1. Chen-Yang Liu, Roland Keunings, Christian Bailly UCL, Louvain la Neuve, Belgium Dynamics of complex fluids: 10 years on, Cambridge, October 2-5 2006 Old New Ideas Questions  …about viscosity, plateau modulus and Rouse chains

2. Objectives - outline Some old and recent results suggest there are still significant inconsistencies/questions about the LVE predictions of tube models Three examples : –Why is Z-dependence of the plateau modulus is less than predicted ? –Is the 3.4 power law fully understood after all ? –Is Rouse really Rouse ?

3. Plateau modulus and zero shear viscosity : questions about constraint release and fluctuations

4. G expl determination Ferry (1980) Minimum G’ method

5. Low polydispersity model polymers ( anionic polymerization) -Polybutadiene -Polyisoprene -Polystyrene Systems analysed Raju VR; Menezes EV; Marin G; Graessley WW; Fetters LJ. Macromolecules 1981 1668 Struglinski MJ; Graessley WW. Macromolecules 1985 2630 Colby RH; Fetters LJ; Graessley WW. Macromolecules 1987 2226 Rubinstein M; Colby RH. J. Chem. Phys. 1988 5291 Baumgaertel M; Derosa ME; Machado J; Masse M; Winter HH. Rheol. Acta 1992 75 Wang SF; Wang SQ; Halasa A; Hsu WL. Macromolecules 2003 5355 Getro JT; Graessley WW. Macromolecules 1984 2767 Santangelo PG; Roland CM. Macromolecules 1998 3715 Watanabe et al. Macromolecules 2004 1937; and 2000 499 Abdel-Goad M; Pyckhout-Hintzen W; Kahle S; Allgaier J; Richter D; Fetters LJ. Macromolecules 2004 8135 Onogi S; Masuda T; Kitagawa K. Macromolecules 1970 109 Graessley WW; Roovers J Macromolecules 1979 959 Schausberger A; Schindlauer G; Janeschitz-Kriegl H. Rheol. Acta 1985 220 Lomellini P. Polymer 1992 1255 Liu, He, Keunings, Bailly Polymer (2006)

6. 2.1 Dependence of G N 0 on Z e Dependence of G expl on Z Reduced G exp

7. LM Theory : Exact CLF treatment + CR Likhtman and McLeish Macromolecules (2002) MW dependence of plateau modulus less than predicted by advanced tube models: Liu et al. Macromolecules (2006) Dependence of G expl on Z Normalized G epxtl

8. 2.2 Comparison experimental data with predictions Excellent accuracy for the terminal relaxation time Significant stress deviations for low Mw samples Relaxation time-modulus contradiction Experimental data vs. predictions of LM theory Inconsistency for the value of 

9. Non-permanent entanglements Fluctuations 3.4  0  MW 3.4 D  MW -2.3 Experimental scaling: 00 MW Zero shear viscosity

10. CLF of Probe chains Unaffected (?) Tube Motion suppressed Separate contributions of tube motion from CLF Idea goes back to Ferry and coworkers (1974-81) Put a small amount of short chains in a very high MW matrix Probe rheology

11. CLF of Probe chains unaffected Tube Motion suppressed Separate contributions of tube motion from CLF Key question : is there a MW dependence of the retardation factor ? Probe rheology

12. CLF of Probe chains unaffected Tube Motion suppressed Separate contributions of tube motion from CLF If yes, there should be a contribution of tube motions to the non reptation scaling of viscosity ! Probe rheology

13. 10% Probe in Matrix

14. Probe Rheology ▪ G’   2 and G’’   ▪ G’ and G’’ cross-point close to G’’ max

15. Retardation Factors as a function of Z

16. dd  d /Z 3 Probe rheology

17. CR parameter: C v = 1 or 0: with or without CR Doi (1981, 1983) Milner and McLeish (1998) Likhtman and McLeish (2002)  d /Z 3 Probe rheology

18. Probe Rheology vs Tracer Diffusion Lodge (1999) Wang (2003) Two entangled environments: in Self-melt or in High Mw Matrix DM 2

19. Rouse region : Longitudinal modes and « is it Rouse ? »

20. PBD 1.2M Master Curve  peak ~ a few multiples of  e

21. PBD 1.2M –80 o C

22. G’’ - (A.  0.71 )

23. Relaxation strength ~ 1/4 G N 0 PBD 1.2M Master Curve Linear-Log

24. Longitudinal Modes Shape of relaxation peak ~ Maxwell

25. Slippage of a polymer chain through entanglement links. Likhtman-McLeish Macromolecules 2002Lin Macromolecules 1984  peak = 3  e LM prediction vs Maxwell Redistribution of monomers along the tube

26. Conclusions - Questions ▪ There seem to be inconsistencies of tube model predictions for time/stress and CR/CLF balance ▪ Probably some of the inconsistencies come from the non- universality of real chains. ▪ Several possible reasons : a chain hits entangled constraint before reaching Rouse behavior local stiffness effects interchain correlations ▪ Moreover: the assumption that fluctuations are unaffected in bimodal blends can be wrong if fluctuations depend on the environment

27. Ferry (1980) Published methods for G expl determination G” Integral method in the terminal region (Kramer-Kronig principle)

28. Raju et al. Macromolecules (1981) If the shape is universal, G app must be proportional to the maximum of the terminal G” peak Maximum G” method Published methods for G expl determination

29. G’’ max vs. Z : data vs. predictions Too strong Z dependence G” max / G expl

30. PBD 99K in 1.2M Matrix ee ▪ Probe in Matrix vs. Probe Self-melt ▪ Probe in Matrix vs. Matrix

31. Probe Rheology vs. LM Model without CR ▪ Same horizontal shift factors for ALL: 5.2  10 6 Vertical shift factor: (1 –  matrix 2 )  G N 0 ▪ Horizontal shift factors: 5.2  10 6 ; 4  10 6 ; 2  10 6 Data from: Likhtman and McLeish (2002) Z = 63, 24, 9; Constraint release parameter c v = 0

32. Graessley (1980) Evaluation of the  d ▪ Narrow G’’ peak ▪ Retardation of the  d Suppression of tube motions Two Key Results for Probe Chain

33. CLF for Well-entangled case ▪ Excellent agreement with model w/o CR Likhtman and McLeish (2002) Vertical shift: (1 –  matrix 2 )  G N 0