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Multiple scaling arguments have been proposed to describe how the entanglement molecular weight depends on polymer architecture and concentration. The Lin−Noolandi (LN) scaling argument, well supported by data for real polymers, assumes that polymers are flexible within their tubes; it must fail at some point as chains become stiffer. Everaers has made a different scaling proposal, which crosses over from semiflexible chains to stiff chains as described by Morse. This ansatz is consistent with simulation data for a range of bead-spring melts but is not consistent with LN. Here, we use simulations to explore a wide range of entangled bead-spring ring chains, to find out how entanglement properties vary with chain stiffness and concentration. To vary the packing length over a wider range, we add side groups to make chains bulkier. We quantify entanglement using three techniques: chain shrinking to find the primitive path, measuring the tube diameter by the width of the "cloud" of monomer positions about the primitive path, and directly measuring the plateau modulus. As chain stiffness and bulkiness vary, we observe three distinct scaling regimes, consistent with LN scaling, semiflexible chains, and stiff chains.

When oppositely charged polyelectrolytes mix in an aqueous solution, associative phase separation gives rise to coacervates. Experiments reveal the phase diagram for such coacervates, and determine the impact of charge...

Most studies of polyelectrolyte coacervate phase behavior focus on symmetric mixtures of oppositely charged polymers. Here we use a coarse-grained simulation, in which all bonded monomers and mobile counterions are represented as Lennard-Jones particles with unit charge and diameter equal to the Bjerrum length, to study the impact of charge asymmetry on coacervate phase behavior. We study the impact of salt on the concentration of polymers and mobile ions in each phase and qualitatively reproduce the closed-loop behavior observed in recent experiments on nonstoichiometric coacervates. We find that the counterions from added salt distribute unevenly, preferring the dilute phase to maximize their translational entropy, analogous to Donnan equilibrium for a charged membrane. The coacervate phase shrinks under osmotic pressure, leading to increased polymer concentration with small amounts of added salt.

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