On the strength and deformation dependence of the tube‐like topological constraints of polymer networks, melts and concentrated solutions. II. Polymer melts and concentrated solutions

A microscopic theory is developed for the topological constraints in polymer melts or concentrated solutions. The model is based on the screening concept of the global topology effects. It is taken into account the conservation of the local topology only. The constraining potential is assumed to be determined by the dependence of the free energy of the surrounding chains on the position of the considered chain. The ns−1/2 dependence (ns — segment number density) of the tube dimensions is obtained. Combining the calculated formula for the tube dimensions with the expression for the plateau modulus according to the Doi/Edwards theory yields precisely the universal power law for the plateau modulus deduced by Graessley and Edwards.