New model of polymer entanglement: Localized Gauss integral model. Plateau modulus G N, topological second virial coefficient Aθ2 and physical foundation of the tube model

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Abstract
The localized Gauss integral (LGI) model, which has been proposed recently by the authors [Macromolecules 21, 2901 (1988)], is discussed in detail. Plateau modulus GN is computed as a function of polymer concentration c and the topological interaction parameter γ̄. Parameter γ̄ is determined for various polymers using their bulk GN data; for polystyrene (PS), γ̄ determined from GN agrees well with that determined from the topological second virial coefficient, Aθ2. Using γ̄ determined from GN, Aθ2 of various polymers other than PS are computed numerically and it is found that Aθ2 of most polymers are much larger than that of PS. It is further shown that power α to the concentration dependence of GN is estimated to be 1.97–2.12 in agreement with experimental value 2.0–2.3 and that GN/c2lkBT is proportional to Aθ2, where cl is the number concentration of ‘‘localized chains.’’ Finally, LGI model is compared with the Doi–Edwards model and the two basic hypothesis of the latter model, the tensile force along the tube and the rubber-like expression of stress, are examined in view of the present model.