Polymer Reptation vs Rouse

Two polymer dynamics models: Rouse (no entanglements, D~N⁻¹) and reptation (entangled, D~N⁻²). Watch chains diffuse and compare mean-squared displacements on a log-log plot.

Rouse Chain (unentangled)
Reptation (tube model)
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Rouse Model

Diffusion: D_R ~ N⁻¹
Relaxation: τ_R ~ N²
MSD: ⟨Δr²⟩ ~ t (long time)
Valid: dilute / unentangled melts

Reptation (de Gennes 1979)

Diffusion: D_rep ~ N⁻²
Relaxation: τ_d ~ N³
MSD: ⟨Δr²⟩ ~ t^(1/2) → t
Valid: entangled polymer melts