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

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?

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

regions of high stress

regions of low stress

blue >> green

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 …

2 1 2 2

1

4 (1 )( ) A Bxy A A A A A A B B B B

A B

G G G G

N

relaxation times in fixed tubes

convection

Equation of motion

Coupling between

• concentration fluctuations

• Stress fluctuations

AA A BM

t

v σ

thermodynamics

stressgradients

Doi and Onuki J. Phys. II, 1990, vol. 2, 1631

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

s

D

0

+ve

-ve

Increasingly unfavourable interactions

0( ) ( ) exp A At t Dt

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

0 eff( ) ( ) exp A At t D t

Deff depends on• intrinsic dynamics• thermodynamics • stress variation

with composition

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

direction of shear

x

yz

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 2

– opposes fluctuations in z direction

– in y direction shear rate variations dominate and favour fluctuations

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

direction of shear

x

yz

Temperature effects: closed-loops

• Generally A/B has a complex dependence on temperature– due to glass transition

temperature differences between components T

em

per

atu

re

No shear

5s-1

EVA

polyethylene-co-vinyl acetate / solution chlorinated

polyethylene

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

Arbitrary stress relaxation function for blend

Prediction of steady state scattering

Blend rheology data

Improved theory

Predictive tools for phase transitions and microstructure evolution

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

?