Models for Entanglement Formation

In the Doi-Edwards theory the plateau modulus and the tube diameter are related according to Eq. (40). Inserting Eq. (40) into (52) we finally obtain 

This relation is the central result of the scaling model for the entanglement distance. 

In the packing model [50,62,68] the entanglement distance is interpreted by the gradual build-up of geometrical restrictions due to the existence of other chains in the environment or, more precisely, the entanglement distance is determined by a volume which must contain a defined number of different chains. This approach is based on the observation that, for many polymer chains, the product of the density of the chain sections between entanglements is 

Neglecting the influence of chain ends, Eq. (55) yields for the entanglement distance 

With the number of entanglement strands ne/volume, the desired number of binary contacts per entanglement strand becomes 

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