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Entanglements and stress correlations in coarsegrained molecular dynamics

Entanglements and stress correlations in coarsegrained molecular dynamics. Alexei E. Likhtman , Sathish K. Sukumuran, Jorge Ramirez Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK A.Likhtman@leeds.ac.uk. Hierarchical modelling in polymer dynamics.

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Entanglements and stress correlations in coarsegrained molecular dynamics

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  1. Entanglements and stress correlations in coarsegrained molecular dynamics Alexei E. Likhtman, Sathish K. Sukumuran, Jorge Ramirez Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK A.Likhtman@leeds.ac.uk

  2. Hierarchical modelling in polymer dynamics Traditional rheology Tube Model? Traditional physics CR • Constitutive equations • Tube theories • Single chain models • Coarse-grained many-chains models • Atomistic simulations > Quantum mechanics simulations The weakest link Kremer-Grest MD, Padding-Briels Twentanglemets, NAPLES Well established coarse- graining procedures, force-fields, commercial packages

  3. The missing link Many chains system The ultimate goal: Stochastic equation of motion for the chain in self-consistent entanglement field + self-consistent field One chain model

  4. Is there a tube model? Best definition of the tube model:one-dimensional Rouse chain projected onto three-dimensional random walk tube. • Open questions: • Can I have expression for the tube field, please? • How to “measure” tube in MD? • Is the tube semiflexible? • Diameter = persistence length? • Branch point motion • How does the contour length changes with deformation? • Tube parameters for different polymers? • Tube parameters for different concentrations?

  5. Rubinstein-Panyukov network model Rubinstein and Panyukov, Macromolecules 2002, 6670

  6. Construction of the model

  7. Constraint release Hua and Schieber 1998 Shanbhag, Larson, Takimoto, Doi 2001

  8. A.E.Likhtman, Macromolecules 2005

  9. Relaxation of dilute long chains (36K) in a short matrix: constraint release Mwmat 12k 6k 2k labeled Rouse M.Zamponi et al, PRL 2006

  10. Molecular Dynamics -- Kremer-Grest • Polymers – Bead-FENE spring chains • k = 30/2 • R0=1.5 • With excluded volume – Purely repulsive Lennard-Jones interaction between beads Density,  = 0.85 Friction coefficent,  = 0.5 Time step, dt = 0.012 Temperature, T = /k K.Kremer, G. S. Grest JCP 925057 (1990)

  11. g1(t) from MD for N=100,350 1 0.5 1/4 0.5 d R e

  12. g1(i,t)/t0.5 from MD for N=350 ends g1(i,t)/t0.5 middle t

  13. G(t) from MD for N=50,100,200,350 (Ne~50) e

  14. G(t) from MD for N=50,100,200,350 (Ne~50) G(t) from MD for N=50,100,200,350 (Ne~70) e

  15. g1(i,t) -- MD vs sliplinks mapping 1:1 (N=200) 0 d Lines - MD Points - slip-links 1 1 g1(i,t)/t0.5 e t

  16. G(t) -- MD vs sliplinks mapping 1:1 (N=200) 0 d 1 5 G(t)*t1/2 Lines - MD Points - slip-links e t

  17. Questions for discussion • Binary nature of entanglements? • Can one propose an experiment which contradicts this? • Non-linear flows: • do entanglements appear in the middle of the chain? • Is there an instability in monodisperse linear polymers?

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