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

1. Mesoscopic simulations of entangled polymers, blends, copolymers, and branched structures F. Greco,G. Ianniruberto,and G. Marrucci Naples, ITALY Y. Masubuchi Tokyo, JAPAN

2. Network of entangled polymers Actual chains have slack Primitive chains are shortest path

3. 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)

4. Brownian dynamics of primitive chains along their contour Sliplinks move affinely Sliplinks are renewed at chain ends Each sliplink couples the test chain to a virtual companion

5. 3D sliplink model Simulation box typically contains ca. 2 x 104 chain segments

6. Nodes of the rubberlike network are sliplinks (entanglements) instead of crosslinks Crucial difference: Monomers can slide through the sliplink

7. Primitive Chain Network ModelJ. Chem. Phys. 2001 Dynamic variables: node positions R monomer number in each segment n number of segments in each chain Z + 1D monomer sliding along primitive path 3D motion of nodes

8. Chemical potential Elastic springs Node motion Relative velocity of node Brownian force

9. = rate of change of monomers in i-th segment due to arrival from segment i-1 = local linear density of monomers = sliding velocity of monomers from i-1 to i Monomer sliding

10. Network topological rearrangement End ni monomers at the end if Unhooking (constraint release) else if Hooking (constraint creation) n0: average equilibrium value of n

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

12.  Stress tensor: Non-dimensional equations (units: length = a=bno, time = a2z/6kT =  , energy= kT) n=n/no Relevant parameters: Nondimensional simulation: equilibrium value of <Z> (slightly different from initial value Z0) Comparison with dimensional data: modulus G = kT = RT/Me elementary time 

13. LVE prediction of linear polymer melts

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

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

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

17. G =  kT = RT/Me <Z> = M/Me

18. Polystyrene solution by Inoue et al., Macromolecules 2002 Simulations by Yaoita with the NAPLES code

19. Step strain relaxation modulus G(t,g)

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

21. Primary normal stress coefficient. Shear rates as before.

22. Polystyrene solution fitting parameters: • Vertical shift, G = 210 Pa Horizontal shift, t = 0.55 s <Z> = 18.4 implying Me = 296

23. Blends and block copolymers

24. Phase separation kinetics in blends 2.5 5.0 t=0 10.0 20.0 40.0 <Z> = 10 (td ~ 40), f=0.5, c=4.0

25. BLOCK COPOLYMERS Block ratio = 0.5  = 0.5 <Z> = 40

27. <Z> = 40  = 2 Block ratio 0.1 Block ratio 0.3

28. Branched polymers Backbone-backbone entanglements cannot be renewed two entangled H-molecules Backbone chains have no chain ends

29. A star polymer with q=5 arms Sliplink Branch point End

30. If one of the arms happens to have no entanglements, … Free arm it has the chance to change topology

31. Possible topological changes The free arm has q options, all equally probable (under equilbrium conditions) 1/q 1/q 1/q 1/q 1/q

32. It can penetrate a sliplink of another arm, thus forming a … Double-entanglement

33. If later another arm becomes entanglement-free, …

34. the topological options are … 2/q 1/q 1/q 1/q Enhanced probability for the double entanglement because the coherent pull of the 2 chains makes the branch point closer to double entanglement

35. If the multiple entanglement is “chosen”, … the branch point is “sucked” through the multiple entanglemet

36. The multiple entanglement has now the chance to be “destroyed” by arm fluctuations Similar topological changes would allow backbone-backbone entanglements in H polymers to be renewed

37. H-polymer simulations Click to play

38. 20 10 10 10 10 10 Relaxation modulus for H-polymers without(solid behavior) With the topologicalchange(liquid behavior)

39. Stress auto-correlation

40. Effect on diffusion of 3-arm star polymers

41. Diffusion coefficient For 3-arm stars For H’s having arms with Za= 5

42. 5 10 10 Backbone-backbone entanglement (BBE) cluster The largest BBE cluster for H05 including 58 molecules

43. Size distribution of BBE cluster H05 H10 H20

44. Conclusions • Mesoscopic simulations based on the entangled network of primitive chains describe many different aspects of the slow polymer dynamics • For 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.

45. Conclusion (social) NAPLES New Algorithm for Polymeric Liquids Entangled and Strained http://masubuchi.jp to get the code & docs.