Chen-Yang Liu, Roland Keunings, Christian Bailly UCL, Louvain la Neuve, Belgium

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

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. Gexpl determination Minimum G’ method Ferry (1980)

5. Systems analysed • Low polydispersity model polymers (anionic polymerization) • -Polybutadiene • -Polyisoprene • -Polystyrene Raju VR; Menezes EV; Marin G; Graessley WW; Fetters LJ. Macromolecules1981 1668 Struglinski MJ; Graessley WW. Macromolecules1985 2630 Colby RH; Fetters LJ; Graessley WW. Macromolecules1987 2226 Rubinstein M; Colby RH. J. Chem. Phys.1988 5291 Baumgaertel M; Derosa ME; Machado J; Masse M; Winter HH. Rheol. Acta1992 75 Wang SF; Wang SQ; Halasa A; Hsu WL. Macromolecules 2003 5355 Getro JT; Graessley WW. Macromolecules1984 2767 Santangelo PG; Roland CM. Macromolecules1998 3715 Watanabe et al. Macromolecules2004 1937; and 2000 499 Abdel-Goad M; Pyckhout-Hintzen W; Kahle S; Allgaier J; Richter D; Fetters LJ. Macromolecules2004 8135 Onogi S; Masuda T; Kitagawa K. Macromolecules1970 109 Graessley WW; Roovers J Macromolecules1979 959 Schausberger A; Schindlauer G; Janeschitz-Kriegl H. Rheol. Acta1985 220 Lomellini P. Polymer1992 1255 Liu, He, Keunings, Bailly Polymer (2006)

6. Dependence of Gexpl on Z 2.1 Dependence of GN0 on Ze Reduced Gexp

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

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

9. Zero shear viscosity 0 3.4 Non-permanent entanglements Fluctuations Experimental scaling: MW 0  MW3.4 D  MW-2.3

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

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

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

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. Probe rheology td td/Z3

17. Probe rheology td/Z3 CR parameter: Cv = 1 or 0: with or withoutCR Doi (1981, 1983) Milner and McLeish (1998) Likhtman and McLeish (2002)

18. Probe Rheology vs Tracer Diffusion DM2 Two entangled environments: in Self-melt or in High Mw Matrix Lodge (1999) Wang (2003)

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 oC

22. G’’ - (A.0.71)

23. PBD 1.2M Master Curve Linear-Log Relaxation strength ~ 1/4 GN0

24. Longitudinal Modes Shape of relaxation peak ~ Maxwell

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

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

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

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

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

31. Probe Rheology vs. LM Model without CR Data from: Likhtman and McLeish (2002) Z = 63, 24, 9; Constraint release parameter cv = 0 Vertical shift factor: (1 – matrix2)  GN0 ▪Horizontal shift factors: 5.2  106; 4  106; 2  106 ▪Same horizontal shift factors for ALL: 5.2  106

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

33. CLF for Well-entangled case ▪Excellent agreement with model w/o CR Vertical shift: (1 – matrix2)  GN0 Likhtman and McLeish (2002)