Polymer Reptation — de Gennes Tube Model
Entangled Polymer Melt · Tube Diameter · Reptation Time · Curvilinear Diffusion
Reptation Parameters
Chain length N (monomers)
100
Entanglement length Ne
20
Monomer size b (nm)
0.5
Curvilinear diffusion Dc (nm²/ns)
1.0
Regenerate Chain
Animate Reptation
Stop
Tube diameter a:
—
nm
Contour length L:
—
nm
Reptation time τ_d:
—
ns
Diffusion D_cm:
—
nm²/ns
Tube model (de Gennes 1971):
a = b√Ne
(tube diameter)
L = Nb²/a
(tube contour length)
Reptation time:
τ_d = L²/(π²Dc) = N³b⁴/(π²Dc·Ne·b²)
τ_d ~ N³ (key prediction!)
Center-of-mass diffusion:
D_cm = a²/(3τ_d) ~ N⁻²
MSD regimes:
t<τe:
⟨r²⟩ ~ t^(1/2)
(Rouse)
τe<t<τR:
⟨r²⟩ ~ t^(1/4)
(in tube)
t>τ_d:
⟨r²⟩ ~ t
(free diffusion)