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Chain-Entanglements Model

A theoretical framework describing polymer behavior based on the interactions and constraints imposed by chain entanglements.
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The statement of the theorem

Let r(s)\mathbf{r}(s) be the position of a monomer along the contour length ss of a polymer chain. The chain-entanglement model introduces a characteristic relaxation time τe\tau_e and an effective tube diameter aa. The mean-squared end-to-end distance ⟨R2⟩\langle R^2 \rangle is constrained by the entanglement length aa and the total contour length LL: \n⟨R2⟩≈La\langle R^2 \rangle \approx L a \nFurthermore, the characteristic relaxation time τ\tau scales with the molecular weight MM (or LL) according to the reptation model: \nτ∝M3.0 to M3.6\tau \propto M^{3.0} \text{ to } M^{3.6}
Source: Wikipedia