11 soft active materials zhigang suo harvard university iii. polyelectrolytes
TRANSCRIPT
11
Soft Active Materials
Zhigang Suo
Harvard University
III. Polyelectrolytes
2
Polyelectrolyte: polymer with electrolyte group
In a solvent, the electrolyte dissociates.
solvent
fixed charge
counterionCa
Clco-ion
counterion
covalent bond
ionic bond
polymer chain
3
Polyelectrolyte gel
-
- --
--
--
-
-
-
-
-
-
-
-
-
-
+
+
+
+
++
+
+
+
+
++
+
+
+
++
+
+
-
-
-
-
-
--
--
-
-
-
GelExternal solution
Fixed charges
Counterions
Co-ions
-
+
-
A network of polymers Solvent (e.g., water)
Crosslinks
4
Many tissues are polyelectrolyte gels
Structure and function:•Cartilage is polyelectrolyte. •Does this fact have anything to do with low friction of a joint?
5
Plant cell walls are polyelectrolytes
Pectin
6
Gels regulate flow in plants
Zwieniecki, Melcher, Holbrook,Hydrogel control of xylem hydraulic resistance in plants Science 291, 1095 (2001)
Missy Holbrook
7
Osmosis in a polyelectrolyte gel
mem
bran
e
solution
solvent
Osmosis balanced by gravity
•Network tatters fixed charges.•To maintain electroneutrality, fixed charges are balanced by counterions. •Counterions cause osmosis
crosslink
-
-
-
-
-
- -
-
--
+
++
+
+
++
++
fixed charge
counterion
water
network
Osmosis balanced by elasticity
8
Super absorbent diaper
Sodium polyacrylate: polyelectrolyte
Masuda, Trends in the development of superabsorbent polymers for diapers, pp. 88-89, Superabsorbent polymers: science and technology (1994).
9
Ion exchanger
2NaXCaCaXNa2
10
pH-sensitive gel
HRCOORCOOHfixed mobile
K
RCOOHHRCOO
11
pH-sensitive hydrogel
HlogpH 10
12
pH-sensitive valves in microfluidics
Beebe, Moore, Bauer, Yu, Liu, Devadoss, Jo, Nature 404, 588 (2000)
Deformation and force regulated by physiological variables (pH, salt, temperature…)Mechanics and chemistry
David Beebe
13
Adaptive optics with soft materials
Dong, Agarwal, Beebe, Jiang, Nature 442, 551 (2006)
14
Electric potential Electrochemical potential
Gibbs (1878)
electrode
battery, pump,
ele
ctro
ns,
q
Ions, M
MqF
0 Mezq
MezF
MF
ez
electroneutrality
equilibrium
Material A
Material B
electrode
•Battery does work on electrons, q•Pump does work on ions, M•Helmholtz free energy of system, F
15
Lithium-ion battery
Electrolyte
Li-ion
LoadNegativeelectrode
Positive electrode
Wang, Wu, Wang, Chen, 2005. Journal of Power Sources 140, 125
Chan et al., 2008. Nature Nanotechnology 3, 31
electron
LiFePO4
SiliconJohn B. Goodenough
16
3 ways of doing work to a gel
a
aa
iiii
dVC
dAqdV
dAxTdVxB
state reference in volume species of ions of#
,a
tCa X
gel
apump
Pweight δx
δMa
a) reference state
b) current state
dry polymer
X = (X1, X2, X3)
x(X, t)
batteryΦ
δQq
a
Hong, Zhao, Suo. J. Mech. Phys. Solids 58 (2010) 558-577.
17
A field theory of thermodynamic equilibriumDeformation gradient
K
iiK X
txtF
,
,X
X
K
K Xt
tE
,
,~ X
X 0,
,
tBX
tsi
K
iK XX
tQX
tD
K
K ,,
~X
X
Equivalent conditions of equilibrium
iKiK F
Ws
K
KD
WE ~~
Gauss’s law
aaa
C
Wez
,,,~
, 21 CCWW DF
tCa ,X
fixfixaa CezCezqQ
Concentrations
Material model:
constanta
a
aaiiii dVCdAqdVdAxTdVxBWdV Equilibrium:
Hong, Zhao, Suo. J. Mech. Phys. Solids 58 (2010) 558-577.
18
microscopic processes
•Swelling increases entropy by mixing solvent and polymers.•Swelling decreases entropy by straightening the polymers.•Redistributing mobile ions increases entropy by mixing.•Neutrality reduces electrostatic energy.
-
-M
-
-
X
X
M
gel external solution
19
Free-energy function
DFFDF~
,,,~
,, 21pms
a WCCWWCW
FF detlog2321 iKiKs FFNkTW
Flory, Rehner, J. Chem. Phys., 11, 521 (1943)
sb
bs
bb
ss
ssa
m cvCC
CkTvCvχ
vCvC
CkTCW 1log11
log0
Free energy of mixing
Free-energy function
Free energy of polarization LKiLiK
p DDFF
εW
~~det2
1~,
FDF
Free energy of stretching
Zhao, Hong, Suo, Physical Review B 76, 134113 (2007)
20
Swelling regulated by concentration of ions
10-6
10-5
10-4
10-3
10-2
35
40
45
50
55
60
65
70
0.005
vc0
vCs +
1
Nv = 0.001 = 0.1
0.002
vC0 = 0.01
vC*s + 1
nonionic gel
Sw
ellin
g ra
tio
Concentration of ions in external solution
Concentration of fixed ions
21
Constrained swelling
Concentration of ions in external solution
10-6
10-5
10-4
10-3
10-2
30
32
34
36
38
40
42
0.005
vc0
vCs +
1
Nv = 0.001 = 0.1
0.002
vC0 = 0.01
vC*s + 1
Concentration of fixed ions
Sw
ellin
g ra
tio
gel
External solution
5.10
22
Debye length
x0
-
-
-
-
-
-
-
+
+
+
+
+
+
+
+0
22 ce
kTLD
0
gel external solution
23
-5 -4 -3 -2 -1 0-2
-1.5
-1
-0.5
0
x/LD
e/k
T
vc0 = 10-5
10-410-3
-5 -4 -3 -2 -1 00
2
4
6
8x 10
-5
x/LD
vs22
/kT
vc0 = 10-5
10-4
10-3
-5 -4 -3 -2 -1 0
-1
-0.5
0x 10
-3
x/LD
vQ/e
10-5
10-4
vc0 = 10-3
Nv = 0.001 = 0.1vC
0 = 0.002
-5 -4 -3 -2 -1 0
39
40
41
42
x/LD
vCs
vc0 = 10-5
10-4
10-3
In gel, near interface
x0
-
-
-
-
-
-
-
+
+
+
+
+
+
+
+
00 cc infinity
10 cv22s
22s
liquidgel
24
pH-sensitive hydrogel
HRCOORCOOHfixed mobile
aK
RCOOHHRCOO
25
ionsol
NkT
11
321
1
2
321321321
111log
Ssol v
kT
HH// cccc 1
HH//
cccc
cccccckTion HH
Acccc
H
KNc
ccA
AH
A H
321 vf
ccAAH
Donnan equilibrium
Electroneutrality
Constant of acidic dissociation
Conservation of particles
1
11
12
3
Marcombe, Cai, Hong, Zhao, Lapusta, Suo, Soft Matter 6, 784 (2010)Ricka, Tanaka,Macromolecules17, 2916 (1984).
Osmosis is balanced by elasticity
26
Free swelling
27
Constrained swelling
28
Finite element method
SSCCCWW )()(ˆHH
ccWW ,,ˆˆH
F
dAxTdVxBdVW iiii ˆ
dAxTdVxBnnnnWdV iiiiSS HH
H
,,, CCCWW F
HH// cccc
1
HH//
cccc
aAKN
cccvf
cccc
H
1HH
det/ F
Condition of equilibrium
Legendre transformation
Shengqiang Cai
Marcombe, Cai, Hong, Zhao, Lapusta, Suo, Soft Matter 6, 784 (2010)ABAQUS UMAT posted online.
29
pH-sensitive valve
DB
A
gel
pillar
Channel wall
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40
1
2
x 10-4
x/L
pvs/K
T
A/D=0.1
32.0DB
35.0DB
36.0DB
4.0DB
pH = 2
pH = 6
30
Summary
• Couple large deformation and electrochemistry.
• Swelling regulated by concentration of ions.
• Swelling regulated by pH.