This document summarizes research on the universal aging dynamics of synthetic hectorite suspensions. It discusses how aging behavior is ubiquitous in colloidal systems and can be studied through rheological measurements. The kinetics and dynamics of aging in hectorite suspensions are found to depend on factors like temperature, clay concentration, and aging time. The relaxation time of the suspensions increases with longer aging times. The document also presents models of the interaction potential and kinetics of the clay particles to explain the observed aging behavior.

1. 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

2. Colloidal phase diagram
Volume fraction
Temperature
Glass line
Spinodal
Glass
Liquid
Credit: Eric R. Weeks Laboratory
http://www.physics.emory.edu/~weeks/la
b/aging.html
Gel
Low vol. fraction
Attractive
High vol. fraction
Repulsive

3. Gel
Glass
Colloidal Dynamics
Credit: Eric R. Weeks Laboratory
http://www.physics.emory.edu/~weeks/la
b/aging.htmlPhysics 4, 42 (2011) J. Phys. Chem. 100, 13200 (1996)

4. Aging: Out-of-equilibrium dynamics

5. Universal aging dynamics

6. Aging is ubiquitous

7. Aging is ubiquitous

8. Rheology for aging dynamics
L. 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).

9. Multi-wave time sweep
E. E. Holly et al. J. Non-Newtonian Fluid Mech., 1988, 27, 17-26.

10. Repeated Frequency Sweep
M. Mours and H. H. Winter, Rheol. Acta 33, 385 (1994).

11. Repeated time sweep
A. S. Negi and C. O. Osuji, Phys. Rev. E 82, 031404 (2010).

12. 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+

13. 
i
0
= 0
 = 2f0
tw
i
= 3000 s
-1
ti
= 100 s
Methods
tw = 0
G
Applying a
sample
Pre-shear Measurement
tw
1. Kinetics
Single freq. time
swp.
2. Dynamics
Multi-wave time
swp.
Pre-age

14. 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
bT
G',bT
G''(Pa)
tw
/aT
(s)
Clay: 3.5 wt%
Pre-age: 4 d
Tref
= 10°C
20 40
0.0
0.5
1.0
Shiftfactors
T (°C)
aT
bT
Preshearing at high rate
~ equilibrate at high T
“Shear melting”

15. Kinetics of aging – temperature dependence
10 20 30 40 50
0.0
0.5
1.0
1.5
aT
T (°C)
L2.9-2d
L3.2-2d
L3.5-2d
L3.5-4d

16. Modeling: Interaction potential
Electrical potential
clayparticle
A1: Attractive with
barrier

17. Modeling: Interaction potential
10 20 30 40
0.8
1.0
1.2
1.4
c
(mScm-1
)
T (°C)
L2.9-2d
L3.2-2d
L3.5-2d
L3.5-4d
(a)
10 20 30 40
0.016
0.018
0.020
0.022
0.024
0.026
[Na+
](M)
T (°C)
(b)
0 50 100
0
2
4
(10-7
m2
s-1
V-1
)
T (°C)
Na+
OH-
Na+
Na+
Na+
Na+ Na+
Na+
1
2 2
A
0 r B
1000 Nae N
k T

 

    
 
 
κ-1 = 3.4~8.2 nm
A2: ϕeff < 0.0857
Cluster / Gel
Q2: Glass or gel?

18. Modeling: Interaction potential
Na+
Na+
Na+
Na+ Na+
Na+
H. Ohshima, J. Colloid Interface Sci. 247, 18 (2002).
Surface Charge Density /
Surface Potential
Relationship

19. Modeling: Reaction-limited colloidal aggregation
10 20 30 40
0.0
0.5
1.0
1.5
2.0
aT
T (°C)
L2.9-2d
L3.2-2d
L3.5-2d
L3.5-4d

20. Modeling: Reaction-limited colloidal aggregation

21. Modeling: Kinetics
10 20 30 40
0.0
0.5
1.0
1.5
2.0
aT
T (°C)
L2.9-2d
L3.2-2d
L3.5-2d
L3.5-4d
10 20 30 40
3.2
3.4
3.6
3.8
4.0
L3.5-2d
L3.5-4d
L3.2-2d
Umax
(10-19
J)
T (°C)
(c)
L2.9-2d
10 20 30 40
85
90
95
L3.5-4d
L3.5-2d
L3.2-2d
Umax
/kB
T
T (°C)
(d)
L2.9-2d
Increased
potential barrier
Increased collision
probability
Q3: Origin of the non-
monotonic dependence?
A3:

22. 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!

23. Dynamics of aging
Dyn. freq. swp. At different tw of aging
Time – aging time superposition

24. Dynamics of aging
Time – temp. superposition at
different tw’s.
Time – aging time – temp.
superposition

25. Relaxation time dependence
τ(T, tw; cL)

26. Relaxation time dependence
τ(25°C, tw; cL)

27. Relaxation time spectra
   
   
2 2
2 2
2 2
ln
1
ln
1
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.

28. Relaxation time spectra
   
 
 
c
0
,
,
0,
n n
n G
H
 
 


 
  
   
  
     
              


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 G
H

 



 
  
 
  
     


  0 max
0
max
,
,
0,
n
H
H
   
 

     
  
 
Spectrum for gels: critical gel theory
M. 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 max
0
max
,
,
0,
n
H
H
   
 

     
  
 
Powerlaw distribution:

29. Relaxation time spectra
  0
max max
exp
n
H H

 

 
    
     
     
cut-off function
Transition from gel-like
to glass-like behavior

30. 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?

31. Hectorite + PEG
0.0 5.0x10
-9
1.0x10
-8
1.5x10
-8
-20
0
20
Potential(kB
T)
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).

32. 10
-1
10
1
10
3
10
5
10
0
10
1
10
2
cp
= 0.63 wt%, tw,ref
= 90 s
tw
/ s
30
40
60
90
200
400
700
G',G''(Pa)
at
 (rad/s)
10
-5
10
-3
10
-1
10
1
10
0
10
1
10
2
tw
= 90 s, cp,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
10
0
10
2
10
-1
10
0
10
1
10
2
G',G''(Pa)
rel
 (rad/s)
cp,ref
= 0.1 wt%
tw,ref
= 90 s
Relaxation time：
cp
tw “older”
aging
“younger”
rejuvenation

33. Conclusions
Na+
Na+
Na+
Na+ Na+
Na+
Increased
potential barrier
Increased collision
probability

34. 青年科学基金
21204023
Prof. Z. Tong C. Liang
W. Sun

35. Thank you!