mesoscopic simulations of entangled polymers, blends, copolymers, and branched structures

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Mesoscopic simulations of entangled polymers, blends, copolymers, and branched structures. F . Greco , G . Ianniruberto , and G . Marrucci Naples, ITALY Y. Masubuchi Tokyo , JAPAN. Network of entangled polymers. Actual chains have slack Primitive chains are shortest path. - PowerPoint PPT Presentation


  • Mesoscopic simulations of entangled polymers, blends, copolymers, and branched structures F. Greco, G. Ianniruberto, and G. Marrucci Naples, ITALY

    Y. MasubuchiTokyo, JAPAN

  • Network of entangled polymersActual chains have slackPrimitive chains are shortest path

  • Microscopic simulations:

    Atomistic molecular dynamics (Theodorou, Mavrantzas, etc.) Coarse-grained molecular dynamics (Kremer, Grest, Everaers et al.; Briels et al.) Lattice Monte Carlo methods (Evans-Edwards, Binder, Shaffer, Larson et al.)

    Mesoscopic simulations:

    Brownian dynamics of primitive chains (Takimoto and Doi, Schieber et al.) Brownian dynamics of the primitive chain network (NAPLES)

  • Brownian dynamics of primitive chains along their contourSliplinks move affinelySliplinks are renewed at chain endsEach sliplink couples the test chain to a virtual companion

  • 3D sliplink modelSimulation box typically contains ca. 2 x 104 chain segments

  • Nodes of the rubberlike network are sliplinks (entanglements) instead of crosslinksCrucial difference: Monomers can slide through the sliplink

  • Primitive Chain Network ModelJ. Chem. Phys. 2001+3D motion of nodes1D monomer sliding along primitive pathDynamic variables: node positions R monomer number in each segment n number of segments in each chain Z

  • Node motionBrownian forceRelative velocity of node

  • Monomer sliding

  • Network topological rearrangementni monomers at the endEndifUnhooking (constraint release)else ifHooking (constraint creation)n0: average equilibrium value of n

  • Chemical potential of chain segment from free energy EThe numerical parameter e was fixed at 0.5, which appears sufficient to avoid unphysical clustering. The average segment density is not a relevant parameter. We adopted a value of 10 chain segments in the volume a3, where a is the entanglement distance.

  • Non-dimensional equations(units: length = a=bno , time = a2z/6kT = , energy= kT)n=n/no Relevant parameters:

    Nondimensional simulation: equilibrium value of (slightly different from initial value Z0)Comparison with dimensional data: modulus G = kT = RT/Me elementary time

  • LVE prediction of linear polymer melts

  • Polybutadiene melt at 313K from Wang et al., Macromolecules 2003

  • Polyisoprene melt at 313K from Matsumiya et al., Macromolecules 2000

  • Polymethylmethacrylate melts at 463K from Fuchs et al., Macromolecules 1996

  • G = kT = RT/Me = M/Me

    PolymersG (MPa)Me (kDa)Me literature Me (s)PS (453K) 0.33111.70.002PB (313K) (313K) 0.633.51.45x10-5PMMA (463K)

  • Polystyrene solution by Inoue et al., Macromolecules 2002

    Simulations by Yaoita with the NAPLES code

  • Step strain relaxation modulus G(t,g)

  • Viscosity growth. Shear rates (s-1) are: 0.0113, 0.049, 0.129, 0.392, 0.97, 4.9

  • Primary normal stress coefficient. Shear rates as before.

  • Polystyrene solution fitting parameters:

    Vertical shift, G = 210 Pa

    Horizontal shift, t = 0.55 s

    = 18.4 implying Me = 296

  • Blends and block copolymers

  • Phase separation kinetics in blendst=02.5 = 10 (td ~ 40), f=0.5, c=

  • Block ratio = 0.5

    = 0.5


  • Block ratio 0.1Block ratio 0.3 = 40 = 2

  • Branched polymers

    Backbone-backbone entanglements cannot be renewedtwo entangled H-moleculesBackbone chains have no chain ends

  • SliplinkBranch pointEndA star polymer with q=5 arms

  • Free armIf one of the arms happens to have no entanglements, it has the chance to change topology

  • Possible topological changes1/q1/q1/q1/q1/qThe free arm has q options, all equally probable (under equilbrium conditions)

  • Double-entanglementIt can penetrate a sliplink of another arm, thus forming a

  • If later another arm becomes entanglement-free,

  • the topological options are Enhanced probability for the double entanglement because the coherent pull of the 2 chains makes the branch point closer to double entanglement2/q1/q1/q1/q

  • If the multiple entanglement is chosen, the branch point is sucked through the multiple entanglemet

  • The multiple entanglement has now the chance to be destroyed by arm fluctuationsSimilar topological changes would allow backbone-backbone entanglements in H polymers to be renewed

  • H-polymer simulationsClick to play

  • Relaxation modulus for H-polymersWith the topological change (liquid behavior)without (solid behavior)

  • Stress auto-correlation

  • Effect on diffusion of 3-arm star polymers

  • Diffusion coefficientFor 3-arm starsFor Hs having arms with Za= 5

    Arm molecular weight, Za




    Topological change







    Diffusion Coefficient

    4.8 e-3

    6.0 e-3

    4.3 e-4

    4.3 e-4

    2 e-6

    2 e-6

    Acceleration Ratio








    Topological change







    Diffusion Coefficient







    Acceleration Ratio




  • Backbone-backbone entanglement (BBE) clusterThe largest BBE cluster for H05 including 58 molecules

  • Size distribution of BBE clusterH05H10H20

  • ConclusionsMesoscopic simulations based on the entangled network of primitive chains describe many different aspects of the slow polymer dynamicsFor linear polymers, quantitative agreement is obtained with 2 (or at most 3) chemistry-and-temperature-dependent fitting parameters.More complex situations are being developed, and appear promising.A word of caution: Recent data by several authors (McKenna, Martinoty, Noirez) on thin films (nano or even micro) show that supramolecular structures can exist. These can hardly be captured by simulations.

  • Conclusion (social) to get the code & docs.NAPLESNew Algorithm for Polymeric Liquids Entangled and Strained

  • Diffusion of H-polymersWith the topological changeConventional (some still diffuse in the network)

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