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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

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

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

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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?

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

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Construction of the model

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

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A.E.Likhtman, Macromolecules 2005

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

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Molecular Dynamics -- Kremer-Grest Polymers – Bead-FENE spring chains With excluded volume – Purely repulsive Lennard-Jones interaction between beads k = 30 / 2 R 0 =1.5 Density, = 0.85 Friction coefficent, = 0.5 Time step, dt = 0.012 Temperature, T = /k K.Kremer, G. S. Grest JCP 92 5057 (1990)

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g1(t) from MD for N=100,350 1 0.5 1/4 0.5 ee dd RR

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g1(i,t)/t 0.5 from MD for N=350 g1(i,t)/t 0.5 ends middle t

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G(t) from MD for N=50,100,200,350 (Ne~50) ee

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G(t) from MD for N=50,100,200,350 (Ne~70) ee G(t) from MD for N=50,100,200,350 (Ne~50)

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g1(i,t) -- MD vs sliplinks mapping 1:1 (N=200) g1(i,t)/t 0.5 t 11 00 ee dd Lines - MD Points - slip-links Lines - MD Points - slip-links

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G(t) -- MD vs sliplinks mapping 1:1 (N=200) G(t)*t 1/2 t 15 00 ee dd Lines - MD Points - slip-links Lines - MD Points - slip-links

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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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