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

Elisa Tamborini Laurence RamosLuca Cipelletti

Laboratoire Charles CoulombCNRS-Université Montpellier 2Montpellier, France

MotivationMECHANICAL PROPERTIES OF ATOMIC POLYCRYSTALS

[Kumar Acta Mater. 2003]

2 competiting processes to control deformation• Grain-boundary (GB) sliding• Dislocation slip

[Richeton Nature Materials2005]

DISLOCATION GB

J. W

eiss

, LG

GE

/CN

RS

Extremely small grains Unrealistically high strains

Numerical simulations

Experiments on metals

Difficulty of preparing samples with small grainsDifficulty of measurements

MotivationOUR 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 experimentswere on «monocrystals»

Polycrystals = a disordered network of grain-boundaries

Experimental sample3D 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 mm

Home-made shear cell

laserspring

motor

moving slide

fixed slide

25 mm

Observation by confocal microscopy

t

g = 3.6 %

t = 1 t = 2 t = 3g=0

50 µm

t = 1t = 2617

Overlay of 2 images taken at

~ 5000 cycles

Deformation of the crystalline grains

PROTOCOL (analogy to fatigue test in material science)

10 µm

10-6 10-5 10-4 10-3 10-2 10-110-2

10-1

100

101

102

103

104

105

106

107

108

SANS SLS USALS MALS

q (Å-1)

I (ar

b. u

n.)

q1 = 0.12 µm-1 - q10 = 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

g2(t,t)-1=

q// tt = i t = i+1 t = i+2g=0

t timet delay between shear cycle

t =1t =2

100 101 102 103 1040.0

0.2

0.4

0.6

0.8

1.0

t = 1

g 2-1 t

Elasticity vs PlasticityELASTIC SAMPLE (PDMS)

0 1 2 3 40,0

0,2

0,4

0,6

0,8

1,0 t = 1

g 2-1

t

Elasticity vs Plasticity

ELASTIC SAMPLE (PDMS)

PLASTIC SAMPLE (POLYCRYSTAL)

100 101 102 103 1040.0

0.2

0.4

0.6

0.8

1.0

t = 1

g 2-1

t

100 101 102 103 104 1050.0

0.2

0.4

0.6

0.8

1.0g 2 -1

t tr

Visco-elasticty

CHOICE OF THE STRAIN AMPLITUDES

0.01 0.1 1 1010

100

1000

10000

storage modulus loss modulus

G',

G"

(Pa)

g (%)

0.025°C/minf = 0.5 Hz

Elastic Plastic Viscous

g = 1.6 %

g = 2.5 %

g = 4.6 %

g = 5.2 %

g = 3.5 %

Relaxation time vs # of shear cycles

g = 4.6 %

1 10 100 1000 100000.0

0.2

0.4

0.6

0.8

1.0 2 3 4 7 10 25 50 100 150 250 500 1500

g 2-1

t1 10 100 1000 10000

0.1

1

10

100

1000

t r

t

AGING law

Relaxation time vs # of shear cycles

1 10 100 1000 100000.1

1

10

100

1000

t r

t

q1

q2

q3

q4

q5

q6

q7

q8

q9

q10

1 10 100 1000 100000.0

0.2

0.4

0.6

0.8

1.0

g 2-1

t

0.130.200.240.390.781.161.582.202.833.72

q (mm-1)

q AGING laws

g = 4.6 %

Scaling

),(/ c* gqttt =

),(/* gttt qrr =

10-2 10-1 100 101 102 103 10410-4

10-3

10-2

10-1

100

t r/t

t/tc

g = 4.6 %

Scaling

),(/* gttt qrr =

10-2 10-1 100 101 102 103 10410-4

10-3

10-2

10-1

100

g = 1.5%

g = 2.5%

g = 3.5%

g = 4.6%

g = 5.2%

t r/t

t/tc

),(/ c* gqttt =

0.1 1102

103

104

g = 4.6%

t

q (mm-1)

STEADY STATE RELAXATION TIME

Steady state

-1

q-1 ballistic motion

2 p /(grain size)

0.1 1102

103

104

g = 1.5%

g = 2.5%

g = 3.5%

g = 4.6%

g = 5.2%

t

q (mm-1)

STEADY STATE RELAXATION TIME

Steady state and cross-over from aging to steady

CROSSOVER TIME FROM AGING TO STEADY

0.1 1

100

101

102

q (mm-1)

g = 1.5%

g = 2.5%

g = 3.5%

g = 4.6%

g = 5.2%

t c

-1

q-1 ballistic motion

g = 0

GB dynamics under shear – a physical picture

TYPICAL SAMPLE CONFIGURATION

L

g 0Stationary state

« reshuffling » length scale

0.1 1

100

101

102

q (mm-1)

g = 1.5%

g = 2.5%

g = 3.5%

g = 4.6%

g = 5.2%

t c

)1(2=

=Lctqp

GB dynamics under shear – a physical picture

CROSSOVER TIME FROM AGING TO STEADY

RESHUFFLING LENGTH SCALE

tc=1

1 2 3 4 5 60

10

20

30

40

50

60

70

L (m

m)

g (%)

grain size

Conclusion and open questions

Scaling of the “reshuffling” length scale when approaching the elastic and flow regimes?

Role of the microstructure ?

1 10

10

100

L (m

m)

g (%)

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 CipellettiElisa Tamborini

Julian Oberdisse

Laurence Ramos

Data analysis

q//

q1 = 0.12 µm-1 51 µmq2 = 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

10 µm

51 mm

1.65 µm

grain size: 10 µm

INTENSITY CORRELATION & CARACTERISTIC LENGTH SCALES

Elasticity vs Plasticity

ELASTIC SAMPLE (PDMS)

PLASTIC SAMPLE (POLYCRYSTAL)

100 101 102 103 1040.0

0.2

0.4

0.6

0.8

1.0

t = 1

g 2-1

t

100 101 102 103 104 1050.0

0.2

0.4

0.6

0.8

1.0g 2 -1

t

0.007 °C/Min

0.0005 °C/Min

Partitioning p=[NP] in GB

[NP] inside grains

fNP=0.05 %, sNP = 100 nm

Design of a colloidal analog of a metallic alloy NANOPARTICLE PARTIONING

Pluronics F108PEO-PPO-PEO

Design of a colloidal analog of a metallic alloy

fcc crystal latticea = 31.7 nm

SANS

110-23

10-22

10-21

10-20

10-19

I/(

)² (c

m3 )

q (nm-1)

~ 30 nm

fcc lattice

BLOCK-COPOLYMER IN WATER

THERMOSENSITIVITY OF F108 PEOx-PPOy-PEOx

temperature

~ 30 nm

fcc lattice

Design of a colloidal analog of a metallic alloy

T

f

16 17 18

0.76

0.78

0.80

0 5 10 15 20 250.0

0.2

0.4

0.6

0.8

1.0

crystallization

Hea

t Flo

w (a

rb. u

n.)

T (°C)

micellization

RheologyDSC

0 10000 20000 300000.1

1

10

100

1000

10000

0

4

8

12

16

20

24

G',

G" (

Pa)

time (s)

G' G"

T (°C) T

0.02 °C/Min

T

0.007 °C/Min

0.0005°C/Min

0.00025°C/min

Fluorescent polystyrene NPsNP = 36 nmfNP=0.5 %

Controlling the microstructure

.

ROLE OF THE HEATING RATE

0.02 °C/Min

0.007 °C/Min

0.0005°C/Min

0.00025°C/min

fNP=0.5 % (v/v)s = 36 nm

Effect of the heating rate on the microstructure

fNP

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 microstructureROLE OF THE NP CONCENTRATION

0.05% v/v

0.5% v/v

1% v/v

0.1% v/v

Controlling the microstructureROLE OF THE NP CONCENTRATION

vs heating ratevs NP content

0.0001 0.001 0.01

10

R (m

m)

fNP

0.001 0.01

10

R (m

m)

T (°C min-1).

Controlling the microstructure

AVERAGE CRYSTALLITE SIZE

SHEAR CELL

LASER

L1a L1b

PDT

L2a L2b L3a L3b

M

LPDT

CCD

PC

S

PDM

OF

BS

Z

COLLIMATOR

Experimental set-up

Tamborini & Cipelletti, Rev. Sci. Instr. 2012

DLS undershear strain GBs dynamics

10-5 10-4 10-3 10-2 10-110-1

100

101

102

103

104

105

106

107

q (Å-1)

I (ar

b. u

n.)

USALS SALS SLS SANSx

d10 µm

~ 1/x

~1/d

10-6 10-5 10-4 10-3 10-2 10-110-2

10-1

100

101

102

103

104

105

106

107

108

SANS SLS USALS MALS

q (Å-1)

I (ar

b. u

n.)

~ 1/x

~ 1/d

INTENSITY CORRELATION

q1 = 0.12 µm-1 - q10 = 3.72 µm-1