Entanglement strand orientation

Eq. (18.17) is simply the definition of the Doi-Edwards damping function with the independent-alignment approximation (Chapters 8 and 12). The damping functions of Doi and Edwards with and without the independent-alignment approximation both explain well the experimental results of a well-entangled nearly monodisperse polymer system (Fig. 9.2). Note that here the unit vector u° represents the orientation of a Fraenkel segment as opposed to the orientation associated with an entanglement strand or primitive step in the Doi-Edwards theory. 

Hoffmann has attempted to estimate the magnitude of Me directly from the structure (246). He suggests that entanglements comprise a special class of inter-molecular contacts in which one chain is looped tightly around another, and in which the four strands leading away from this contact are oriented such that the loop resists rapid deformations in the manner of a cross-link. His estimation of the concentration of such arrangements in polyethylene goes as follows. 

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