Goal: Understand Principles of Rheology: stress = f (deformation, time)

1. Goal: Understand Principles of Rheology: stress = f (deformation, time) Key Rheological Phenomena • shear thinning (thickening) • time dependent modulus G(t) • normal stresses in shear N1 • extensional > shear stress hu> h • NeoHookean: Newtonian: t = h2D

2. Outline • Definitions • Stress relaxation • Maxwell element • Dynamic moduli • Compliance • Polymer solutions, gels, and melts

3. Definitions Stress: t Strain: g Strain rate: g (shear) modulus: G = t / g viscosity: h = t / g stress relaxation modulus: G(t,g) = t (t,g) / g linear response: g small enough so that G is independent of g log G t t log t

4. Limiting cases t Hookean g time time t t Newtonian viscoelastic solid viscoelastic liquid time time

5. Maxwell Element Go ho G(t) t

6. Dynamic shear modulus Elastic “storage” modulus, viscous “loss” modulus, loss tangent

7. Maxwell element wl Limiting slopes: low w, G’ ~ w2 , G” ~ w high w, G’ ~ w0 , G” ~ w-1

8. Complex notation Dynamic viscosity:

9. Maxwell element wl

10. Creep compliance t to Maxwell element: time J Jeo Jeo General LVE: 1/h time

11. Outline • Definitions • Stress relaxation • Maxwell element • Dynamic moduli • Compliance • Polymer solutions, gels, and melts

12. Meet the suspects 6 typical materials Dilute Polymer Solution Entangled Polymer (M/S) Surfactant Solution Gel Emulsion Suspension

13. G’, G” for a single flexible chain in a solvent Bead-spring model Random coil P. E. Rouse, Jr. J. Chem. Phys. 21, 1872 (1953) B. H. Zimm, J. Chem. Phys. 24, 269 (1956) www.joogroup.com/graphics/single_poly_cg.jpg

14. G’, G” for a high M chain in an oligomer G” always > G’  = G”/ “Internal modes” “Terminal” regime Longest relaxation time D. Tan, unpublished results

15. G’, G” for a single chain in a theta solvent Sahouani and Lodge, Macromolecules, 25, 5632 (1992)

16. Polyisoprene: an entangled melt New solid-like regime J. C. Haley, Ph. D. Thesis, Univ. Minn., (2005)

17. Worm-like micelles The “Gel” Samples Can be Interpreted Simply 4 nm Bernheim-Groswasser, A., Zana, R., and Talmon, Y., J. Phys. Chem. B104, 4005 (2000).

18. Maxwellian response The “Gel” Samples Can be Interpreted Simply 100 mmol cetyl pyridinium chloride 60 mmol sodium salicylate 100 mmol sodium chloride Candau et al., J. Phys. IV, 3, 197 (1993).

19. Gelation of ABA triblock copolymers Physical gel Gel point G’, G” Liquid  Triblock copolymers C << C* C > C*

20. SOS gel point in an ionic liquid Y. He, P. G. Boswell, P. Bühlmann, T. P. Lodge, J. Phys. Chem. B,111, 4645, (2007)

21. Newtonian droplets in a Newtonian fluid The “Gel” Samples Can be Interpreted Simply 10% low molar mass PIB in low molar mass PDMS I. Vinckier et al., J. Rheol. 40, 613 (1996)

22. Polyisoprene: an entangled melt J. C. Haley, Ph. D. Thesis, Univ. Minn., (2005)

23. Meet the suspects 6 typical materials Dilute Polymer Solution Entangled Polymer (M/S) Surfactant Solution Gel Emulsion Suspension

24. Entangled polymers NIST standard 11 wt% high MW PIB (MW~106, Aldrich) in Pristane LVE properties Data from Snijkers et al, J. Rheology, 53, pp. 459-480 (2009)

25. Colloidal Suspension 10 4 φ c 0.421 10 3 0.426 0.437 0.452 10 2 0.455 0.471 0.482 10 1 0.502 G' (Pa) 0.515 0.534 10 0 10 -1 10 -2 10 -2 10 -1 10 0 10 1 10 2 ω (rad/s) Polystyrene-butylacrylate latices L. Raynaud et al, J. Coll. Int. Sci, 81, 11 (1996))