Self-Healing Polymer: Chain Interdiffusion at a Crack

Healing Conditions

Temperature 400 K

Molecular weight 100 kDa

Clock speed ×60

Healing State

Strength recovered: 0%

Elapsed healing time

0 s

Full-heal time τ_h

—

Chains fully crossed

0 / 0

Interdiffusion depth

0 nm

How it works

This models intrinsic self-healing — no capsules, no embedded healing agent. When two freshly-cut faces of an amorphous thermoplastic (or a vitrimer above its topology-freezing temperature) are pressed into contact, chain ends on each side execute reptation: they crawl, snake-like, back and forth along their own confining tube, and a fraction of each chain diffuses across the interface into the opposite block.

De Gennes' reptation model gives a characteristic disentanglement time that scales steeply with chain length and, being a thermally-activated hopping process, follows Arrhenius scaling in temperature:

τ_h(T,M) = τ_ref · (M/M_ref)^3 · exp[ (Eₐ/R)(1/T − 1/T_ref) ]

Wool & O'Connor's minor-chain healing theory then relates the fraction of virgin fracture strength recovered to how long the interface has had those chains interdiffusing, up to the point full entanglement density is restored:

σ(t)/σ∞ = min[ 1, (t/τ_h)^(1/4) ]

Temperature — raises segmental mobility exponentially; +20 K can cut healing time several-fold.
Molecular weight — longer chains entangle more (tougher when healed) but reptate far slower — τ_h ∝ M³, the classic reptation cube law.
Clock speed — real interdiffusion takes minutes to hours; this speeds up simulated time so you can watch it complete.
The green worms crossing the crack plane are individual chains; each has its own random reptation phase, so they cross raggedly rather than in lock-step, exactly as a real ensemble of chains does.

Real-world relevance: this t^(1/4) law is the standard design equation for hot-plate welding, polymer 3D-print layer bonding, and vitrimer/dynamic-covalent-network self-healing coatings.

Diffusing chain Crack interface

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