physical chemistry and colloid science ...1 physical chemistry and colloid science multiple...

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PHYSICAL CHEMISTRY AND COLLOID SCIENCE

MULTIPLE SHEAR-BANDING TRANSITIONS IN SOLUTIONS OF A SUPRAMOLECULAR POLYMER Jasper van der Gucht1Wout Knoben1

Mark Lemmers1

M. Pavlik Lettinga2

N. A. M. (Klaas) Besseling1,3

1 Wageningen University, Physical Chemistry and Colloid Sciencethe Netherlands2 Forschungszentrum Julich, IFF, Weiche MaterieGermany3 After Oct. 1: Delft University, NanoStructured Materials Groupthe Netherlands

EUROMECH 2007


Outline- What are Reversible Supramolecular Polymers?- The experimental system: “EHUT”- Flow curves

- 6 regimes, of which 3 with shear banding- birefringence- transients (stress relaxation after shear-rate increase)- velocity profiles

- Effect of temperature increase vs. “stopper” adition- Conclusions

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What are Reversible Supramolecular Polymers (RSPs)(living polymers, equilibrium polymers, supramolecular polymers,reversible linear aggregates)

Chains of small “bifunctional” units (molecules) linked together by reversible interactions.

Have much in common with ‘ordinary’ polymers, but there are interesting fundamental differences:

- chains are ‘dynamic’ (break/reassemble continuously)

- chain lengths assume equilibrium distribution . . .

- which responds to conditions (e.g.:concentration, presence of surfaces, hydrodynamic forces, . . .)

?


DNA-based stickersFogleman et al,

Angew Chem. 41, 4026, ‘02

N N

O

H H

N O

C13 H27

H

H H

O N

C13 H27H

N

O

NN N

O

H H

N O

C13 H27

H

H H

O N

C13 H27H

N

O

N

n

metal-ion complexation

wormlike micelles formed by certain surfactants

Some examples

(Sijbesma et al, Science, 278: 1601-4,’97)

multiple hydrogen bonding

(Vermonden et al, Macromolecules, 36, 7035-44,’03)

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€

c N( ) =C

N2 exp −

N

N

Chain-length distribution:

€

with N ≈ 2 KC ∝ C expE2kT

N = degree of polymerisationK = association constantE = ‘scission energy’ = 2 x ‘end-cap energy’C = overall monomer concentration

Bifunctional monomers self-assemble into supramolecular chains


dodecane

EHUTNH

NH

O

H5C2

C4H9

NH

NH

O

C4H9

C2H5

Present experimental system

stiff supramolecular chains~ 2 monomers / repeat unit

€

l p > 200 nm

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‘Standard picture’ of shear banding (gradient direction)

schematic constitutive relation- coexistence of bands 1 and 2- and constant - fraction of gap with increases upon increasing- horizontal stress plateau (BE)

€

γ

€

‘metastable’ unstable

€

γ

€

˙ γ

€

˙ γ 1 < ˙ γ < ˙ γ 2

€

˙ γ 2

€

˙ γ 1

€

˙ γ 2


flow curves (controled shear rate)20oC, concentrations: 0.75, 1.4, 2.0, 3.1, 5.9, 6.4 g/l (all > entanglement conc.)

c

c

each curve renormalised by “Maxwellian” plateau modulus and relaxation time

J. van der Gucht e.a., Phys. Rev. Lett, 97 (2006) 108301

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flow curve (example at 5.9 gr/l) 6 regimes: overviewA - linear regimeB - shear banding, stressovershoots, slow transients,metastability,C - no shear banding, stressovershoots, fast transientsD - shear banding, slow oscilatorytransients, birefringent texturesE - shear banding, fastertransients, birefringent texturesF - no shear banding,birefringence

black symbols: stable steady statesopen symbols: metastable points, increasing shear rate


E (3rd s.b.):overshoots, slow irregularrelaxation

F:overshoots,fast relaxation

A (linear regime):exponentialrelaxation

B (1st s.b):‘metastable’states

C:overshoots, fast relaxation

D (2nd s.b.):oscilatorytransients,‘tumbling’(?) E

F

BC

transients

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waarde_11 pwf2−

pwf0

1

pwf1

:=

a

0.02 0.03 0.04 0.05

0

100

200

300

Shear rate (1/s)

Plat

eau

dura

tion

(s)

0

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plat( ˙ γ ) = 0.577 + 6.6 ⋅103exp(−176 ⋅ ˙ γ )

transients (regime B)

- Life-time of metastable stress ‘plateau’ vs. shear rate

- Decrease of stress during life-time of ‘plateau’ is constant

€

Δt ≈ Aexp −B ˙ γ ( )A ≈ 6.6 103 s−1

B ≈176 s−1

€

Δσ ≈ −0.04 Pa( )

1/s

€

˙ γ


birefringence D

D E

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velocity profilesdirect measurement by heterodyne dynamic light scattering / laser Doppler velocimetry(setup at Jülich)

two beams

gapCouette2.5 mm

detector,correlator

typical intensity correlation function frequency of oscilations ~ velocity

lens


velocity profiles

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avarage shear rates in each of the

two bands

fraction of gapoccupied by

high-shear-rate band

‘standard picture’does not apply


Effect of temperature / “stoppers”

(5 g/l EHUT)

reduce viscosity η by- increasing the temperature (filled markers)- adding “stoppers” (open markers)(“stoppers” = monofunctional monomers whichreduce average chain lengthnumber of stoppers determines number of chainends and hence average chain-length)

relaxation times & non-linear rheology:different for cases where η was reduced byeither T-increase or stopper addition

W. Knoben e.a., J. Chem. Phys., 126, (2007) 024907

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Effect of temperature / “stoppers”

- Reduced flow curves are largely the samefor cases where η was reduced to the samevallue by either T-increase or stopperaddition,- But not for the shear-banding regime B

At shear banding regime B: coupling between flow and reversible polymerisation

relaxation time reduced more strongly by temperature increase than by stopper addition


Conclusions

- The RSP “EHUT” exhibits complex non-linear rheology- three shear-banding regimes- with peculiar dependencies upon average shear rate (shear rates within separate bands, position of interface, no stress plateau)

- 1st shear-banding regime (B) probably associated with a mechanicalinstability (no birefringence / alignment of chains)

- 2nd and 3rd shear-banding regimes (D&E) probably associated with‘nematic’ alignment (birefringent textures, oscilatory transients)

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