Polymer Reptation: Entanglement & Melt Viscosity

In a dense polymer melt, chains longer than a critical entanglement length N_e cannot pass through one another — each chain is effectively caged inside a tube-shaped constraint formed by its neighbours. de Gennes' reptation model describes the resulting motion as a slow, one-dimensional slither along the chain's own contour, punctuated by tube renewal at both ends. This simulator renders that tube, the confined chain sliding through it, and the surrounding entangling chains in 3D, while live formulas compute the number of entanglements Z = N/N_e, the disengagement time τ_d, the diffusion coefficient, and the zero-shear viscosity — including the empirical η ∝ N^3.4 law that governs how molecular weight controls the processing viscosity of real plastics. A mode toggle lets you compare the same chain's behaviour with and without entanglement, contrasting reptation against simple Rouse dynamics.