Goal: Understand Principles of Rheology: stress = f (deformation, time) NeoHookean: Newtonian: shear...
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Transcript of Goal: Understand Principles of Rheology: stress = f (deformation, time) NeoHookean: Newtonian: shear...
![Page 1: Goal: Understand Principles of Rheology: stress = f (deformation, time) NeoHookean: Newtonian: shear thinning (thickening) time dependent modulus G(t)](https://reader035.fdocuments.us/reader035/viewer/2022062321/56649e0b5503460f94af2fb0/html5/thumbnails/1.jpg)
Goal: Understand Principles of Rheology:
stress = f (deformation, time) NeoHookean: Newtonian:
• shear thinning (thickening) • time dependent modulus G(t)
• normal stresses in shear N1
• extensional > shear stress u>
Key Rheological Phenomena
Gτ B - I = 2D
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Outline
1. Definitions
2. Stress relaxation
3. Maxwell element
4. Dynamic moduli
5. Compliance
6. Polymer solutions, gels, and melts
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Definitions
t log t
log G
Stress: Strain: Strain rate:
(shear) modulus: G = / viscosity: = /
stress relaxation modulus: G(t,) = (t,) /
linear response: small enough so that G is independent of
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Limiting cases
time
time
Hookean
time
Newtonian
time
viscoelastic solid
viscoelastic liquid
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Maxwell Element
o el vis
Ý o 0 Ý el Ý vis
0 1
GoÝ
1
o
(t) (0) exp( t /)
(0) Go o
o / Go
Go o
G(t)
t
![Page 6: Goal: Understand Principles of Rheology: stress = f (deformation, time) NeoHookean: Newtonian: shear thinning (thickening) time dependent modulus G(t)](https://reader035.fdocuments.us/reader035/viewer/2022062321/56649e0b5503460f94af2fb0/html5/thumbnails/6.jpg)
Dynamic shear modulus
o sint Ý o cost
o sin(t )
o ' sint o"cost
G' o '
o, G"
o"
o, tan
G"
G'
Elastic “storage” modulus, viscous “loss” modulus, loss tangent
'
"
time
.
![Page 7: Goal: Understand Principles of Rheology: stress = f (deformation, time) NeoHookean: Newtonian: shear thinning (thickening) time dependent modulus G(t)](https://reader035.fdocuments.us/reader035/viewer/2022062321/56649e0b5503460f94af2fb0/html5/thumbnails/7.jpg)
Maxwell element
G' Go22
122 ; G" Go
122
Limiting slopes:
low , G’ ~ 2 , G” ~
high , G’ ~ 0 , G” ~
10-4
10-3
10-2
10-1
100
101
10-3 10-2 10-1 100 101 102
G'/Go
G"/Go
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Complex notation
G*() *
* G' i G"
*() *
Ý * ' i "
G* i*; G' "; G" '
Dynamic viscosity:
* 2 2 1/2( ' " ) /G G
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Maxwell element
10-4
10-3
10-2
10-1
100
101
10-3 10-2 10-1 100 101 102
G'/Go
G"/Go
10-4
10-3
10-2
10-1
100
101
10-3 10-2 10-1 100 101 102
'/ Go
''/ Go
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Creep compliance
J(t) (t)
o
(t) el vis o
Go
1
odt
J(t) 1
Go1 t
Maxwell element:
J(t) J eo
t
General LVE:
time
o
time
J
1/
Jeo
Jeo
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Outline
1. Definitions
2. Stress relaxation
3. Maxwell element
4. Dynamic moduli
5. Compliance
6. Polymer solutions, gels, and melts
![Page 12: Goal: Understand Principles of Rheology: stress = f (deformation, time) NeoHookean: Newtonian: shear thinning (thickening) time dependent modulus G(t)](https://reader035.fdocuments.us/reader035/viewer/2022062321/56649e0b5503460f94af2fb0/html5/thumbnails/12.jpg)
Meet the suspects6 typical materials
Surfactant Solution
Dilute Polymer Solution
Entangled Polymer (M/S)
EmulsionSuspension
Gel
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G’, G” for a single flexible chain in a solvent
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
Random coil Bead-spring model
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G’, G” for a high M chain in an oligomer
10-1100101102103104105106100101102103104105106G', G" (Pa) aTPS-650,0003.1% in PS-3,000Tref = 180 ºC
10-1
100
101
102
103
104
105
106
100 101 102 103 104 105 106
G',
G"
(Pa
)
aT
PS-650,000
3.1% in PS-3,000
Tref
= 180 ºC
= G”/
“Internal modes”
Longest relaxation time“Terminal” regime
G” always > G’
D. Tan, unpublished results
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G’, G” for a single chain in a theta solvent
Sahouani and Lodge, Macromolecules, 25, 5632 (1992)
10-9
10-8
10-7
10-6
10-5
10-4
10-2 10-1 100 101 102 103
[G'] R
, [G
"]R
1
Polybutadiene in DOP
T = 18.0 oC ()
Zimm theory(Dynamic scaling, = 0.50
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Polyisoprene: an entangled melt
101
102
103
104
105
106
107
10-2 100 102 104 106
G' a
nd G
" ,
Pa
aT
Polyisoprene
Mw
= 80,000
Tr = 20
oC
G'
G"
J. C. Haley, Ph. D. Thesis, Univ. Minn., (2005)
New solid-like regime
QuickTime™ and a decompressor
are needed to see this picture.
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The “Gel” Samples Can be Interpreted Simply
Worm-like micelles
Bernheim-Groswasser, A., Zana, R., and Talmon, Y., J. Phys. Chem. B 104, 4005 (2000).
4 nm
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The “Gel” Samples Can be Interpreted Simply
Maxwellian response
100 mmol cetyl pyridinium chloride60 mmol sodium salicylate 100 mmol sodium chloride
QuickTime™ and a decompressor
are needed to see this picture.
Candau et al., J. Phys. IV, 3, 197 (1993).
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Gelation of ABA triblock copolymers
G’, G”
Liquid
Physical gel
Gel point
C > C*
Triblock copolymers
C << C*
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SOS gel point in an ionic liquid
0.001
0.01
0.1
1
10
100
1000
G',
G"
(Pa
)
0.01 0.1 1 10 100
(rad/s)
G' G''10 wt% 4 wt% 1 wt%
G' ~ 2
G'' ~
G'=G'' ~
G' ~
A
O
Y. He, P. G. Boswell, P. Bühlmann, T. P. Lodge, J. Phys. Chem. B, 111, 4645, (2007)
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The “Gel” Samples Can be Interpreted Simply
Newtonian droplets in a Newtonian fluid
I. Vinckier et al., J. Rheol. 40, 613 (1996)
10% low molar mass PIB in low molar mass PDMS
![Page 22: Goal: Understand Principles of Rheology: stress = f (deformation, time) NeoHookean: Newtonian: shear thinning (thickening) time dependent modulus G(t)](https://reader035.fdocuments.us/reader035/viewer/2022062321/56649e0b5503460f94af2fb0/html5/thumbnails/22.jpg)
Polyisoprene: an entangled melt
101
102
103
104
105
106
107
10-2 100 102 104 106
G' a
nd G
" ,
Pa
aT
Polyisoprene
Mw
= 80,000
Tr = 20
oC
G'
G"
J. C. Haley, Ph. D. Thesis, Univ. Minn., (2005)
![Page 23: Goal: Understand Principles of Rheology: stress = f (deformation, time) NeoHookean: Newtonian: shear thinning (thickening) time dependent modulus G(t)](https://reader035.fdocuments.us/reader035/viewer/2022062321/56649e0b5503460f94af2fb0/html5/thumbnails/23.jpg)
Meet the suspects6 typical materials
Surfactant Solution
Dilute Polymer Solution
Entangled Polymer (M/S)
EmulsionSuspension
Gel
![Page 24: Goal: Understand Principles of Rheology: stress = f (deformation, time) NeoHookean: Newtonian: shear thinning (thickening) time dependent modulus G(t)](https://reader035.fdocuments.us/reader035/viewer/2022062321/56649e0b5503460f94af2fb0/html5/thumbnails/24.jpg)
NIST standard
11 wt% high MW PIB (MW~106, Aldrich) in Pristane
LVE properties
Entangled polymers
Data from Snijkers et al, J. Rheology, 53, pp. 459-480 (2009)
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L. Raynaud et al, J. Coll. Int. Sci, 81, 11 (1996))
Colloidal Suspension
(rad/s)
10-2 10-1 100 101 102
G' (P
a)
10-2
10-1
100
101
102
103
104
0.4210.4260.4370.4520.4550.4710.4820.5020.5150.534
φc
Polystyrene-butylacrylate latices