Goal Understand Principles of Rheology stress f deformation

Goal: Understand Principles of Rheology: stress = f (deformation, time) Neo. Hookean: Newtonian: t = h 2 D Key Rheological Phenomena • • shear thinning (thickening) time dependent modulus normal stresses in shear extensional > shear stress G(t) N 1 u >

Outline 1. Definitions 2. Stress relaxation 3. Maxwell element 4. Dynamic moduli 5. Compliance 6. Polymer solutions, gels, and melts

Definitions Stress: t Strain: g Strain rate: (shear) modulus: G = t / g g viscosity: = 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

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

Maxwell Element Go ho G(t) t

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

Maxwell element Limiting slopes: low , G’ ~ 2 , G” ~ high , G’ ~ 0 , G” ~ -1 l

Complex notation Dynamic viscosity:

Maxwell element l

Creep compliance t to Maxwell element: time J Je o General LVE: 1/ Je o time

Outline 1. Definitions 2. Stress relaxation 3. Maxwell element 4. Dynamic moduli 5. Compliance 6. Polymer solutions, gels, and melts

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

G’, G” for a single flexible chain in a solvent Random coil Bead-spring model 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

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 G’ = G”/ “Internal modes” “Terminal” regime Longest relaxation time D. Tan, unpublished results

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

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

The “Gel” Samples Can be Interpreted Simply Worm-like micelles 4 nm Bernheim-Groswasser, A. , Zana, R. , and Talmon, Y. , J. Phys. Chem. B 104, 4005 (2000).

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

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

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

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

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

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

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)

Colloidal Suspension Polystyrene-butylacrylate latices 104 φc 0. 421 0. 426 0. 437 0. 452 0. 455 0. 471 0. 482 0. 502 0. 515 0. 534 103 102 G' (Pa) 101 100 10 -1 10 -2 10 -1 100 101 ω (rad/s) L. Raynaud et al, J. Coll. Int. Sci, 81, 11 (1996)) 102