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

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

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

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

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

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)

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

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

Elasticity vs Plasticity ELASTIC SAMPLE (PDMS)

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

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

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

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

Scaling  = 4.6 %

Scaling

STEADY STATE RELAXATION TIME Steady state ballistic motion 2  grain size)

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

 GB dynamics under shear – a physical picture TYPICAL SAMPLE CONFIGURATION    0 Stationary state « reshuffling » length scale

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

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

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

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

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

0.007 °C/Min °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

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

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

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

0.02 °C/Min °C/Min °C/Min °C/min  NP =0.5 % (v/v)  = 36 nm Effect of the heating rate on the microstructure

 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

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

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

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 DLS undershear strain  GBs dynamics ~ 1/  ~ 1/  INTENSITY CORRELATION q 1 = 0.12 µm -1 - q 10 = 3.72 µm -1