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Universal aging dynamics of synthetic hectorite suspensions合成水辉石悬浮液老化的动态普适性孙尉翔华南理工大学 材料科学研究所2015-07 第九届复杂流体流变学研讨会
Colloidal phase diagram
Volume fraction
Tem
pera
tur
eGlass line
Spinodal
GlassLiquid
Credit: Eric R. Weeks Laboratoryhttp://www.physics.emory.edu/~weeks/lab/aging.html
Gel
Low vol. fraction Attractive
High vol. fraction Repulsive
Gel
Glass
Colloidal Dynamics
Credit: Eric R. Weeks Laboratoryhttp://www.physics.emory.edu/~weeks/lab/aging.htmlPhysics 4, 42 (2011) J. Phys. Chem. 100, 13200 (1996)
Aging: Out-of-equilibrium dynamics
Universal aging dynamics
Aging is ubiquitous
Aging is ubiquitous
Rheology for aging dynamicsL. C. E. Struik, Physical Aging in Amorphous Polymers and Other Materials (Elsevier Science, New York, 1978).
L. C. E. Struik, Physical Aging in Amorphous Polymers and Other Materials (Elsevier Science, New York, 1978).
Multi-wave time sweep
E. E. Holly et al. J. Non-Newtonian Fluid Mech., 1988, 27, 17-26.
Repeated Frequency Sweep
M. Mours and H. H. Winter, Rheol. Acta 33, 385 (1994).
Repeated time sweep
A. S. Negi and C. O. Osuji, Phys. Rev. E 82, 031404 (2010).
Materials a synthetic hectorite, [Mg5.34Li0.66Si8O20(OH)4]Na0.66
Layer size: 30 nm in diameter & 1 nm in thickness
tw
suspension in water Liquid – solid trans.
Na+Na+
Na+
Na+ Na+
Na+
i
0 = 0 = 2f0
tw
i = 3000 s-1
ti = 100 s
Methods
tw = 0
GApplying a sample
Pre-shear Measurement
tw
1. KineticsSingle freq. time swp.
2. DynamicsMulti-wave time swp.
Pre-age
Kinetics of aging: T-dependence
101 102 103
10-1
100
101
102
T (°C) 10 15 20 25 30 35 40 45
G', G''
(Pa)
tw (s)
Clay: 3.5 wt%Pre-age: 4 d
G'
G''
0 = 0.5%, = 6.28 rad/s
101 102 103 104
10-1
100
101
102
T (°C) 10 15 20 25 30 35 40 45
b TG', b TG''
(Pa)
tw/aT (s)
Clay: 3.5 wt%Pre-age: 4 dTref = 10°C
20 400.0
0.5
1.0
Shi
ft fa
ctor
s
T (°C)
aT
bT
Preshearing at high rate ~ equilibrate at high T
“Shear melting”
Kinetics of aging – temperature dependence
10 20 30 40 500.0
0.5
1.0
1.5a T
T (°C)
L2.9-2d L3.2-2d L3.5-2d L3.5-4d
Modeling: Interaction potential
Electrical potential
clay particle
A1: Attractive with barrier
Modeling: Interaction potential
10 20 30 40
0.8
1.0
1.2
1.4
c (m
S c
m-1)
T (°C)
L2.9-2d L3.2-2d L3.5-2d L3.5-4d
(a)
10 20 30 400.016
0.018
0.020
0.022
0.024
0.026
[Na+ ] (
M)
T (°C)
(b)
0 50 1000
2
4
(1
0-7 m
2 s-1V
-1)
T (°C)
Na+
OH-
Na+Na+
Na+
Na+ Na+
Na+1
2 2A
0 r B
1000 Nae N
k T
κ-1 = 3.4~8.2 nm
A2: ϕeff < 0.0857Cluster / Gel
Q2: Glass or gel?
Modeling: Interaction potentialNa+
Na+Na+
Na+ Na+
Na+
H. Ohshima, J. Colloid Interface Sci. 247, 18 (2002).
Surface Charge Density / Surface Potential
Relationship
Modeling: Reaction-limited colloidal aggregation
10 20 30 400.0
0.5
1.0
1.5
2.0
a T
T (°C)
L2.9-2d L3.2-2d L3.5-2d L3.5-4d
Modeling: Reaction-limited colloidal aggregation
T (°C)0 10 20 30 40
a T10-60
10-40
10-20
100
L3.5-2dL3.2-2dL2.8-2dL3.5-4d
Modeling: Kinetics
10 20 30 400.0
0.5
1.0
1.5
2.0
a T
T (°C)
L2.9-2d L3.2-2d L3.5-2d L3.5-4d
10 20 30 403.2
3.4
3.6
3.8
4.0
L3.5-2d
L3.5-4d
L3.2-2d
Um
ax (1
0-19 J)
T (°C)
(c)
L2.9-2d
10 20 30 40
85
90
95
L3.5-4d
L3.5-2d
L3.2-2d
Um
ax/k
BT
T (°C)
(d)L2.9-2d
Increased potential barrier
Increased collision probability
Q3: Origin of the non-monotonic dependence?A3:
Modeling
H. Tanaka, J. Meunier, and D. Bonn, Phys. Rev. E 69, 031404 (2004).
B. Ruzicka and E. Zaccarelli, Soft Matter 7, 1268 (2011).
No direct relationship between Cs and I under counterion-condensation!
Dynamics of aging
Dyn. freq. swp. At different tw of aging
Time – aging time superposition
Dynamics of aging
Time – temp. superposition at different tw’s.
Time – aging time – temp. superposition
Relaxation time dependenceτ(T, tw; cL)
Relaxation time dependenceτ(25°C, tw; cL)
Relaxation time spectra
2 2
2 2
2 2
ln1
ln1
G H d
G H d
J. Ramirez and A. E. Likhtman, Rheology of Entangled Polymers: Toolbox for the Analysis of Theory and Experiments, 2007.
Relaxation time spectra
c0
,,
0,
n n
n GH
Spectrum for glasses: BSW spectrum mapped to mode-coupling theory (MCT):H. Winter, M. Siebenbürger, D. Hajnal, O. Henrich, M. Fuchs, and M. Ballauff, Rheol. Acta 48, 747 (2009).
c ,,
0,
n
n GH
0 max0
max
,,
0,
n
HH
Spectrum for gels: critical gel theoryM. Mours and H. H. Winter, Macromolecules 29, 7221 (1996).
H. H. Winter, Macromolecules 46, 2425 (2013).
ε: distance to transition (near-equilibrium)Gels: ε = |p – pc|Glass: ε = |ϕ – ϕg|
0 max0
max
,,
0,
n
HH
Powerlaw distribution:
Relaxation time spectra
0max max
expn
H H
cut-off function
Transition from gel-like to glass-like behavior
Modeling
H. Tanaka, J. Meunier, and D. Bonn, Phys. Rev. E 69, 031404 (2004).
B. Ruzicka and E. Zaccarelli, Soft Matter 7, 1268 (2011).
Gel – glass:ϕ – dependence or age – dependence?
Hectorite + PEG
0.0 5.0x10-9 1.0x10-8 1.5x10-8-20
0
20
Pot
entia
l (k BT)
h (m)
UvdW
Udl
Usteric
U
Quenched by increasing U (old results)
U=UvdW+Udl+Usteric
√
W. Sun, T. Wang, C. Wang, X. Liu, and Z. Tong, Soft Matter 9, 6263 (2013).
10-1 101 103 105100
101
102
cp = 0.63 wt%, t
w,ref = 90 s
tw/ s
30 40 60 90 200 400 700G
', G'' (
Pa)
at (rad/s)
10-5 10-3 10-1 101
100
101
102
tw = 90 s, c
p,ref = 0.1 wt%
cp / wt%
0 0.1 0.25 0.4 0.63 0.8 1.0
ap (rad/s)
Time – aging time superposition Time – PEG conc. superposition
10-4 10-2 100 10210-1
100
101
102
G', G''
(Pa)
rel (rad/s)
cp,ref
= 0.1 wt%tw,ref
= 90 s
Relaxation time :
cp
tw “older”aging
“younger”rejuvenation
ConclusionsNa+
Na+Na+
Na+ Na+
Na+
Increased potential barrier
Increased collision probability
青年科学基金21204023
Prof. Z. Tong
C. LiangW.
Sun
Thank you!