Chain structure and entanglement

It is shown that the entanglement junction may be modeled as a binary hooking contact of Kuhn nodes between two chains. The entanglement behavior is thus determined by chain tortuosity and given by Nv = (1/β)C ∞α, where Nv is the number of real or virtual skeletal bonds in an entanglement strand, C∞ is the characteristic ratio, α = 2 is the number of hooks involved at an entanglement junction, and β = 1/3 is the fraction of binary hooking configurations out of all possible configurations at a binary nodal contact. In other words, we have Nv = 3C ∞2, which is verified experimentally for 44 polymers, covering a wide variety of skeletal, pendant, and stereoisomeric (tacticity) structures. Since C∞ may be estimated by group additivity, the present equation may be used to predict the entanglement behavior from chemical structure.