Embed Size (px)
Citation preview
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
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]
DISLOCATION GB
J. W
eis
s, L
GG
E/C
NR
S
Extremely small grains Unrealistically high strains
Numerical simulations
Experiments on metals
Difficulty of preparing samples with small grainsDifficulty 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 experimentswere 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 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 (a
rb. 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+2
g=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
Elasticity vs Plasticity
ELASTIC SAMPLE (PDMS)
0 1 2 3 40,0
0,2
0,4
0,6
0,8
1,0 t = 1
g 2-1
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
100 101 102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0g 2 -
1
tr
Visco-elasticty
CHOICE OF THE STRAIN AMPLITUDES
0.01 0.1 1 1010
100
1000
10000
storage modulus loss modulus
G',
G"
(Pa)
(%)
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
1 10 100 1000 10000
0.1
1
10
100
1000
r
t
AGING law
Relaxation time vs # of shear cycles
1 10 100 1000 100000.1
1
10
100
1000
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
0.130.200.240.390.781.161.582.202.833.72
q (m-1)
q AGING laws
g = 4.6 %
Scaling
),(/ c* qttt
),(/* qrr
10-2 10-1 100 101 102 103 10410-4
10-3
10-2
10-1
100
r/
t/tc
g = 4.6 %
Scaling
),(/* qrr
10-2 10-1 100 101 102 103 10410-4
10-3
10-2
10-1
100
= 1.5%
= 2.5%
= 3.5%
= 4.6%
= 5.2%
r/
t/tc
),(/ c* qttt
0.1 1102
103
104
= 4.6%
q (m-1)
STEADY STATE RELAXATION TIME
Steady state
-1
q-1 ballistic motion
2 /(p grain size)
0.1 1102
103
104
= 1.5%
= 2.5%
= 3.5%
= 4.6%
= 5.2%
q (m-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 (m-1
)
= 1.5%
= 2.5%
= 3.5%
= 4.6%
= 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 (m-1
)
= 1.5%
= 2.5%
= 3.5%
= 4.6%
= 5.2%
t c
)1(
2
ctq
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
(
m)
(%)
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
(
m)
(%)
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//
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
100 101 102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0g 2 -
1
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 (
cm3 )
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 (
arb.
un.
)
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 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
0.0001 0.001 0.01
10
R (m
)
NP
0.001 0.01
10
R (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 (a
rb. 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 (a
rb. u
n.)
~ 1/x
~ 1/d
INTENSITY CORRELATION
q1 = 0.12 µm-1 - q10 = 3.72 µm-1
