal chain) · ν=1/3 (collapsed, bad solvent)
Flory exponent ν
0.59
Ensemble size
500