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Evolving structure and rheology across Kuhn scale interfaces in entangledpolymer fluids under flow play a prominent role in processing of manufacturedplastics, and have numerous other applications. Quantitative tracking of chainconformation statistics on the Kuhn scale is essential for developingcomputational models of such phenomena. For this purpose, we formulate here atwo-scale/two-mode model of entangled polymer chains under flow. Each chain ispartitioned by successive entanglements into strands that are in one of twomodes: entangled or dangling. On the strand scale, conformation statistics ofideal (non-interacting) strands follows a differential evolution equation forthe second moment of its end-to-end distance. The latter regulates persistentrandom walks sampling conformation statistics of ideal entangled strands on theKuhn scale, as follows from a generalized Green-Kubo relation and the MaximumEntropy Principle. We test it numerically for a range of deformation rates atthe start-up of simple elongational and shear flows. A self-consistentpotential, representing segmental interactions, modifies strand conformationstatistics on the Kuhn scale, as it renormalizes the parameters controlling thepersistent random walk. The generalized Green-Kubo relation is then inverted todetermine how the second moment of the strand end-to-end distance is changed bythe self-consistent potential. This allows us to devise a two-scale propagationscheme for the statistical weights of subchains of the entangled chain. Thelatter is used to calculate local volume fractions for each chemical type ofKuhn segments in entangled chains, thus determining the self-consistentpotential.

Flow-deformed conformations of entangled polymers as persistent random walks