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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

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

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Motivation OUR OBJECTIVES Use colloidal crystals as analog of atomic crystals to get time- and space-resolved data on the behavior of the materials under mechanical stress Investigate POLYCRYSTALLINE samples, whereas most previous experiments were on «monocrystals» Polycrystals = a disordered network of grain-boundaries

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Experimental sample 3D NETWORK OF Grain Boundaries NPs confined in the grain-boundaries analogy with impurities in atomic & molecular systems [Lee Metall. Mater. Trans. A 2000] [Losert PNAS 1998] Block-copolymer micellar crystal (fcc, lattice parameter ~ 30 nm) + nanoparticles (~ 1% or less, diameter 35 nm) = temperature ~ 30 nm fcc lattice 10 m

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

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

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10 µm q 1 = 0.12 µm -1 - q 10 = 3.72 µm -1 Experimental set-up DLS under shear strain GBs dynamics Tamborini et al., Langmuir 2012 Shear-cell coupled to Mid-Angle Light Scattering set-up

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Data analysis INTENSITY CORRELATION & CHARACTERISTIC LENGTH SCALES g 2 (t, )-1= q // t t = it = i+1t = i+2 t time delay between shear cycle =1 =2

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Elasticity vs Plasticity ELASTIC SAMPLE (PDMS)

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Elasticity vs Plasticity ELASTIC SAMPLE (PDMS) PLASTIC SAMPLE (POLYCRYSTAL) rr

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Visco-elasticty CHOICE OF THE STRAIN AMPLITUDES ElasticPlasticViscous = 1.6 % = 2.5 % = 4.6 % = 5.2 % = 3.5 %

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

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

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Scaling = 4.6 %

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Scaling

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STEADY STATE RELAXATION TIME Steady state ballistic motion 2 grain size)

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

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GB dynamics under shear – a physical picture TYPICAL SAMPLE CONFIGURATION 0 Stationary state « reshuffling » length scale

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

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

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Neda Ghofraniha People - Acknowledgements Ameur Louhichi Luca Cipelletti Elisa Tamborini Julian Oberdisse Laurence Ramos

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Data analysis q // q 1 = 0.12 µm -1 51 µm q 2 = 0.19 µm -1 q 3 = 0.24 µm -1 q 4 = 0.39 µm -1 q 5 = 0.78 µm -1 q 6 = 1.16 µm -1 q 7 = 1.58 µm -1 q 8 = 2.2 µm -1 q 9 = 2.83 µm -1 q 10 = 3.72 µm -1 10 µm 51 m 1.65 µm grain size: 10 µm INTENSITY CORRELATION & CARACTERISTIC LENGTH SCALES

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

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

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

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THERMOSENSITIVITY OF F108 PEO x -PPO y -PEO x temperature ~ 30 nm fcc lattice Design of a colloidal analog of a metallic alloy T Rheology DSC

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

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

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

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

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vs heating ratevs NP content. Controlling the microstructure AVERAGE CRYSTALLITE SIZE

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SHEAR CELL LASER L 1a L 1b PDT L 2a L 2b L 3a L 3b M L PDT CCD PC PDM OF BS Z COLLIMATOR Experimental set-up Tamborini & Cipelletti, Rev. Sci. Instr. 2012 DLS undershear strain GBs dynamics ~ 1/ ~ 1/ INTENSITY CORRELATION q 1 = 0.12 µm -1 - q 10 = 3.72 µm -1

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