Length scale dependent aging and plasticity of a colloidal polycrystal under oscillatory shear

1. Length scale dependent aging and plasticity of a colloidal polycrystal under oscillatory shear Elisa Tamborini Laurence Ramos Luca Cipelletti Laboratoire Charles Coulomb CNRS-Université Montpellier 2 Montpellier, France

2. Motivation MECHANICAL PROPERTIES OF ATOMIC POLYCRYSTALS • 2 competitingprocesses to control deformation • Grain-boundary(GB) sliding • Dislocation slip J. Weiss, LGGE/CNRS DISLOCATION GB [Richeton Nature Materials2005] Numerical simulations Extremely small grains Unrealistically high strains Experiments on metals [Kumar Acta Mater. 2003] Difficulty of preparing samples with small grains Difficulty of measurements

3. Motivation OUR OBJECTIVES • Use colloidalcrystals as analog of atomiccrystalsto get time- and • space-resolveddata on the behavior of the materialsundermechanical stress • InvestigatePOLYCRYSTALLINE samples, whereasmostpreviousexperiments • were on «monocrystals» Polycrystals = a disordered network of grain-boundaries

4. Experimentalsample 10 mm 3D NETWORK OF Grain Boundaries Block-copolymer micellarcrystal (fcc, lattice parameter ~ 30 nm) +nanoparticles(~ 1% or less, diameter 35 nm) = ~ 30 nm fcclattice temperature • NPsconfined in the grain-boundaries • analogywithimpurities in atomic & molecularsystems • [Lee Metall. Mater. Trans. A2000] [Losert PNAS 1998]

5. Home-made shear cell fixed slide moving slide motor laser spring 25 mm

6. Observation by confocal microscopy PROTOCOL (analogy to fatigue test in material science) g = 3.6 % g=0 t = 1 t = 2 t = 3 t ~ 5000 cycles t = 1 t = 2617 Overlay of 2 images taken at Deformation of the crystalline grains 50 µm

7. Experimentalset-up Shear-cell coupled to Mid-Angle Light Scattering set-up 10 µm DLS under shear strain  GBs dynamics q1 = 0.12 µm-1-q10 = 3.72 µm-1 Tamboriniet al., Langmuir 2012

8. Data analysis INTENSITY CORRELATION & CHARACTERISTIC LENGTH SCALES g=0 q// t = i t = i+1 t = i+2 t t=1 t=2 t time tdelay between shear cycle g2(t,t)-1=

9. Elasticity vs Plasticity ELASTIC SAMPLE (PDMS)

10. Elasticity vs Plasticity ELASTIC SAMPLE (PDMS) PLASTIC SAMPLE (POLYCRYSTAL) tr

11. Visco-elasticty CHOICE OF THE STRAIN AMPLITUDES Elastic Plastic Viscous g = 1.6 % g = 2.5 % g = 3.5 % g = 4.6 % g = 5.2 %

12. Relaxation time vs # of shear cycles AGING law g = 4.6 %

13. Relaxation time vs # of shear cycles AGING laws q g = 4.6 %

14. Scaling g = 4.6 %

15. Scaling

16. Steady state STEADY STATE RELAXATION TIME 2 p /(grain size) -1 q-1 ballistic motion

17. Steady state and cross-over from aging to steady STEADY STATE RELAXATION TIME CROSSOVER TIME FROM AGING TO STEADY -1 q-1 ballistic motion

18. GB dynamics under shear – a physical picture g = 0 TYPICAL SAMPLE CONFIGURATION g 0 Stationary state L « reshuffling » lengthscale

19. GB dynamics under shear – a physical picture CROSSOVER TIME FROM AGING TO STEADY tc=1 RESHUFFLING LENGTH SCALE grain size

20. Conclusion and open questions Length scale dependence of the aging and plasticity of a colloidal polycrystal under cyclic shear ? FLOW Scaling of the “reshuffling” length scale when approaching the elastic and flow regimes? ELASTIC ? Grain size Role of the microstructure ? Analogy with the plasticity of other disordered materials?

21. People - Acknowledgements Julian Oberdisse Elisa Tamborini Luca Cipelletti AmeurLouhichi NedaGhofraniha Laurence Ramos

23. Data analysis INTENSITY CORRELATION & CARACTERISTIC LENGTH SCALES 10 µm q// grain size: 10 µm q1 = 0.12 µm-1 51 µm q2 = 0.19 µm-1 q3 = 0.24 µm-1 q4 = 0.39 µm-1 q5 = 0.78 µm-1 q6 = 1.16 µm-1 q7 = 1.58 µm-1 q8 = 2.2 µm-1 q9 = 2.83 µm-1 q10 = 3.72 µm-1  51 mm 1.65 µm

24. Elasticity vs Plasticity ELASTIC SAMPLE (PDMS) PLASTIC SAMPLE (POLYCRYSTAL)

26. Design of a colloidal analog of a metallic alloy NANOPARTICLE PARTIONING 0.007 °C/Min 0.0005 °C/Min Partitioning p= [NP] in GB [NP] inside grains fNP=0.05 %, sNP= 100 nm

27. Design of a colloidal analog of a metallic alloy BLOCK-COPOLYMER IN WATER Pluronics F108 PEO-PPO-PEO fcclattice ~ 30 nm SANS fcc crystal lattice a = 31.7 nm

28. Design of a colloidal analog of a metallic alloy THERMOSENSITIVITY OF F108 PEOx-PPOy-PEOx DSC Rheology ~ 30 nm T fcclattice f temperature

29. Controlling the microstructure ROLE OF THE HEATING RATE 0.0005°C/Min 0.00025°C/min T . 0.02 °C/Min 0.007 °C/Min Fluorescent polystyrene NP sNP= 36 nm fNP=0.5 %

30. Effect of the heating rate on the microstructure 0.0005°C/Min 0.00025°C/min 0.02 °C/Min 0.007 °C/Min fNP=0.5 % (v/v) s = 36 nm

31. Controlling the microstructure ROLE OF THE NP CONCENTRATION fNP 0.05% v/v 0.1% v/v 0.5% v/v 1% v/v . Analogy to grain refinement in metallic alloys T=0.007°C/Min

32. Controlling the microstructure ROLE OF THE NP CONCENTRATION 0.1% v/v 0.05% v/v 0.5% v/v 1% v/v

33. Controlling the microstructure AVERAGE CRYSTALLITE SIZE vs NP content vsheating rate .

34. Experimentalset-up COLLIMATOR SHEAR CELL L1b L2a L2b L3b L1a L3a S Z M BS CCD LPDT PDM OF LASER PDT PC Tamborini & Cipelletti, Rev. Sci. Instr. 2012 DLS undershear strain  GBs dynamics INTENSITY CORRELATION ~ 1/x ~ 1/d q1 = 0.12 µm-1-q10 = 3.72 µm-1