“Strain Hardening” in Simple Shear of Branched Polystyrene Solutions

Gengxin Liu, Shi-Qing Wang Department of Polymer Science, The University of Akron, Akron, Ohio, USA 44325-3909

February 11, 2013, Monday, 10:50 AM

84th Society of Rheology annual meeting, Pasadena, CA 10

2

103

104

105

106

102

103

104

105

106

107

108

109

1010

10-2

10-1

100

101

102

103

104

+

E

(Pa.s)

+

(Pa.s)

t (s)

shear rates s-1

extension Hencky rates s-1

LCB-PS 4M TCP 7% -15 oC

LCBPS 4M melt 190 oC

0.1 at 25 oC

0.01

0.1

0.30.6

1.52

3

5

1

0.0030.03

0.01

0.1

1

0.3

310

2 Read, D. J.; Auhl, D.; Das, C.; den Doelder, J.; Kapnistos, M.; Vittorias, I.; McLeish, T. C. B., Linking Models of Polymerization and Dynamics to Predict Branched Polymer Structure and Flow. Science 2011, 333 (6051), 1871-1874

Extension – hardening? Shear – softening? Long chain branching

Low rates Extension Shear

Long chain Branched

hardening softening

Linear softening softening

Low Density Polyethylene

Meissner, J., Modifications of the weissenberg rheogoniometer for measurement of transient rheological properties of molten polyethylene under shear. Comparison with tensile data. J. Appl. Polym. Sci. 1972, 16 (11), 2877-2899. Laun, H. M.; Munstedt, H., Elongational behavior of a low-density polyethylene melt .1. strain rate and stress dependence of viscosity and recoverable strain in steady-state - comparison with shear data - influence of interfacial-tension. Rheol. Acta 1978, 17 (4), 415-425.

hardening

softening

3

Extension – hardening? Shear – softening? Pom-Pom Model (Dr. McLeish and Dr. Larson )

Bishko, G.; McLeish, T. C. B.; Harlen, O. G.; Larson, R. G. Phys. Rev. Lett. 1997, 79, 2352.

“Gaussian chain statistics … curvilinear tension of kT/a.”

“The backbone can readily be stretched, until their tension is sufficient to withdraw. “The macroscopic consequence of chain stretch is elongation hardening”

q=3 pom-pom polymer

Malmberg, A.; Gabriel, C.; Steffl, T.; Münstedt, H.; Löfgren, B. Macromolecules 2001, 35, 1038.

Auhl, D.; Chambon, P.; McLeish, T. C. B.; Read, D. J. Phys. Rev. Lett. 2009, 103.

In start-up of shear … backbone stretches temporarily, and eventually collapses as the molecule is aligned, producing strain softening.”

4

s g

t

Extension – hardening, Shear – softening Our Understanding: Yielding

Yield point

"New experiments for improved theoretical description of nonlinear rheology of entangled polymers", S. Q. Wang, Y. wang, S. Cheng, X. Lin，X. Zhu and H. Sun submitted to Macromolecules

gtotal

gmax

grecov

Yield point

5

Extension – hardening, Shear – softening Our Understanding: Geometry

sengr

e

t

Yield point

0

2 104

4 104

6 104

8 104

1 105

0 5 10 15 20lamda

sen

grP

a

HDPE(linear)

LDPE(branch)

irrecoverable Yield point Elastic recoverable

105

106

0.1 1 10

+

E

(Pa.s)

t (s)

+

E /

+

E /

HDPE(linear)

0.3 s-1

180 oC

LDPE(branch)

1 s-1

150 oC

sengr = F/A0= s/

s = F/A(t)=F/A0

Branch: Yields later

Liu, G.; Sun, H.; Rangou, S.; Ntetsikas, K.; Avgeropoulos, A.; Wang, S. Q., Studying the origin of "strain hardening": Basic difference between extension and shear. J. Rheol. 2013, 57 (1), 89-104. Dealy, J. M., DO POLYMERIC LIQUIDS EXHIBIT STRAIN-HARDENING. J. Rheol. 1990, 34 (7), 1133-1147.

6

Extension – hardening, Shear – softening Our Understanding: Geometry, Yielding

Liu, G.; Sun, H.; Rangou, S.; Ntetsikas, K.; Avgeropoulos, A.; Wang, S. Q., Studying the origin of "strain hardening": Basic difference between extension and shear. J. Rheol. 2013, 57 (1), 89-104.

0

2 104

4 104

6 104

8 104

1 105

0 5 10 15 20lamda

sen

grP

a

HDPE(linear)

LDPE(branch)

Yielding of entanglement

Geometrical shrinkage of cross-section area.

Force in shear and extension t

7

Meissner, J., Modifications of the weissenberg rheogoniometer for measurement of transient rheological properties of molten polyethylene under shear. Comparison with tensile data. J. Appl. Polym. Sci. 1972, 16 (11), 2877-2899.

Extension – hardening, Shear – softening

Effect of rates? Low rates Extension Shear

Long chain Branched

hardening softening

Linear softening softening

8

Extension – hardening, Shear – softening

At high rates-Linear Extension High rates Extension Shear

Linear hardening

Wang, Y.; Wang, S.-Q., From elastic deformation to terminal flow of a monodisperse entangled melt in uniaxial extension. J. Rheol. 2008, 52 (6), 1275-1290.

Auhl, D.; Chambon, P.; McLeish, T. C. B.; Read, D. J., Elongational flow of blends of long and short polymers: effective stretch relaxation time. Phys. Rev. Lett. 2009, 103).

9

Meissner, J., Modifications of the weissenberg rheogoniometer for measurement of transient rheological properties of molten polyethylene under shear. Comparison with tensile data. J. Appl. Polym. Sci. 1972, 16 (11), 2877-2899.

Extension – hardening, Shear – softening

At high rates-Linear Shear High rates Extension Shear

Linear hardening Softening

105

106

107

0.4 0.8 1.2 1.6 2 2.4 2.8

Crosslinked SBR 160K

sliding plate shear at rate 1.1 s-1

|*|+

+

, |

*| (

Pa

.s)

t (s), 1/

SUN Hao, W. S.-Q., Shear and extensional rheology of entangled polymer melts: Similarities and differences. SCIENCE CHINA Chemistry 2012, 55 (5), 779-786.

What if slightly crosslinked (1%)?

In shear, chains sliding by each other.

No overshoot, no yielding.

tmax << t, Wi>>1

V

s

elastic irrecoverable

Yield point

0

Meissner, J., Modifications of the weissenberg rheogoniometer for measurement of transient rheological properties of molten polyethylene under shear. Comparison with tensile data. J. Appl. Polym. Sci. 1972, 16 (11), 2877-2899.

Extension – hardening, Shear – softening

High rates-Branches in shear??? High rates Shear

Long chain Branched

Softening Hardening?

Linear softening

11

McLeish, T. C. B.; Allgaier, J.; Bick, D. K.; Bishko, G.; Biswas, P.; Blackwell, R.; Blottière, B.; Clarke, N.; Gibbs, B.; Groves, D. J.; Hakiki, A.; Heenan, R. K.; Johnson, J. M.; Kant, R.; Read, D. J.; Young, R. N. Macromolecules 1999, 32, (20), 6734-6758.

Model branch samples in literatures:

11

Archer, L. A.; Juliani, Linear and Nonlinear Viscoelasticity of Entangled Multiarm (Pom-Pom) Polymer Liquids. Macromolecules 2004, 37 (3), 1076-1088.

Polyisoprene: Arm (21k)2.9-backbone 89k-A2.9

Polybutadiene: Arm (20k)2-backbone 110k-A2

12

Nielsen, J. K.; Rasmussen, H. K.; Denberg, M.; Almdal, K.; Hassager, O., Nonlinear branch-point dynamics of multiarm polystyrene. Macromolecules 2006, 39 (25), 8844-8853.

Model branch samples in literatures:

Polystyrene: Arm (27k)2.5-backbone 140k-A2.5

Grafted Comb PS

Hepperle, J.; Münstedt, H.; Haug, K., Peter ; Eisenbach, D. C., Rheological properties of branched polystyrenes: linear viscoelastic behavior. Rheol. Acta 2005, 45, 151-163. Rheological properties of branched polystyrenes: nonlinear shear and extensional behavior. Rheol. Acta 2005, 45, 717-727.

13

Only shear softening is observed

Outline:

Current information:

• Synthesis Long-chain branching (LCB)

• Different regions of dynamics from SAOS

• Simple shear of LCB polystyrene solutions

-> Strain hardening

-> Non-Gaussian chain stretching

->Extraordinary elastic recovery

• Summary

Liu, G., S. Cheng, H. Lee, H. Ma, H. Xu, T. Chang, R. P. Quirk and S. Q. Wang, "Strain Hardening in Startup Shear of Long-Chain Branched Polymer Solutions," Phys. Rev. Lett. 111, 068302 (2013).

Long chain branched Polystyrenes

Sample Molecular weight Polydispersity index

LCB-PS 1M 1.5* 106 g/mole 2.6

LCB-PS 4M 4.7* 106 g/mole 1.5

Polymer Solvent Volume Fraction

Relaxation time

LCB-PS 1M TCP 11% 0.9s (-15 oC)

LCB-PS 4M TCP 7% 20s (-15 oC)

LCB-PS 4M TCP 14% 40s ( oC)

LCB-PS 4M TCP 21% 1780s (25 oC)

LCB-PS 4M DEP 22% 2000s (25 oC)

TCP

DEP

Fixtures: Anton Paar Physica MCR 301 D=15mm, Cone-Plate 4o

D=25mm, Cone-Plate 2o

Solvents:

15

Shear: LCB-PS 4M in TCP 21 %

Dynamics of long chain branching in different regions

tbackbone tarm

101

102

103

104

105

100

101

102

103

104

105

106

10-1

101

103

105

107

10-4

10-3

10-2

10-1

100

101

102

103

104

De = t

(rad/s)

LCB-PS 4M

(21%-TCP)

t = 1780s

Ref. T= 25 oC

|*| (P

a.s

)

G' ,

G''

(Pa)

0

50000

1 105

1.5 105

2 105

0 1000 2000 3000 4000 5000 6000

Strain(%)

10s-1

6s-1

3s-1

1s-1

0.6s-1

0.3s-1

shear rates at -10 oC

aT to 25

oC= 273

LCB-PS 4M

(21%-TCP)

s

Pa

𝝈 = 𝑮 × 𝜸

102

103

104

105

106

102

103

104

105

106

107

108

109

1010

10-2

10-1

100

101

102

103

104

+

E

(Pa.s)

+

(Pa.s)

t (s)

shear rates s-1

extension Hencky rates s-1

LCB-PS 4M TCP 7% -15 oC

LCBPS 4M melt 190 oC

0.1 at 25 oC

0.01

0.1

0.30.6

1.52

3

5

1

0.0030.03

0.01

0.1

1

0.3

310

Shear: LCB-PS 4M in TCP 7wt %

Shear: LCB-PS 1M in TCP 11 %

102

103

104

0.1 1 10 100 1,000

Startup simple shear

30 s-1

20 s-1

10 s-1

7 s-1

1 s-1

3 s-1

LCB-PS 1M in TCP 11 %

t (s)

+ (

Pa.

s)

T = -15oC

|*|

Transient viscosity higher than the envelope:

“hardening”

17

5 103

1 104

1.5 104

2 104

2.5 104

3 104

3.5 104

4 104

0 20 40 60 80 100 120Strain (1)

5

3

21.5

1

0.6

LCB-PS 4M TCP

7% -15 oC

s

Pa

shear rates: s-1

neo Hookean: s=G*g

Shear hardening: Non-Gaussian stretching

18

Strain recovery

Straighten an entanglement strand of Me g*≈lent/(b(C+1))=lent/lKuhn=4 Yielding of linear Chain Straighten between two branch point of 22.7Me

g* ≈ √22.7 ×lent/lKuhn = 20 Straighten between two end of 152Me

g* ≈ = √152 ×lent/lKuhn= 50

s g

t

gtotal grecov

19

0

1000

2000

3000

4000

5000

6000

0 5000 10000 15000 20000 25000 30000

reco

ver

Str

ain

(%)

Strain(%)

100%

recovery

line

-15 oC rate 3 s

-1

LCB2PS-TCP 7%

0 oC rate 1 s

-1

Strain recovery

Straighten an entanglement strand of Me g*≈lent/(b(C+1))=lent/lKuhn=4 Yielding of linear Chain Straighten between two branch point of 22.7Me

g* ≈ √22.7 ×lent/lKuhn = 20 Straighten between two end of 152Me

g* ≈ = √152 ×lent/lKuhn= 50

20

Summary, long chain branching (LCB) can:

1. Disentanglement (sliding from chain end) is easy; 2. Unless at high rates in extension;

Linear chains

Chains with long branching

LCB will not easily retracts/ pull out: 1. Non-Gaussian stretching,

strain hardening in shear; 2. Breakdown is delayed; postpones stress overshoot huge strain recovery in shear; strain hardening in extension;

Thank you for your time This work is supported by NSF DMR-1105135

High rates Extension Shear

Long chain Branched

hardening hardening

Linear hardening softening

Low rates Extension Shear

Long chain Branched

hardening softening

Linear softening softening

102

103

104

105

106

102

103

104

105

106

107

108

109

1010

10-2

10-1

100

101

102

103

104

+

E

(Pa.s)

+

(Pa.s)

t (s)

shear rates s-1

extension Hencky rates s-1

LCB-PS 4M TCP 7% -15 oC

LCBPS 4M melt 190 oC

0.1 at 25 oC

0.01

0.1

0.30.6

1.52

3

5

1

0.0030.03

0.01

0.1

1

0.3

310

22