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Fluctuating Entanglements in Single-Chain Mean-Field Models
Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 S. Dearborn Street, Chicago, IL 60616, USA
Department of Chemical and Biological Engineering, Illinois Institute of Technology, 10 W. 33rd Street, Chicago, IL 60616, USA
Department of Physics, Illinois Institute of Technology, 3101 S. Dearborn Street, Chicago, IL 60616, USA
* Author to whom correspondence should be addressed.
Received: 22 March 2013; in revised form: 9 May 2013 / Accepted: 20 May 2013 / Published: 3 June 2013
Abstract: We consider four criteria of acceptability for single-chain mean-field entangled polymer models: consistency with a multi-chain level of description, consistency with nonequilibrium thermodynamics, consistency with the stress-optic rule, and self-consistency between Green–Kubo predictions and linear viscoelastic predictions for infinitesimally driven systems. Each of these topics has been considered independently elsewhere. However, we are aware of no molecular entanglement model that satisfies all four criteria simultaneously. Here we show that an idea from Ronca and Allegra, generalized to arbitrary flows, can be implemented in a slip-link model to create a model that does satisfy all four criteria. Aside from the direct benefits of agreement, the result modifies the relation between the initial relaxation modulus G(0) and the entanglement molecular weight Me. If this implementation is correct, current estimates for Me would require modification that brings their values more in line with estimates based on topological analysis of molecular dynamics simulations.
Keywords: entangled polymers; single-chain models; fluctuations
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Schieber, J.D.; Indei, T.; Steenbakkers, R.J.A. Fluctuating Entanglements in Single-Chain Mean-Field Models. Polymers 2013, 5, 643-678.
Schieber JD, Indei T, Steenbakkers RJA. Fluctuating Entanglements in Single-Chain Mean-Field Models. Polymers. 2013; 5(2):643-678.
Schieber, Jay D.; Indei, Tsutomu; Steenbakkers, Rudi J.A. 2013. "Fluctuating Entanglements in Single-Chain Mean-Field Models." Polymers 5, no. 2: 643-678.