Effect of Shear Flow on Polymer Demixing- the unanswered questions

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Effect of Shear Flow on Polymer Demixing- the
unanswered questions

• H. GERARD, J. T. CABRAL, J. S. HIGGINS
• Department of Chemical Engineering
• Imperial College, London

2
Polymer miscibility
Thermodynamics
Flory-Huggins lattice theory
Combinatorial entropy
Enthalpy
1
3
Phase separation
2
4
Spinodal decomposition
3
5
Cahn-Hilliard
Cahn-Hilliard linearised theory
equation of motion concentration fluctuations
M diffusional mobility f(D1,D2)
-Dapp
4
6
Scattering
solid angle d?
photodiode array
? S(Q,w)
Heating block
Structure factor
He-Ne 5mW laser
?m characteristic length of phase separation
1?m (LS)
LS schematic
7
7
Light scattering
TMPC/PS 5050
Tjump240.6oC
30
I (au)
-1
q0.00124 A
LS
25
deep
quench
20
2000
15
Intensity (au)
1000
10
shallow
quench
5
time (s)
0
0
0
300
600
900
1200
1500
Time (s)
q (nm-1)
8
8
350
0.03
TMPC/PSd 7030 MM
180 s
o
300
254
C
TMPC/PSd 7030 MM
250
o
254
C
0.02
R (s-1)
200
Intensity (cm)-1
150
Q
0.01
M
100
x 15 s
Q
C
50
0
0.00
0.002
0.004
0.006
0.008
0.010
0.000
0.004
0.008
0.012
0.016
-1
Q (A
)
-1
Q (A
)
Light scattering
8
TMPC/PS
d
7030
e
4
-3
-1
Q4.9x10
A
258
o
C
6
e
3
Intensity (au)
-1
LS

Q
0.00152 A
4
Intensity
e
2
TMPC/PSd 7030
2
o
T252
C
e
1
0
11
0
200
400
600
0
100
200
300
Time (s)
Time (s)
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• In 1996 we had observed apparent SID at
  temperatures well below the quiescent LCST for a
  number of amorphous blends.
• Shifts in LCST ranged from 40K to less than 5K
  and seemed to correlate with differences in the
  component rheological behaviour.
• We had not followed the kinetics of SID, and
  there was no theoretical development to describe
  such kinetics
• We believed that observing the kinetics might
  answer the question of SID (ie a true
  thermodynamic phase separation) v enhanced
  concentration fluctuations

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Theoretical Approaches

• Wolf
• Add a stored energy term to the Gibbs free
  energy
• with
• ? May dramatically influence
• ?2DGm/ ?2f
• ? Good qualitative description of the shear
  behaviour of PS/PVME, SMA/PMMA and SAN/PMMA
  blends.
• But
• no description of the anisotropy
• equilibrium thermodynamics applied to such a
  case?

• Clarke McLeish
• They use, following Doi and Onuki, the two-fluid
  model considering the visco-elastic behaviour of
  both components.
• ? For low shear rates, in the y,z plane
• ????? ???
• quiescent part shear part
• where a((zA/fA)-(zB/fB))/(zA zB),
• zi being the frictional drag per monomeric
  volume associated with component i, related to
  the monomeric friction coefficient per volume by
• zi fi (Ni/Nei) z0i

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Shear Light Scattering Experiments

• 1D LS Shear Experiments
• samples sheared in plate-plate geometry, the
  scattered light (He-Ne Laser, l632.8 nm,
  incident beam // to the velocity gradient
  direction) being collected along the vorticity
  direction
• For blends 1 and 2 (critical composition) and for
  a shear rate , scattered intensity
  increases with time after a delay time td

Diode array
Velocity Gradient
Characteristics of the three 30/70 w/w PS/PVME
blends studied
Vorticity

• early stage R(q)

I(q)I(q,td)exp(2R(q)(t- td))
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LS Results and Theoretical Predictions

• Clarke and McLeish
• ?
• ???
• extracted from shear LS experiments
• Decent fit for low shear rates

May also be obtained from remixing quiescent LS
experiments
Dapp0
? Influence of molecular deformation on
blends thermodynamics? ? Estimation of shear
rate? ? Did we miss the early stage?
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• Small Angle Neutron Scattering the aim is to
  look at much smaller size scale and catch the
  early stages
• One component is deuterated to give contrast -
  this may shift the LCST.
• We had no shear cell for SANS and had to use
  quenched samples.
• The neutron beam is much larger than the laser
  beam so we were averaging over a range of shear
  rates

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shear-quenched SANS
(highest shear rate)
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Conclusions

• Our first SANS results seem to partially confirm
  what was first observed through light scattering
  in similar (from a rheological point of view)
  protonated blends.
• ?For low q the rise of S(q) for high shear
  rates may be due to an enhancement of
  concentration fluctuations in accordance with our
  LS results
• ?For high q higher shear rates seem to reduce
  concentration fluctuations, a feature not
  explained by two-fluid models inspired approaches
  such as Clarke McLeishs one.

Might explain the discrepancy between the
apparent diffusion coefficients obtained from
quiescent experiment and deduced from
Due to the effect of molecular deformation on the
thermodynamics of the system?
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The Unanswered Questions

• Is the D from SID really different from the D
  obtained in re-mixing experiments?-experiments
  first and if confirmed theory needs some thought.
• Would a more sophisticated statistical mechanics
  description of the free energy help? We have
  been having considerable success in quiescent
  systems using a version of BGY which includes
  compressibility and non-random mixing.
• What happens in the early stages of SID? can we
  find a system where deuteration does not have
  such a large effect on LCST? or can we use
  another technique, eg AFM on quenched samples?
• All these Qs aimed at the big one is this SID
  or just enhanced concentration fluctuations?

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Lattice Born-Green-Yvon (BGY) theory links the
microscopic character of a polymer/blend to its
thermodynamic properties
Parameters which characterize the pure fluid
eii ri
v
volume per mole of lattice sites
strength of nearest-neighbour
interaction
number of contiguous lattice sites per molecule
and the mixture
g eij/(eii ejj)1/2
characterizes the deviation from the
geometric mean approximation
Macromolecules 36, 2977 (2003)
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A few remarks about the theory
Formal definition of p(i,j), pair distribution
function
approximations
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gexp e12,exp/(e11 e22)1/2
When (gexp-1) is negative/positive the geometric
mean is over/underestimating
the strength of the 1-2 interaction
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Ornstein Zernicke Formulae
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Blend Rheology

• Rheological Experiments
• The Clarke McLeish approach has been developed
  for the weak shear regime ( t lt 1 where t is the
  longest relaxation time of the blend). It also
  assumes that both components present different
  relaxation times in the blend.
• Rheological experiments were performed on a Paar
  Physica UDS 200 Rheometer to check both
  assumptions

Relaxation time and for blend 1
Critical time -1
? weak shear regime if we assume that t
corresponds to the intercept of G and G. ? in
our frequency range, only one relaxation time may
be detected in the blend.
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Concentration Fluctuations in Polymer Blends
Concentration fluctuations enhancement (for the
early stage inside the spinodal line) and decays
(for the late stage in the one phase region)
may be described Cahn-Hilliard theory, giving an
expression for their growth rate R(q) with
the apparent diffusion coefficient
? Effect of shear flow shear (dispersed phase)
droplet break-up (Taylor) influence on
thermodynamics (Wolf) stress/concentration
fluctuations coupling (Doi, Onuki)
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Small Angle Neutron Scattering
Beam centre shear rate
These features are not described by the available
theoretical models
Structure Factor S(q) for blend 3 sheared at
T86.6ºC then quenched in liquid N2

• Ornstein-Zernike at high q

S(0)-1 ? ? (
from 100 to 300 Å )
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Enhancement of Concentration Fluctuations in the
(x,z) Plane
a)
100 mm
b)
0
5
10
q (mm-1)
10 mm
Optical micrograph of the bulk of a quenched
sample after 25 min. shear at DT -17.2 K and
1.4 s-1 for two different magnifications.
2D LS patterns for blend 1 at T84.6ºC a)
before shear and b) after 26.5 min. of
shearing with 5 s-1
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Small Angle Neutron Scattering

• Blend 3 deuterated PS/PVME blend sheared at T
  86.6ºC ( DT - 54 K)
• Two samples with ? maximal (2.1 and 5.2 s-1)
  but similar maximal strain ( g ? 450)
• ? Rheological steady state is reached with no
  change in LS patterns
• The shearing is then stopped and the sample
  quenched in liquid N2
• SANS (on D22 under cryostat at the ILL,
  Grenoble)
• ? No obvious anisotropy in our q range (7. 10-3
  to 1.1 10-1 Å-1)
• ? High q (gt 4 10-2 Å-1) S(q) ? with
• ? reduction of small wavelength
  concentration
• fluctuations with shear
• S(0)-1 obtained from high q fits is increasing
  with ? Shear Induced Mixing
• ? Low q (lt 4 10-2 Å-1) S(q) ? then ? with
• intermediate scale structure growing (as seen in
  PS/DOP)? ? Shear Induced Demixing?
• But similar low q high scattering for unsheared
  blend!
• Effect of quench?

But we are scanning ? local flow directions
incident beam