Bead-Spring Polymer Viscoelasticity

The Rouse model connects polymer bead-spring dynamics to viscoelastic moduli. Each normal mode decays with its own Rouse time, producing G'(ω) and G''(ω) frequency sweeps characteristic of polymer melts.

Controls

Num beads N8

Spring const k1.0

Friction ζ1.0

Temperature T1.0

Theory (Rouse Model)

Mode times:
τ_p = ζ/(4k sin²(pπ/2N))

G(t) = G₀ Σ_p e^(−t/τ_p)

G'(ω) = G₀ Σ_p ω²τ_p²/(1+ω²τ_p²)
G''(ω)= G₀ Σ_p ωτ_p/(1+ω²τ_p²)

ω*: crossover G'=G''
Rouse peak: G''~ω^½