Nigel Clarke Department of Chemistry Durham University Effect of Shear Flow on Polymer-Polymer Miscibility: Theoretical Advances and Challenges With.

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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

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 hblue >> hgreen regions of high stress regions of low stress

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

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

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

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

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

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

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

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

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

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 ?