An Introduction of Salt-Free Systems
曾琇瑱
淡大數學系
徐治平
臺大化工系
Charged entity (surface) in an electrolyte
solution
+
-
+
-
+
+
+
-
+
+
-
+
-
-
-
+
-
-
-
+
+
+
-
-
Salt-free Dispersion
• The dispersion medium contains no or
negligible amount of ionic species except
those dissociated from the dispersed
entities.
+
-
+
+
-
-
+
-
+
+
-
Ex. Polyelectrolytes
• Polyelectrolytes are polymers bearing
dissociable functional groups, which, in
polar solvents (water), can dissociate into
charged polymer chains (macroions) and
small counterions.
• Like salts, their solutions are electrically
conductive. Like polymers, their solutions
are often viscous.
PAA (polyacrylic acid)
NaCl
H2O
Na+ + Cl-
+ H 3 O+
+ H2O
-
Synthetic Polyelectrolytes
• PSS (polystyrene sulfonate )
A flexible polyelectrolyte
Counterion
Microion (charged backbone)
Constitution formula
Simulation model
• PPP (polyparaphenylene)
A stiff polyelectrolyte
Counterion
Microion (charged backbone)
Constitution formula
Analytical model
Natural Polyelectrolytes
• Proteins
Primary protein structure
is sequence of a chain of amino acids
Amino acids
NH2
COOH
Amino acid
R
1/4 basic units may be ionized :
basic : lysine, arginine, histidine (-NH2+)
acidic : aspartic, glutamic (-COO-)
0.4 nm
Linear charge density = 1 /( 4  4 Å) ≒ 0.6 e / nm
• Deoxyribonucleic acid (DNA)
0.34 nm
Linear charge density = 2 e / 3.4 Å ≒ 6 e / nm
 One of the most highly charged systems
2 nm
Applications
• Polyelectrolyte gel for artificial muscles, cartilage, organs, etc.
• Hydrophobically modified polyelectrolytes and polyelectrolyte
block-copolymers for biomedical applications
• Ion exchange resins for separation, purification, and
decontamination processes
• Controlled drug delivery
• Composite polyelectrolyte self-assembled films for sensor
applications
• Layer-by-layer polyelectrolyte-based thin films for electronic
and photonic applications
• Polyelectrolyte multilayer membranes for materials separation
• Nanostructures of Polyelectrolyte–Surfactant Complexes
Ex. Surfactants
(like a tadpole)
• An amphiphilic molecule! A surfactant
consists of a hydrophobic (non-polar)
hydrocarbon "tail" and a hydrophilic (polar)
"head" group.
SDS (sodium dodecyl sulfate)
Oil loving tail
Water loving head
Counterion
Hydrophobic group
2 nm
Hydrophilic group
Self-Assembly
• In order to minimize interactions between
solvent and the insoluble portion of an
amphiphilic molecule, the monomers
aggregate into ordered structures.
CMC
Micelle
14
12
10
8
6
4
2
0
0
Conc.
Monolayer
Monomers
CMC
Micelles
Surfactant conc.
Below CMC only monomers are present
 Above CMC there are micelles in equilibrium with monomers
 After that, they can act as emulsifiers
1
Surfactant Aggregates
Cubic phase
Surfactant
Reverse cubic phase
Lamellar phase
Hexagonal phase
Cylindrical/Rodlike micelles
Irregular bicontinuous phase
Spherical micelles
Monolayer
Reverse micelles
Water
Oil
Monolayer
Phase diagram of a surfactant-water-oil ternary solution
Oil (Non-polar) = 50 %
S
Surfactant = 25 %
Water = 25 %
75
25
50
50
25
W
75
75
50
25
O
Only certain region creates reverse micelles
Applications
• As wash and cleaning reagents
• As emulsion stabilizers
Oil-in-water emulsion (micelle)
Water-in-oil emulsion (reverse micelle)
• As micro/nano-reactors for material
synthesis (organic or inorganic particles)
Emulsion polymerization
Microemulsion 1
Aq. phase
of metal salt
Mix
Aq. phase
of reductant
1. Fusion
2. Exchange
3. Reduction
4. Nucleation
5. Growth
Metal or metal
oxide nanoparticle
Microemulsion 2
silver colloids (yellow), gold colloids (red) and silver-core, gold-shell particles (violett)
• Preparation of nanotubes via surfactant
micelle-template
• As containers for targeted drug delivery
Problem I – Stability of a micelle system
oil
oil
Water phase contains counterions
• Electrical potential outside a micelle (ionic surfactant)
• Total interaction energy between two micelles
• Critical coagulation (coalescence) concentration
• Various shapes: planar, cylindrical, spherical
Problem II – Ionic distribution inside a
reverse micelle
water
water phase contains
counterions
• Electrical potential inside a reverse micelle
• Ionic distribution
• Presence of other entity
• Influence of ionic size
Stability of a Colloidal Dispersion
stable
unstable
DLVO Theory: Total interaction energy VT
= Electrical (repulsive) energy VR + van der Waals
(attractive) energy VA
Stable system VT > 0; Unstable system VT < 0
Double Layer Compression Mechanism
+
+
+ - - - +
- - -- - +
+
Increase in
electrolyte
concentration
(1 /  )  (1 / n0 )
-
- +
- -- - +
- -- - -
+
+
+
+
+
-
- - +
+ - - - +
-+ - -- - +
+
+
+ +
+
+
- - +
+ - - -- +
-+ - - - +
+
+
+
Electrical Double Layer
concentration gradient
+
-
+
-
+
+
+
-
+
+
-
+
-
• Electrical potential
• Ionic distribution
-
-
-
+
-
-
-
+
+
+
-
-
electrical gradient
Problem I
oil
oil
Only the electrostatic
stabilization is
considered
Steric stabilization is
neglected
Analysis
Analytical model = charged backbone + dissociated counterions
+
+
+
+
a0
O
+
+
r
+
-
oil
+
+
-
a0: radius of particle
b : valence of counterions
r : distance from particle center
Poisson-Boltzmann Equation
d 2  r   d  r  bFCb0
 bF  r  


exp 

2
dr
r dr

RT


Let
y  F / RT
x   r   a0   r   a
I  Cb0b2 / 2
  (2IF 2 / RT )1/ 2
Form factor
ω=0, θ=0: planar
ω=1, θ=1: cylindrical
ω=2, θ=1: spherical
-
+
+
+
d y
 dy 1 by

 e
2
dx
x  a dx b
2
a
O
+
-
+
0
+
r
+
+
+
-
-
 dy 1 by


e
2
x  a dx b
dx
d2y
boundary conditions
-
+
+
-
+
+
a0
O
+
+
r
+
-
+
+
-
Planer micelle (ω =0)
d2y
 dy
1 by

 e
2
x  a dx b
dx
d 2 y 1 by
 e
2
b
dx
Multiplying both sides by 2(dy/dx) gives
dy d 2 y 2 by dy
2
 e
2
dx dx
b
dx
d dy 2
2
dy
[( ) ]  eby
dx dx
b
dx
dy 2
2
) ]   ebydy
dx
b
dy 2
2 by
d[( ) ]  e dy
dx
b
 d[(
dy 2
2 by
( )  2 e C
dx
b
dy
2 by

e C
dx
b
y planar
1/ 2  
1  2 1
bys
1
 ln sec  
x  tan e  1  
b 
 2



Spherical micelle (ω =2)
d2y
 dy
1 by

 e
2
x  a dx b
dx
Let u  [1  ( x / a)] y
d2y
2 dy 1 by

 e
2
x  a dx b
dx


d 2u [1  ( x / a)]
bu

exp 

2
dx
b
[1

(
x
/
a
)]


2
d
u
1
bu
If x / a  1,

e
dx 2 b
1/ 2  

1
1

by
2

1
s
Therefore, u  ln sec 
x  tan e  1  

b 
 2


yspherical




1/ 2  
 1 
1  2  1
bys
1

x  tan e  1  
 ln sec  
 2

 1  x   b 


 a  


Cylindrical micelle (ω =1)
d2y
 dy
1 by

 e
2
x  a dx b
dx
Let
v
d2y
1 dy 1 by

 e
2
x  a dx b
dx
y
  x 
K 0  a 1    e
  a 
 x
a 1 
 a


  x 
K
a
1

 x
1 


 a1 x 
a
  x   a1 a  d 2v
  x  
1



  2  e  a  dv 
K 0  a 1    e

K
a
1


2

0  
 
2
x
a
dx
a
dx



x










  a 1

K
a
1



0  

  a 

  a 



   x 
 x
K
a
1

  x   a1 a 
1 


 a1 x 


a 
  x  
1
1
1 K0 a1 a  e bv
  a



K 0  a 1    
 2 
 2 e
v e
b
 x 
  x 
  a    a 1  x  

a
1

K
a
1




 0 

  a  

a
 a  



K0,K1=zeroth and first-order modified Bessel function of the second kind
If x/a<<1 and a  a0   1, then
2
d
v 1 K0  a eabv
a
K0  a  e
 e
2
dx
b
1
x

a 1  
 a
  x 
K1  a 1   
  a   1
  x 
K 0  a 1   
  a 
0
d 2  K0  a  ea v 
dx2
1 
 2  1
bK0  a ea vs
a
1
K0  a  e v  ln sec 
x  tan e
1
b 
 2


ycylindrical

1
2
1 K0  a eabv
 e
b



 

   x  
 K 0  a 1  a    x 
1/ 2  
1
  
  e
bys
2 
1

x  tan e  1  
 ln sec  
K0  a 
 2


b 




Potential distribution near a single micelle
y planar
1/ 2  
1  2 1
bys
1
 ln sec  
x  tan e  1  
b 
 2

yspherical  x  

1
 x
1  
 a
y planar  x 

x/a << 1
  x 
K 0  a 1   
 a  x

ycylindrical  x  
e y planar  x 
K0  a 
x/a << 1
Potential distribution between two identical micelles
boundary conditions
y planar
bym



1/ 2 
1 
e
 bym

D
b
y

y
 ln e sec2 
x  tan 1 e  s m   1  0  x 
2
b 
2






using analogy
If
yspherical =
ycylindrial =
e
b  y s  ym 
 1
1
2  D
2  2 by s
then y m 
ln
 e
2
b  2





Electrostatic Interaction Energy
• Osmotic pressure

p  RT C e
0 by m
b


• Electrical energy (repulsive force)
Vp  
1

D


 2 bym 2   p  2 e by m  1
 C  IRT 2 e  2 
2
IRT
b
b
b


0
b
pdD
• Derjarguin approximation (planar
a 
VR  2  V p dD
 D
spherical)
DLVO theory
• Total energy:
VT  D  VR  D  VA  D
Aa
VA  
12 D
VT  0
At CCC: D=Dc is a critical
distance
VT  0
dVT
0
dD
Comparison with Schulze-Hardy rule
Schulze-Hardy rule
0
Cb
b
6
Present result
Cb0,c  Kb 6 Fa,c
144 R T 
K
2
6
A F
6
5
5
3
Correction factor Fa,c=Fa,c(b,ys,ym,c)

Fa ,c   3  bym,c  e
bym ,c
 4e

bym ,c / 2 2
2e
bym ,c / 2
 2 2e

bys / 2 2
1.0
Correction Factor, Fa,c
0.839
3
2
b=1
0.5
0.0
1
10
Scaled Surface Potential, ys
100
+ +
+
+
+
+
+
Problem II
+
+
Aqueous phase
+
+
+
+
+
+
+
+
+
R
+
+
+
+
+
+
+
+
+
+
+
+
a
+
+
+
a
++
Aqueous phase
Distribution of ions
in+ a submicron+
+
+
sized reverse micelle
+
(b) A cylindrical or a spherical reverse micelle
+
2R
(a) A planar reverse micelle
Counterions
Surfactant ions
Neutral Surfactants
+ +
+
+
+
+
+
+
+
+
+
R
+
+
+
+
+
+
+
Aqueous phase
+
Aqueous phase
+
+
+
+
+
a
water
+
+
+
+
+
+
+
+
+
+
a
+
+
+
++
+
2R
(a) A planar reverse micelle
(b) A cylindrical or a spherical reverse micelle
+
Counterions
Analysis
planar slit
cylindrical or
spherical cavity
Results
y planar
by planar c
1  2  2

 ln sec
x  a e 2
 2
b 

yspherical
ycylindrical

  y planar c


bu c



1
1
2
2
2




ln
sec
x

a
e


 2


2

x
/
a
b





   uc


bvc
K1 a2  x / a e a 2 x / a  1  2  2
2




ln
sec
x

a
e

 2
K 0 a e a
b 


  vc


2r
by s by planar c


tan  e
1  
e


2
1

2 

uc  ln
 b 2  x / a  y s
b 
2
 2 r  2e
by planar c
2






2 

vc  ln
 bK 0 a e a  y s / K 0 a 2  x / a e a  2 x / a 
b 
2
 2 r  2e





bym


1/ 2 
e
1 

 bym
b ys  ym 
1
2
 1 
x  tan e
y planar  ln e sec 
2
b 






by planar c

1  2  2
2
  y planar c

y planar  ln sec
x  a e
 2

b 


yspherical  x  
yspherical
ycylindrical
1
 x
1  
 a
y planar  x 
outside
bu c

 1  2 2
1
2




ln
sec
x

a
e


 2
 2  x / a  b 


   uc


   x  
 K 0  a 1  a    x 
1/ 2  
1


  e
bys
2 
1
 
ln
sec

x

tan
e

1


 2

K0  a 



b 


ycylindrical
planar slit


inside
outside
bvc
K1 a2  x / a e a 2 x / a  1  2  2
2




ln
sec
x

a
e

 2
K 0 a e a
b 


  vc


inside
+
+
+
a
+
++
Aqueous phase
+
+
+
+
+
+
+
+
+
+
+
R
Effect of Ionic Size
ical or a spherical reverse micelle
2R
(a) A planar reverse micelle
Counterions
Surfactant ions
Neutral Surfactants
+ +
+
+
Aqueous phase
+
+
a
+
+
Aqueous phase
+
+
+
+
+
R
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
a
+
+
+
++
+
2R
A planar reverse micelle
(b) A cylindrical or a spherical reverse micelle
+
Counterions
+
Tsao,
+ Sheng, and Lu, J. Chem. Phys. 113, 10304 (2000) –
Surfactant ions
+
+
+Ionic +size becomes unimportant when (R/a)>40
+
Neutral Surfactants
+ +
+
+
Aqueous phase
+
+
+
+
+
a
+
+
+
Distributions of Electrical Potential and Ionic Concentration*
1 d  2 d 
exp ze 
 c0 ze 
r






r 2 dr  dr 


 1      exp ze 
c(r ) 
c0  exp ze  
1      exp ze  
  (k BT ) 1
1 d  2 dy 
exp y 
2
x
  R 
2
x dx  dx 
1      exp y 
c( x)
exp y 

c0
1      exp y 
0rR
  a3c0
0  x 1
  z e c0 / k BT 
2 2
1/ 2
* Borukhov, Andelman, & Orland, Electrochimica Acta. 46, 221 (2000)
Main Results
2R
(a) A planar reverse micelle
60
 =1
+ +
nm-2,
Kd=5
+
nm-3
50
+
+
+
+
+
SC( s)  S(Zs)  C(Zaq)
+
Xs=0.519
+
+
R
+
+
+
+
+
+
+
+
+
+
a
+
+
+
Aqueous phase
+
40
c(x)/c0
+
a=0 nm
+
+
R=15 nm
+
+
+
+
+
+
+
++
Aqueous phase
+
+
+
a
a=0.5 nm
2R
(b) A cylindrical or a spherical reverse micelle
Xs=0.641
30
20
Counterions
Surfactant ions
Neutral Surfactants
+
a=1 nm
(a) A planar reverse micelle
Xs=0.775
+ +
+
3
10
+
+
1
Aqueous phase
+
+
+
+
+
+
+
R
+
+
0
+
+
+
+
+
Aqueous phase
+
2
a
+
+
+
+
+
+
+
+
+
+
+
+
+
+
a
+
+
+
++
+
2R
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(a) A planar reverse micelle
1.0
(b) A cylindrical or a spherical reverse m
x
Counterions
1.Neglecting size effect will underestimate the charge density
on
Surfactant ions
Neutral Surfactants
surfactant shell
+ +
+
+
+
+
+
+
+
+
Aqueous phase
+
+
+
+
+
+
+
+
+
+
+
a
+
+
+
2. Size effect is inappreciable if (R/a) exceeds about 40
+
+
+
R
+
+
25
 =1 nm-2, Kd=5 nm-3
20
1
cS/c0
15
a=0 nm
0.5 nm
10
2
3
5
1 nm
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
XS
The larger the XS, or the larger the size of counterions, the
greater the deviation in CS if the size of counterions is neglected
0.8
 =1 nm-2
Kd=5 nm-3
2
0.7
1
0.6
a=0.5 nm
a=0.7 nm
XS
Kd=1 nm-3
4
0.5
3
0.4
0.3
0
3
6
R/a
9
12
15
Increase in the size of a reverse micelle has the effect of raising
the degree of dissociation of surfactants; XS reaches the
equilibrium value when R/a exceeds a certain value
 d / k BT =free energy per surfactant molecule due to dissociation
0
1
Kd=1 nm-3
2
-1
d/kBT
a=0 nm
a=0.3 nm
Kd=10 nm-3
3
-2
4
0
1
2
3
4
5
6
7
8
R (nm)
The larger the counterions, the smaller the chemical potential, i.e.,
the steric effect of counterions is positive to the decrease of
chemical potential
a=0.3 nm
0.6
Kd=2 nm-3
1
0.5
2
0.4
XS
Kd=0.5 nm-3
3
0.3
4
a=0 nm
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
xp
Variation of fractional dissociation as a function of the scaled size of a particle for
the case when  =2 nm-2 and R=10 nm.
Thank you
Ex. Suspensions of polyelectrolytes and
surfactant micelles
Rod-like
polyelectrolyte
Bilayer sheet
Spherical
polyelectrolyte brush
Star-shaped
polyelectrolyte
Spherical
micelle
Liposome
Nature
Physico-chemical properties of polyelectrolyte solutions differ significantly from
that of low-molecular electrolytes as also from those of neutral polymers, e.g.
NaCl
A neutral polymer molecule
tangled in a random coil.
A polyelectrolyte expands because
it’s like charges repel each other.
more viscous
Salt makes polyelectrolytes in solution collapse into random coils.
What? You don't believe me?
1. Take some hair gel and put a big glob of it in a bowl.
2. Now take a salt shaker, and pour on the salt.
3. When you do this, the gel will collapse into a pretty boring ordinary liquid.
• Actin filaments
7 nm
• As a cell membrane-mimetic medium for
the study of protein-membrane
interactions.
Mechanism 1 - Charge adsorption and neutralization
+
------ - - - --+ - +
+
+
+
-
+ +
+ + +
+
+
+
+
+
+
-
+
-
- - - + - +
+
+
-
+
------ - - - --+ - +
+
+
- + + +
+ +
-
+ + +
+ +
-
Mechanism 2 - Polymer Bridging
colloid
polymer
Mechanism 3 – Entrapped by complex mesh
Stability of a Colloidal Dispersion
Origin of surface charge
•
•
•
•
表面官能基解離
特定離子吸附
離子結晶體溶解
同型置換作用
H+
H+
H
-
H
H
-COOH
Ag+
Al+3
Clay
Si+4
-
AgI