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Evolving structure and rheology across Kuhn scale interfaces in entangled polymer fluids under flow play a prominent role in processing of manufactured plastics, and have numerous other applications. Quantitative tracking of chain conformation statistics on the Kuhn scale is essential for developing computational models of such phenomena. For this purpose, we formulate here a two-scale/two-mode model of entangled polymer chains under flow. Each chain is partitioned by successive entanglements into strands that are in one of two modes: entangled or dangling. On the strand scale, conformation statistics of ideal (non-interacting) strands follows a differential evolution equation for the second moment of its end-to-end distance. The latter regulates persistent random walks sampling conformation statistics of ideal entangled strands on the Kuhn scale, as follows from a generalized Green-Kubo relation and the Maximum Entropy Principle. We test it numerically for a range of deformation rates at the start-up of simple elongational and shear flows. A self-consistent potential, representing segmental interactions, modifies strand conformation statistics on the Kuhn scale, as it renormalizes the parameters controlling the persistent random walk. The generalized Green-Kubo relation is then inverted to determine how the second moment of the strand end-to-end distance is changed by the self-consistent potential. This allows us to devise a two-scale propagation scheme for the statistical weights of subchains of the entangled chain. The latter is used to calculate local volume fractions for each chemical type of Kuhn segments in entangled chains, thus determining the self-consistent potential.
We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et al. (PRE, 60, 5657, 1999) to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities
It is well-known that the degeneracy of two-phase microstructures with the same volume fraction and two-point correlation function $S_2(mathbf{r})$ is generally infinite. To elucidate the degeneracy problem explicitly, we examine Debye random media,
We study the lifetime of the persistent spin helix in semiconductor quantum wells with equal Rashba- and linear Dresselhaus spin-orbit interactions. In order to address the temperature dependence of the relevant spin relaxation mechanisms we derive a
The flow and deformation of macromolecules is ubiquitous in nature and industry, and an understanding of this phenomenon at both macroscopic and microscopic length scales is of fundamental and practical importance. Here we present the formulation of
Nonlinear extensional flows are common in polymer processing but remain challenging theoretically because dramatic stretching of chains deforms the entanglement network far from equilibrium. Here, we present coarse-grained simulations of extensional