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!