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

Title: 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
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)

View Accepted Manuscript (Publisher)

Cite

Export

Save

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

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

Grant/Contract Number:: FG02-07ER46471

OSTI ID:: 1465948

Alternate ID(s):: OSTI ID: 1361789

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

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

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 8 works

Citation information provided by
Web of Science

References (62)

Many chain correlated dynamics in polymer fluids Guenza, Marina The Journal of Chemical Physics, Vol. 110, Issue 15 https://doi.org/10.1063/1.478660	journal	April 1999
Scaling of the glassy dynamics of soft repulsive particles: A mode-coupling approach Berthier, Ludovic; Flenner, Elijah; Jacquin, Hugo Physical Review E, Vol. 81, Issue 3 https://doi.org/10.1103/physreve.81.031505	journal	March 2010
Macromolecular crowding: an important but neglected aspect of the intracellular environment Ellis, R. John Current Opinion in Structural Biology, Vol. 11, Issue 1 https://doi.org/10.1016/S0959-440X(00)00172-X	journal	February 2001
Increasing the density melts ultrasoft colloidal glasses Berthier, Ludovic; Moreno, Angel J.; Szamel, Grzegorz Physical Review E, Vol. 82, Issue 6 https://doi.org/10.1103/physreve.82.060501	journal	December 2010
Connection between Polymer Molecular Weight, Density, Chain Dimensions, and Melt Viscoelastic Properties Fetters, L. J.; Lohse, D. J.; Richter, D. Macromolecules, Vol. 27, Issue 17 https://doi.org/10.1021/ma00095a001	journal	August 1994
Tubes, Topology, and Polymer Entanglement Qin, Jian; Milner, Scott T. Macromolecules, Vol. 47, Issue 17 https://doi.org/10.1021/ma500755p	journal	August 2014
New View of Entanglements in Dense Polymer Systems Kavassalis, Tom A.; Noolandi, Jaan Physical Review Letters, Vol. 59, Issue 23 https://doi.org/10.1103/physrevlett.59.2674	journal	December 1987
Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids Weeks, John D.; Chandler, David; Andersen, Hans C. The Journal of Chemical Physics, Vol. 54, Issue 12 https://doi.org/10.1063/1.1674820	journal	June 1971
Rheology and Microscopic Topology of Entangled Polymeric Liquids Everaers, R. Science, Vol. 303, Issue 5659 https://doi.org/10.1126/science.1091215	journal	February 2004
Reptation as a dynamic mean‐field theory: Self and tracer diffusion in a simple model of rodlike polymers Szamel, Grzegorz; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 100, Issue 4 https://doi.org/10.1063/1.466403	journal	February 1994
Entangled Polymer Dynamics in Equilibrium and Flow Modeled Through Slip Links Schieber, Jay D.; Andreev, Marat Annual Review of Chemical and Biomolecular Engineering, Vol. 5, Issue 1 https://doi.org/10.1146/annurev-chembioeng-060713-040252	journal	June 2014
Microscopic theory of the dynamics of polymeric liquids: General formulation of a mode–mode‐coupling approach Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 91, Issue 9 https://doi.org/10.1063/1.457533	journal	November 1989
Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. I. Activated relaxation, kinetic vitrification, and fragility Yang, Jian; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 134, Issue 20 https://doi.org/10.1063/1.3592563	journal	May 2011
Glass Transition of the Monodisperse Gaussian Core Model Ikeda, Atsushi; Miyazaki, Kunimasa Physical Review Letters, Vol. 106, Issue 1 https://doi.org/10.1103/physrevlett.106.015701	journal	January 2011
Mode‐coupling theory of the dynamics of polymer liquids: Qualitative predictions for flexible chain and ring melts Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 91, Issue 9 https://doi.org/10.1063/1.457534	journal	November 1989
Topological interactions between ring polymers: Implications for chromatin loops Bohn, Manfred; Heermann, Dieter W. The Journal of Chemical Physics, Vol. 132, Issue 4 https://doi.org/10.1063/1.3302812	journal	January 2010
Compressing nearly hard sphere fluids increases glass fragility Berthier, L.; Witten, T. A. EPL (Europhysics Letters), Vol. 86, Issue 1 https://doi.org/10.1209/0295-5075/86/10001	journal	April 2009
Tube theory of entangled polymer dynamics McLeish, T. C. B. Advances in Physics, Vol. 51, Issue 6 https://doi.org/10.1080/00018730210153216	journal	September 2002
Topology, structures, and energy landscapes of human chromosomes Zhang, Bin; Wolynes, Peter G. Proceedings of the National Academy of Sciences, Vol. 112, Issue 19 https://doi.org/10.1073/pnas.1506257112	journal	April 2015
The statistical mechanics of polymerized material Edwards, S. F. Proceedings of the Physical Society, Vol. 92, Issue 1 https://doi.org/10.1088/0370-1328/92/1/303	journal	September 1967
Gaussian field model of fluids with an application to polymeric fluids Chandler, David Physical Review E, Vol. 48, Issue 4 https://doi.org/10.1103/physreve.48.2898	journal	October 1993
Theoretical basis for the Rouse‐Zimm model in polymer solution dynamics Zwanzig, Robert The Journal of Chemical Physics, Vol. 60, Issue 7 https://doi.org/10.1063/1.1681433	journal	April 1974
What price success, multi-level science Daugs, Donald R. Science Education, Vol. 55, Issue 4 https://doi.org/10.1002/sce.3730550416	journal	January 1971
Perspectives on the viscoelasticity and flow behavior of entangled linear and branched polymers Snijkers, F.; Pasquino, R.; Olmsted, P. D. Journal of Physics: Condensed Matter, Vol. 27, Issue 47 https://doi.org/10.1088/0953-8984/27/47/473002	journal	November 2015
Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers: A Review of Recent Bond-Fluctuation Model Studies Wittmer, J. P.; Cavallo, A.; Xu, H. Journal of Statistical Physics, Vol. 145, Issue 4 https://doi.org/10.1007/s10955-011-0354-0	journal	October 2011
Integral equation theory of polymer melts: intramolecular structure, local order, and the correlation hole Schweizer, Kenneth S.; Curro, John G. Macromolecules, Vol. 21, Issue 10 https://doi.org/10.1021/ma00188a027	journal	October 1988
The tube axis and entanglements in polymer melts Likhtman, Alexei E. Soft Matter, Vol. 10, Issue 12 https://doi.org/10.1039/c3sm52575a	journal	January 2014
Modeling the Rheology of Polymer Melts and Solutions Larson, R. G.; Desai, Priyanka S. Annual Review of Fluid Mechanics, Vol. 47, Issue 1 https://doi.org/10.1146/annurev-fluid-010814-014612	journal	January 2015
Glass Transition in Rubbery Materials Roland, C. Michael Rubber Chemistry and Technology, Vol. 85, Issue 3 https://doi.org/10.5254/rct.12.87987	journal	September 2012
The topological glass in ring polymers Lo, Wei-Chang; Turner, Matthew S. EPL (Europhysics Letters), Vol. 102, Issue 5 https://doi.org/10.1209/0295-5075/102/58005	journal	June 2013
Intermolecular structure factors of macromolecules in solution: Integral equation results Fuchs, M.; Müller, M. Physical Review E, Vol. 60, Issue 2 https://doi.org/10.1103/physreve.60.1921	journal	August 1999
Unified Theory of Activated Relaxation in Liquids over 14 Decades in Time Mirigian, Stephen; Schweizer, Kenneth S. The Journal of Physical Chemistry Letters, Vol. 4, Issue 21 https://doi.org/10.1021/jz4018943	journal	October 2013
The theory of polymer solutions at intermediate concentration Edwards, S. F. Proceedings of the Physical Society, Vol. 88, Issue 2 https://doi.org/10.1088/0370-1328/88/2/301	journal	June 1966
Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes Anogiannakis, Stefanos D.; Tzoumanekas, Christos; Theodorou, Doros N. Macromolecules, Vol. 45, Issue 23 https://doi.org/10.1021/ma300912z	journal	November 2012
Effects of chain topology on polymer dynamics: Bulk melts Shaffer, J. Scott The Journal of Chemical Physics, Vol. 101, Issue 5 https://doi.org/10.1063/1.467470	journal	September 1994
Microscopic Definition of Polymer Entanglements Likhtman, Alexei E.; Ponmurugan, M. Macromolecules, Vol. 47, Issue 4 https://doi.org/10.1021/ma4022532	journal	February 2014
Microrheology of Entangled F-Actin Solutions Gardel, M. L.; Valentine, M. T.; Crocker, J. C. Physical Review Letters, Vol. 91, Issue 15 https://doi.org/10.1103/physrevlett.91.158302	journal	October 2003
Structure-Property Correlations of Atomistic and Coarse-Grained Models of Polymer Melts Schweizer, K. S.; David, E. F.; Singh, C. Macromolecules, Vol. 28, Issue 5 https://doi.org/10.1021/ma00109a026	journal	September 1995
Rouse Mode Analysis of Chain Relaxation in Homopolymer Melts Kalathi, Jagannathan T.; Kumar, Sanat K.; Rubinstein, Michael Macromolecules, Vol. 47, Issue 19 https://doi.org/10.1021/ma500900b	journal	September 2014
Single-Chain Slip-Link Model of Entangled Polymers: Simultaneous Description of Neutron Spin−Echo, Rheology, and Diffusion Likhtman, Alexei E. Macromolecules, Vol. 38, Issue 14 https://doi.org/10.1021/ma050399h	journal	July 2005
Neutron Spin Echo in Polymer Systems Richter, Dieter; Monkenbusch, Michael; Arbe, Arantxa https://doi.org/10.1007/b106578	book	January 2005
Excess electrons in simple fluids. I. General equilibrium theory for classical hard sphere solvents Chandler, David; Singh, Yashwant; Richardson, Diane M. The Journal of Chemical Physics, Vol. 81, Issue 4 https://doi.org/10.1063/1.447820	journal	August 1984
Tunable dynamic fragility and elasticity in dense suspensions of many-arm-star polymer colloids Yang, Jian; S. Schweizer, Kenneth EPL (Europhysics Letters), Vol. 90, Issue 6 https://doi.org/10.1209/0295-5075/90/66001	journal	June 2010
Number of entanglement strands per cubed tube diameter, a fundamental aspect of topological universality in polymer viscoelasticity Lin, Y. H. Macromolecules, Vol. 20, Issue 12 https://doi.org/10.1021/ma00178a024	journal	December 1987
The Descent into Glass Formation in Polymer Fluids Freed, Karl F. Accounts of Chemical Research, Vol. 44, Issue 3 https://doi.org/10.1021/ar100122w	journal	March 2011
From a melt of rings to chromosome territories: the role of topological constraints in genome folding Halverson, Jonathan D.; Smrek, Jan; Kremer, Kurt Reports on Progress in Physics, Vol. 77, Issue 2 https://doi.org/10.1088/0034-4885/77/2/022601	journal	January 2014
Entropic barriers, activated hopping, and the glass transition in colloidal suspensions Schweizer, Kenneth S.; Saltzman, Erica J. The Journal of Chemical Physics, Vol. 119, Issue 2 https://doi.org/10.1063/1.1578632	journal	July 2003
A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers Rouse, Prince E. The Journal of Chemical Physics, Vol. 21, Issue 7 https://doi.org/10.1063/1.1699180	journal	July 1953
Polymer-mode-coupling theory of the slow dynamics of entangled macromolecular fluids Schweizer, Kenneth S.; Fuchs, Matthias; Szamel, G. Macromolecular Theory and Simulations, Vol. 6, Issue 6 https://doi.org/10.1002/mats.1997.040060604	journal	November 1997
Mode-coupling theory Reichman, David R.; Charbonneau, Patrick Journal of Statistical Mechanics: Theory and Experiment, Vol. 2005, Issue 05 https://doi.org/10.1088/1742-5468/2005/05/p05013	journal	May 2005
Dynamical Theory of Segmental Relaxation and Emergent Elasticity in Supercooled Polymer Melts Mirigian, Stephen; Schweizer, Kenneth S. Macromolecules, Vol. 48, Issue 6 https://doi.org/10.1021/ma5022083	journal	March 2015
Analytic solutions of the PRISM equations for Gaussian polymers Fuchs, Matthias Zeitschrift für Physik B Condensed Matter, Vol. 103, Issue 3 https://doi.org/10.1007/s002570050406	journal	April 1997
Macromolecular Crowding: Biochemical, Biophysical, and Physiological Consequences Zimmerman, S. B.; Minton, A. P. Annual Review of Biophysics and Biomolecular Structure, Vol. 22, Issue 1 https://doi.org/10.1146/annurev.bb.22.060193.000331	journal	June 1993
Entangled Polymers: Constraint Release, Mean Paths, and Tube Bending Energy Read, D. J.; Jagannathan, K.; Likhtman, A. E. Macromolecules, Vol. 41, Issue 18 https://doi.org/10.1021/ma8009855	journal	September 2008
Entangled polymer chain melts: Orientation and deformation dependent tube confinement and interchain entanglement elasticity Sussman, Daniel M.; Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 139, Issue 23 https://doi.org/10.1063/1.4847895	journal	December 2013
A topologically driven glass in ring polymers Michieletto, Davide; Turner, Matthew S. Proceedings of the National Academy of Sciences, Vol. 113, Issue 19 https://doi.org/10.1073/pnas.1520665113	journal	April 2016
Active Entanglement-Tracking Microrheology Directly Couples Macromolecular Deformations to Nonlinear Microscale Force Response of Entangled Actin Falzone, Tobias T.; Robertson-Anderson, Rae M. ACS Macro Letters, Vol. 4, Issue 11 https://doi.org/10.1021/acsmacrolett.5b00673	journal	October 2015
Long-lived interchain contacts in polymer melts Szamel, Grzegorz; Wang, Tian The Journal of Chemical Physics, Vol. 107, Issue 24 https://doi.org/10.1063/1.474195	journal	December 1997
Dynamics of Polymer Molecules in Dilute Solution: Viscoelasticity, Flow Birefringence and Dielectric Loss Zimm, Bruno H. The Journal of Chemical Physics, Vol. 24, Issue 2 https://doi.org/10.1063/1.1742462	journal	February 1956
Linear Viscoelastic Predictions of a Consistently Unconstrained Brownian Slip-Link Model Nair, Deepa M.; Schieber, Jay D. Macromolecules, Vol. 39, Issue 9 https://doi.org/10.1021/ma0519056	journal	May 2006
Scattering of Slow Neutrons by a Liquid Vineyard, George H. Physical Review, Vol. 110, Issue 5 https://doi.org/10.1103/physrev.110.999	journal	June 1958
Statistical mechanics of chain molecules Flory, Paul. J.; Volkenstein, M. Biopolymers, Vol. 8, Issue 5 https://doi.org/10.1002/bip.1969.360080514	journal	November 1969

Similar Records

Dynamic cross-correlations between entangled biofilaments as they diffuse

Journal Article · Fri Mar 10 00:00:00 EST 2017 · Proceedings of the National Academy of Sciences of the United States of America · OSTI ID:1465948

Tsang, Boyce; Dell, Zachary E.; Jiang, Lingxiang; +2 more

Mass dependence of the activation enthalpy and entropy of unentangled linear alkane chains

Journal Article · Wed Oct 14 00:00:00 EDT 2015 · Journal of Chemical Physics · OSTI ID:1465948

Jeong, Cheol; Douglas, Jack F.

Theory of Nanoparticle Diffusion in Unentangled and Entangled Polymer Melts.

Journal Article · Sat Jan 01 00:00:00 EST 2011 · The Journal of Chemical Physics · OSTI ID:1465948

Yamamoto, U.; Schweizer, Kenneth

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS

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

Citation Formats

References (62)

Similar Records

Related Subjects