1. Nigel Clarke Department of Chemistry Durham University Effect of Shear Flow on Polymer-Polymer Miscibility: Theoretical Advances and Challenges
With thanks to: Gavin Buxton, Hervé Gerard,
Julia Higgins, Tom McLeish, Dmitri Miroshnychenko

2. Overview Does flow increase or decrease stability in polymer blends?
Coupling phase separation dynamics and stress relaxation in entangled blends
Scattering – a quantitative test of theory
can we describe concentration fluctuations under shear?

3. Towards a Theoretical Description
Fluctuations in concentration
fluctuation in stress if viscosities are different
Thermodynamic
shear stresses and normal forces directly affect free energy
Dynamic
stresses affect dynamics of concentration fluctuations
hblue >> hgreen
regions of high stress
regions of low stress

4. Stress relaxation in polymer blends
Constraint release
stress relaxed more rapidly if surrounded by short polymers
dynamics depends on concentration
well defined concentration dependence of stresses …
relaxation times in fixed tubes

5. Doi and Onuki J. Phys. II, 1990, vol. 2, 1631
Equation of motion
Doi and Onuki J. Phys. II, 1990, vol. 2, 1631
Coupling between
concentration fluctuations
Stress fluctuations
stress
gradients
convection
thermodynamics

6. Concentrations fluctuations and the diffusion coefficient
One phase region
fluctuations decay: D > 0
Two phase region
fluctuations grow: D < 0
Phase boundary
defined by: D (q  0) = 0 D
+ve cs c
-ve
Increasingly unfavourable interactions

7. Linear stability analysis
Neglect the dynamics of stress evolution
Deff < 0  growth of fluctuations
Define stability by Deff = 0
stability only affected for non-zero Normal forces
Deff depends on
intrinsic dynamics
thermodynamics
stress variation with composition

8. Fluctuations: Polymer Solutions A. Onuki, S.T. Milner
direction of shear x y z
Fluctuations in the z direction are suppressed 
shear induced mixing
Fluctuations in the y direction are enhanced 
shear induced de-mixing

9. Why strong directional dependence?
Stress balance
flow gradient direction
shear stress constant
shear rate must vary with composition
vorticity direction
shear stress can vary
shear rate constant
N1 increases as f2
opposes fluctuations in z direction
in y direction shear rate variations dominate and favour fluctuations

10. Fluctuations: Blends direction of shear x y z
Fluctuations in the z direction are suppressed or enhanced 
shear induced mixing or demixing
Fluctuations in the y direction are enhanced or suppressed 
shear induced de-mixing or mixing

11. Temperature effects: closed-loops
No shear
Generally tA/tB has a complex dependence on temperature
due to glass transition temperature differences between components
Temperature
5s-1
polyethylene-co-vinyl acetate / solution chlorinated polyethylene

12. Beyond stability analysis
Scattering as a more demanding test of theory
scattering patterns can be measured in a steady state
Significant advances in our understanding of the dynamics of miscible polymer blends in the past 10 years
near quantitative constitutive equations that include concentration dependence of friction coefficients

13. Arbitrary stress relaxation function for blend
Blend rheology data
Arbitrary stress relaxation function for blend
Prediction of steady state scattering
Improved theory
Predictive tools for phase transitions and microstructure evolution

14. Summary In polymer blends Scattering patterns
possible to induce mixing or de-mixing in both the shear gradient and the vorticity directions
quantitative description elusive
Scattering patterns
Polymer solutions
e.g., qualitative agreement with experimental results (Hashimoto et al) for oscillatory shear
Miscible polymer blends with viscosity difference
a quantitative test of stress gradient contributions to stability ?