Nigel Clarke Department of Chemistry Durham University Effect of Shear Flow on PolymerPolymer Miscib

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Nigel ClarkeDepartment of ChemistryDurham
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

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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?

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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 gtgt hgreen
regions of high stress
regions of low stress
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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
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Equation of motion
Doi and Onuki J. Phys. II, 1990, vol. 2, 1631

• Coupling between
• concentration fluctuations
• Stress fluctuations

• stress
• gradients

convection
thermodynamics
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Concentrations fluctuations and the diffusion
coefficient

• One phase region
• fluctuations decay D gt 0
• Two phase region
• fluctuations grow D lt 0
• Phase boundary
• defined by D (q ? 0) 0

D
ve
0
c
cs
-ve
Increasingly unfavourable interactions
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Linear stability analysis

• Neglect the dynamics of stress evolution
• Deff lt 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

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Fluctuations Polymer Solutions A. Onuki, S.T.
Milner
Fluctuations in the z direction are
suppressed ? shear induced mixing
Fluctuations in the y direction are
enhanced ? shear induced de-mixing
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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

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Fluctuations Blends
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
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Temperature effects closed-loops

• 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
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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

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

• In polymer blends
• 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

?