Dynamics of a Colloidal Glass During Stress-Mediated Structural Arrest (“Relaxation in Reverse”)...
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Dynamics of a Colloidal Dynamics of a Colloidal Glass During Stress- Glass During Stress- Mediated Structural Mediated Structural Arrest Arrest (“ (“ Relaxation in Relaxation in Reverse Reverse ”) ”) Ajay Singh Negi and Chinedum Osuji Department of Chemical Engineering, Yale University, New Haven, CT.
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Transcript of Dynamics of a Colloidal Glass During Stress-Mediated Structural Arrest (“Relaxation in Reverse”)...
Dynamics of a Colloidal Glass Dynamics of a Colloidal Glass During Stress-Mediated During Stress-Mediated
Structural ArrestStructural Arrest(“(“Relaxation in ReverseRelaxation in Reverse”)”)
Ajay Singh Negi and Chinedum OsujiDepartment of Chemical Engineering,
Yale University, New Haven, CT.
MotivationMotivation
Structural Glass
• At high temperatures (above Tg), system is liquid.
• Below Tg, the viscosity is very high.
• Below Tg, the system shows aging behavior.
Colloidal Glass
• Under high shear, the system flows.
• At low shear rates or rest, the system does not flow.
• Aging behavior is seen at rest or low shear.
Is shear temperature ?
MotivationMotivation
EXPERIMENTS: Ediger et al, Science, 323, 231 (2009)At higher creep stresses, the dynamics was faster and distribution narrower.
SIMULATIONS: Warren and Rottler, 2010: At higher stresses, dynamics is accelerated and distribution is narrowed.
How does stress influence the structural arrest of a colloidal glass?
MotivationMotivation
What is the role of stress on the arrest timescale?
How does stress affect the trajectory of the system during arrest? (peak-width in time-dependent viscosity)
System and MethodSystem and Method
• Laponite XLG
(a) Electrostatic screening length at
pH 10 ≈ 30 nm.
(b) Non-ergodic state at concentration
of 1 wt %.
• Bulk Rheology
(a) Constant stress measurements.
(b) Oscillation over a background steady flow.
time (s)Solid lines: Controlled variable Dashed lines: Measured variable
Schematic of Protocol Schematic of Protocol (constant stress)(constant stress)
t=0
Dynamical ArrestDynamical Arrest
0.1 1 10 100
1E-4
1E-3
0.01
0.1
1
10
100
3 Pa 4 Pa 6 Pa 9 Pa 13 Pa 18 Pa 24 Pa 31 Pa
shea
r ra
te (
1/s)
t (s)
Increasing Stress
Shear rate measured
as a function of time
for a constant applied
stress.
The time for arrest
increase with increase
in the applied stress.
Above a certain stress the system will NOT arrest.
Viscosity Bifurcation Coussot et al, PRL 2002
time (s)Solid lines: Controlled variable Dashed lines: Measured variable
Superposition Rheology ProtocolSuperposition Rheology Protocol
t=0
Linearity of Superposition RheologyLinearity of Superposition Rheology
10 100 1000
1
10
100
10 100 1000
1
10
100
G',
G"
(Pa)
time (s)
0.2 Pa, 5 Pa 0.4 Pa, 5 Pa 0.7 Pa, 5 Pa 1 Pa, 5 Pa 0.2 Pa, 10 Pa 0.4 Pa, 10 Pa 0.7 Pa, 10 Pa 1 Pa, 10 Pa
Same background
stress and
different probe
stresses give the
same result.
This ensured that
we are measuring
the linear
properties of the
system under flow.
WaveformsWaveforms
-1 0 1 2 3 4 5 6 7
-1.0
-0.5
0.0
0.5
1.0
-1.0
-0.5
0.0
0.5
1.0
G' > G"
Phase Angle (rad)
Stress Strain
Str
ess,
Str
ain
G' < G"
Waveforms are
NOT distorted
linear properties
are being
measured.
Finite phase lag for
a liquid sample.
The phase lag
vanishes when the
system solidifies.
Oscillation Over FlowOscillation Over Flow
10 100 10001
10
100
10 100 10001
10
100
filled symbol : G'open symbol : G"
G',
G"
(Pa)
19
t (s)
Dynamic
measurements on
the sample under
steady flow.
Probe stress = 1 Pa.
BentoniteOvarlez and Coussot, PRE, 76, 011406 (2007)
Shahin and Joshi, Langmuir, 26, 4219 (2010)
melting stress > yield stress
(yield stress)
Oscillation Over FlowOscillation Over Flow
10 100 10001
10
100
10 100 10001
10
100
filled symbol : G'open symbol : G"
G',
G"
(Pa)
13 19
t (s)
Dynamic
measurements on
the sample under
steady flow.
Probe stress = 1 Pa.
Oscillation Over FlowOscillation Over Flow
10 100 10001
10
100
10 100 10001
10
100
filled symbol : G'open symbol : G"
G',
G"
(Pa)
13 19 25
t (s)
Dynamic
measurements on
the sample under
steady flow.
Probe stress = 1 Pa.
Oscillation Over FlowOscillation Over Flow
10 100 10001
10
100
10 100 10001
10
100
filled symbol : G'open symbol : G"
G',
G"
(Pa)
10 13 16 19 21 23 25 28
t (s)
Dynamic
measurements on
the sample under
steady flow.
Varying background
stresses, σm.
Probe stress = 1 Pa.
The cross-over between G’ and G” is delayed as the background
stress was increased.
ττ vsvs σσmm
5 10 15 20 25 30
10
100
1000
2.7 3 3.3 3.610
100
0 (P
a), E
(wt %)
0
E
2.75% 3% 3.5%
(s)
m (Pa)
System will not arrest
above a stress σ0.
VFT equation
ττ vsvs σσmm
5 10 15 20 25 30
10
100
1000
2.7 3 3.3 3.610
100
0 (P
a), E
(wt %)
0
E
2.75% 3% 3.5%
(s)
m (Pa)
System will not arrest
above a stress σ0.
VFT equation
Evolution of the arrest time with applied stress? VFT dependenceWidth of the loss mode peak with applied stress?
Width of Loss PeakWidth of Loss Peak
0.1 1 10 100 10001
10
100
G"
a( m
)
t b(m
)
10 13 16 19 21 23 25 28
G” peaks broaden
as stress is
decreased,
precluding time-
stress
superposition.
It is similar to broadening of loss peak on approaching glass transition temperature.
Peak Width of Loss ModulusPeak Width of Loss Modulus
1.0 1.5 2.0 2.5 3.00.4
0.8
1.2
1.6
2.0
2.4
1.0 1.5 2.0 2.5 3.00.4
0.8
1.2
1.6
2.0
2.4
13 16 19 21 23 25 28
log(t) (s)
log
(G'')
(P
a)
Lines are fit to Lorentzian function
12 14 16 18 20 22 24 26 28 300
2
4
6
8
10
Pe
ak
Wid
th
stress (Pa)
Loss mode peak narrows with increasing stress.
Cole Davidson ExponentCole Davidson Exponent
~ 1/peak width12 14 16 18 20 22 24 26 28 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1/(p
eak
wid
th)
stress (Pa)
Stickel et al (1993): decreases on approaching glass transition for PDE, an organic glass former.
SummarySummary
• Stress delays the onset of structural arrest.• Dynamic measurement gives a temporal response
similar to frequency dependence observed in non-aging systems.
• The arrest time τ has an exponential dependence on inverse stress.
• Above a critical stress σ0, the arrest time diverges.
• Loss peak narrows with increasing stress.
Negi and Osuji, EPL, 90, 28003 (2010)
Effect of FrequencyEffect of Frequency
The frequency of the probe stress was varied.
Frequency DependenceFrequency Dependence
At higher frequency system arrests much faster.
3 10 90
0
100
200
300
400
500
600
700
800
900
t_cr
oss
ing
(s)
frequency (rad/s)
1 pa 2 Pa 4 Pa 6 Pa 8 Pa 9 Pa
1
10
100
1000
1
10
100
1000
1
10
100
1
10
100
10 100 1000
0.01
0.1
1
10
100
10 100 1000
0.01
0.1
1
10
100
70 40 20 10 7 4
1 Pa
G',
G"
(Pa)
4 Pa
9 Pa
t (s)
Width of Loss ModulusWidth of Loss Modulus
The lines are fitted to logistic power peak function to estimate the width.
3 10 90
1
2
3
4
5
6
7
pea
k w
idth
freq (rad/s)
1 Pa 2 Pa 4 Pa 6 Pa 8 Pa 9 Pa
1.1
1.2
1.3
1.4
1.5
1.6
1.1
1.2
1.3
1.4
1.5
1.6
0.5 1.0 1.5 2.0 2.5 3.00.0
0.4
0.8
1.2
1.6
2.0
0.5 1.0 1.5 2.0 2.5 3.00.0
0.4
0.8
1.2
1.6
2.0
0.8
1.0
1.2
1.4
1.6
0.8
1.0
1.2
1.4
1.6
1 Pa
70 40 20 10 7 4
log(t) (s)
9 Pa
4 Palog
(G")
(P
a)
SummarySummary
• The response of the system at higher frequency is qualitatively similar to its response at the lower stresses.
• The system seem to be more arrested at higher frequencies.
POSSIBLE REASON• At higher frequency or at short times, the system seems
more solid like.
AcknowledgementsAcknowledgements• Funding.
• Osujilab group.http://www.eng.yale.edu/polymers/index.html
Thank you for your attention!!!
Questions?
