The Stress Tensor in Entangled Polymers

In entangled polymeric liquids, a subchain connecting two entanglements is an open system which can exchange particles (Kuhn segments) with its neighboring subchains along the polymer chain. We present a calculation of the subchain mechanical behavior as determined from the grand canonical formalism of statistical mechanics, with different subchains in the same chain sharing the same chemical potential. It is shown that the linear monomer density is a constant, as originally inferred by Doi and Edwards, but the tension is generally different from one subchain to another. Accounting for the latter effect leads to a new tensorial strain measure, somewhat different from that proposed by Doi and Edwards.