Segment-scale, force-level theory of mesoscopic dynamic localization and entropic elasticity in entangled chain polymer liquids

Dell, Zachary E.; Schweizer, Kenneth S.

doi:10.1063/1.4978774

Segment-scale, force-level theory of mesoscopic dynamic localization and entropic elasticity in entangled chain polymer liquids

Journal Article · Tue Apr 04 00:00:00 EDT 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4978774· OSTI ID:1465948

Dell, Zachary E. ^[1]; Schweizer, Kenneth S. ^[2]

Univ. of Illinois, Urbana, IL (United States). Department of Physics; Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
Univ. of Illinois, Urbana, IL (United States). Department of Materials Science, Department of Chemistry and Frederick Seitz Materials Research Laboratory

In this study, we develop a segment-scale, force-based theory for the breakdown of the unentangled Rouse model and subsequent emergence of isotropic mesoscopic localization and entropic elasticity in chain polymer liquids in the absence of ergodicity-restoring anisotropic reptation or activated hopping motion. The theory is formulated in terms of a conformational N-dynamic-order-parameter generalized Langevin equation approach. It is implemented using a universal field-theoretic Gaussian thread model of polymer structure and closed at the level of the chain dynamic second moment matrix. The physical idea is that the isotropic Rouse model fails due to the dynamical emergence, with increasing chain length, of time-persistent intermolecular contacts determined by the combined influence of local uncrossability, long range polymer connectivity, and a self-consistent treatment of chain motion and the dynamic forces that hinder it. For long chain melts, the mesoscopic localization length (identified as the tube diameter) and emergent entropic elasticity predictions are in near quantitative agreement with experiment. Moreover, the onset chain length scales with the semi-dilute crossover concentration with a realistic numerical prefactor. Distinctive novel predictions are made for various off-diagonal correlation functions that quantify the full spatial structure of the dynamically localized polymer conformation. As the local excluded volume constraint and/or intrachain bonding spring are softened to allow chain crossability, the tube diameter is predicted to swell until it reaches the radius-of-gyration at which point mesoscopic localization vanishes in a discontinuous manner. Finally, a dynamic phase diagram for such a delocalization transition is constructed, which is qualitatively consistent with simulations and the classical concept of a critical entanglement degree of polymerization.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Illinois, Urbana, IL (United States). Department of Materials Science

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: FG02-07ER46471

OSTI ID:: 1465948

Alternate ID(s):: OSTI ID: 1361789

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 13 Vol. 146; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Segment-scale, force-level theory of mesoscopic dynamic localization and entropic elasticity in entangled chain polymer liquids

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