an introduction of salt-free systems 曾琇瑱 淡大數學系 徐治平 臺大化工系
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
An Introduction of Salt-Free Systems
曾琇瑱
淡大數學系
徐治平臺大化工系
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Charged entity (surface) in an electrolyte solution
• The dispersion medium contains no or negligible amount of ionic species except those dissociated from the dispersed entities.
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Salt-free Dispersion
Ex. Polyelectrolytes• Polyelectrolytes are polymers bearing diss
ociable 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.
NaCl Na+ + Cl-H2O
PAA (polyacrylic acid)
+ H2O + H3O+ -
• PSS (polystyrene sulfonate )A flexible polyelectrolyte
Constitution formula Simulation model
Synthetic Polyelectrolytes
Counterion
Microion (charged backbone)
• PPP (polyparaphenylene)A stiff polyelectrolyte
Constitution formula Analytical model
Microion (charged backbone)
Counterion
• Proteins
Linear charge density = 1 /( 4 4 Å) ≒ 0.6 e / nm
Amino acid
Amino acids
Primary protein structureis sequence of a chain of amino acids
1/4 basic units may be ionized : basic : lysine, arginine, histidine (-NH2+) acidic : aspartic, glutamic (-COO-)0.4 nm
COOH
NH2
R
Natural Polyelectrolytes
• Deoxyribonucleic acid (DNA) 2 nm
Linear charge density = 2 e / 3.4 Å ≒ 6 e / nm
0.34 nm
One of the most highly charged systems
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 decontam
ination processes• Controlled drug delivery• Composite polyelectrolyte self-assembled films for sensor appl
ications• Layer-by-layer polyelectrolyte-based thin films for electronic a
nd photonic applications• Polyelectrolyte multilayer membranes for materials separation• Nanostructures of Polyelectrolyte–Surfactant Complexes
Ex. Surfactants• An amphiphilic molecule! A surfactant con
sists of a hydrophobic (non-polar) hydrocarbon "tail" and a hydrophilic (polar) "head" group.
(like a tadpole)
SDS (sodium dodecyl sulfate)
Counterion
Oil loving tail Water loving head
Hydrophobic group Hydrophilic group
2 nm
• In order to minimize interactions between solvent and the insoluble portion of an amphiphilic molecule, the monomers aggregate into ordered structures.
Below CMC only monomers are present Above CMC there are micelles in equilibrium with monomers After that, they can act as emulsifiers
02468
101214
0 1Surfactant conc.
CMCCo
nc.
Monomers
Micelles
CMC
Monolayer
Micelle
Self-Assembly
Lamellar phase
Water
Surfactant
Oil
Cubic phase Reverse cubic phase
Hexagonal phase
Cylindrical/Rod-like micelles
Spherical micelles
Irregular bi-continuous phase
Monolayer
Reverse micelles
Monolayer
Surfactant Aggregates
Phase diagram of a surfactant-water-oil ternary solution
Only certain region creates reverse micelles
W
S
O
50 50
50 25
25
2575
75
75
Surfactant = 25 %
Oil (Non-polar) = 50 %
Water = 25 %
• As wash and cleaning reagents
Applications
• As emulsion stabilizersOil-in-water emulsion (micelle) Water-in-oil emulsion (reverse micelle)
• As micro/nano-reactors for material synthesis (organic or inorganic particles)Emulsion polymerization
1. Fusion2. Exchange3. Reduction4. Nucleation5. Growth
Microemulsion 1
Microemulsion 2
Aq. phaseof metal salt
Aq. phaseof reductant
Mix
Metal or metal oxide nanoparticle
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
• Electrical potential outside a micelle (ionic surfactant)• Total interaction energy between two micelles• Critical coagulation (coalescence) concentration• Various shapes: planar, cylindrical, spherical
oiloil
Water phase contains counterions
• Electrical potential inside a reverse micelle• Ionic distribution• Presence of other entity• Influence of ionic size
Problem II – Ionic distribution inside a reverse micelle
water phase contains counterionswater
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
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)n/1()/1( 0
Increase in electrolyte concentration
Electrical Double Layer
concentration gradient
electrical gradient
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• Electrical potential
• Ionic distribution
Problem I
Only the electrostatic stabilization is considered
Steric stabilization is neglected
oil oil
Analytical model = charged backbone + dissociated counterions
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aa00
rrOO
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a0: radius of particleb : valence of counterionsr : distance from particle center
Analysis
oil
Poisson-Boltzmann Equation
2 0
2expb
d r d r bF rbFC
dr r dr RT
2
2
1 byd y dye
dx x a dx b
RTFy /0x r a r a
2/12 )/2( RTIF 2/20bCI b
LetForm factorω=0, θ=0: planar ω=1, θ=1: cylindricalω=2, θ=1: spherical
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aa
00 rrOO
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boundary conditions
byebdx
dy
axdx
yd 12
2
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aa00
rrOO
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Cebdx
dy by 2
Planer micelle (ω =0)
byebdx
yd 12
2
Multiplying both sides by 2(dy/dx) gives
dx
dye
bdx
yd
dx
dy by22
2
2
dx
dye
bdx
dy
dx
d by2])[( 2
dyebdx
dyd by2
])[( 2 dyebdx
dyd by2
])[( 2
Cebdx
dy by 2
2 2)(
1/ 22 11 1ln sec tan 1
2sby
planary x eb
byebdx
dy
axdx
yd 12
2
Spherical micelle (ω =2)
[1 ( / )]u x a y 2
2
[1 ( / )]exp
[1 ( / )]
d u x a bu
dx b x a
Let
/ 1x a If ,2
2
1 bud ue
dx b
byebdx
dy
axdx
yd 12
2
byebdx
dy
axdx
yd 122
2
Therefore, 1/ 22 11 1ln sec tan 1
2sbyu x e
b
1/ 22 11 1 1ln sec tan 1
21
sbysphericaly x e
x ba
Cylindrical micelle (ω =1)
byebdx
dy
axdx
yd 12
2
bye
bdx
dy
axdx
yd 112
2
Let1
0 1x
aa
yv
xK a e
a
121 1
0 02
0
0
11
1 1 2 21 1
1 11 2
1 1
x xa a
a a
xK a
ax d v x dvK a e K a e
xa dx a dxxa K aa a
xK a
x xaa a
a a
1
01 11
0
11
2
1
xa
axx K a e bvaaa
xK a
ae v e
bxK a
a
K0,K1=zeroth and first-order modified Bessel function of the second kind
10 aa If x/a<<1 and , then 1
0
1
1
1
xK a
a
xK a
a
10
1x
aa
0
2
0 2
1 aK a e bva d vK a e e
dx b 0
20
2
1 aa
K a e bvd K a e v
edx b
0
1
22 10
1 1ln sec tan 1
2
asbK a e vaK a e v x e
b
0
1/ 22 1
0
11
ln sec tan 12
s
xby
cylindrical
xK a
a ey x e
K a b
Potential distribution near a single micelle
1/ 22 11 1ln sec tan 1
2sby
planary x eb
1
1spherical planary x y x
xa
x/a << 1
0
0
1x
cylindrical planar
xK a
ay x e y x
K a
x/a << 1
Potential distribution between two identical micelles
boundary conditions
1/ 22 11
ln sec tan 12
m
s mm
byb y yby
planar
ey e x e
b
0
2
Dx
using analogy
yspherical =
ycylindrial =
1 ms yybeIf
sby
m eD
by 2
1
2
2
2ln
2
then
• Osmotic pressure
• Electrical energy (repulsive force)
• Derjarguin approximation (planar spherical)
2200 22
be
bIRTCeCRTp mm by
bby
b 1
22
mbyebIRT
p
D
p pdDV1
2R pD
aV V dD
Electrostatic Interaction Energy
DLVO theory
• Total energy:
0TV T R AV D V D V D 12A
AaV
D
At CCC: D=Dc is a critical distance
0TdV
dD0TV
Comparison with Schulze-Hardy rule
22/2/22/,, 22243 ,,, scmcmcm bybybybycmca eeeebyF
Correction factor Fa,c=Fa,c(b,ys,ym,c)
Schulze-Hardy rule60 bCb
cacb FKbC ,60
,
62
3556144
FA
TRK
Present result
Scaled Surface Potential, ys
1 10 100
Cor
rect
ion
Fac
tor,
Fa,
c
0.0
0.5
1.0
b=123
0.839
Distribution of ions in a submicron-sized reverse micelle
2R
a
Aqueous phase
(a) A planar reverse micelle
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Aqueous phase
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R
a
(b) A cylindrical or a spherical reverse micelle
+ Counterions
Surfactant ions
Neutral Surfactants
2R
a
Aqueous phase
(a) A planar reverse micelle
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Aqueous phase
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R
a
(b) A cylindrical or a spherical reverse micelle
+ Counterions
Surfactant ions
Neutral Surfactants
2R
a
Aqueous phase
(a) A planar reverse micelle
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Aqueous phase
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R
a
(b) A cylindrical or a spherical reverse micelle
+ Counterions
Surfactant ions
Neutral Surfactants
Problem II
water
planar slit cylindrical or spherical cavity
Analysis
cplanar
by
planar yeaxb
ycplanar
22
2
2secln
1
Results
c
bu
spherical ueaxbax
yc
22
2
2secln
1
/2
1
c
bv
a
axa
lcylindrica veaxbeaK
eaxaKy
c
22
0
/21
2
2secln
1/2
21
2
21tan
cplanar
cplanars
bybyby e
re
2
/2
22
ln2
syaxbc
erb
u
2
/2/ /200
22
ln2
axas
a eaxaKyeaKbc
erb
v
1
1spherical planary x y x
xa
c
bu
spherical ueaxbax
yc
22
2
2secln
1
/2
1
outside
inside
c
bv
a
axa
lcylindrica veaxbeaK
eaxaKy
c
22
0
/21
2
2secln
1/2
0
1/ 22 1
0
11
ln sec tan 12
s
xby
cylindrical
xK a
a ey x e
K a b
outside
inside
1/ 22 11
ln sec tan 12
m
s mm
byb y yby
planar
ey e x e
b
cplanar
by
planar yeaxb
ycplanar
22
2
2secln
1planar slit
Effect of Ionic Size
2R
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Aqueous phase
(a) A planar reverse micelle
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R
a
(b) A cylindrical or a spherical reverse micelle
+ CounterionsSurfactant ions
Neutral Surfactants
2R
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Aqueous phase
(a) A planar reverse micelle
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Aqueous phase
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R
a
(b) A cylindrical or a spherical reverse micelle
+ Counterions
Surfactant ions
Neutral Surfactants
2R
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Aqueous phase
(a) A planar reverse micelle
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Aqueous phase
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R
a
(b) A cylindrical or a spherical reverse micelle
+ Counterions
Surfactant ions
Neutral Surfactants
Tsao, Sheng, and Lu, J. Chem. Phys. 113, 10304 (2000) – Ionic size becomes unimportant when (R/a)>40
Distributions of Electrical Potential and Ionic Concentration*
* Borukhov, Andelman, & Orland, Electrochimica Acta. 46, 221 (2000)
ze
zezec
dr
dr
dr
d
r
exp1
exp1 022
Rr 0
ze
zecrc
exp1
exp)( 0 1)( TkB 0
3ca
y
yR
dx
dyx
dx
d
x
exp1
exp1 222
y
y
c
xc
exp1
exp)(
0 2/1
022 / Tkcez B
10 x
Main Results
1.Neglecting size effect will underestimate the charge density on surfactant shell
2. Size effect is inappreciable if (R/a) exceeds about 40
2R
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Aqueous phase
(a) A planar reverse micelle
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Aqueous phase
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R
a
(b) A cylindrical or a spherical reverse micelle
+ CounterionsSurfactant ionsNeutral Surfactants
2R
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Aqueous phase
(a) A planar reverse micelle
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Aqueous phase
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R
a
(b) A cylindrical or a spherical reverse micelle
+ Counterions
Surfactant ions
Neutral Surfactants
2R
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Aqueous phase
(a) A planar reverse micelle
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Aqueous phase
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R
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(b) A cylindrical or a spherical reverse micelle
+ Counterions
Surfactant ions
Neutral Surfactants
=1 nm-2, Kd=5 nm-3
a=0.5 nm
Xs=0.641
a=0 nm
Xs=0.519
a=1 nm
Xs=0.775
R=15 nm
Zaq
Zss CSSC )()()(
=1 nm-2, Kd=5 nm-3
a=0 nm
0.5 nm
1 nm
The larger the XS, or the larger the size of counterions, the greater the deviation in CS if the size of counterions is neglected
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
R/a0 3 6 9 12 15
XS
0.3
0.4
0.5
0.6
0.7
0.8
1
2
4
3
=1 nm-2
a=0.7 nma=0.5 nm
Kd=1 nm-3
Kd=5 nm-3
=free energy per surfactant molecule due to dissociation TkBd /
Kd=1 nm-3
Kd=10 nm-3
a=0.3 nm
a=0 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
xp
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
XS
0.1
0.2
0.3
0.4
0.5
0.6
1
2
3
4
a=0.3 nm
a=0 nm
Kd=2 nm-3
Kd=0.5 nm-3
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
Rod-like polyelectrolyte
Star-shapedpolyelectrolyte
Spherical polyelectrolyte brush
Ex. Suspensions of polyelectrolytes and surfactant micelles
Bilayer sheet Sphericalmicelle
Liposome
Nature
A neutral polymer molecule tangled in a random coil.
A polyelectrolyte expands becauseit’s like charges repel each other.
more viscous
NaCl
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.
Physico-chemical properties of polyelectrolyte solutions differ significantly fromthat of low-molecular electrolytes as also from those of neutral polymers, e.g.
• Actin filaments 7 nm
• As a cell membrane-mimetic medium for the study of protein-membrane interactions.
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Mechanism 1 - Charge adsorption and neutralization
Mechanism 2 - Polymer Bridging
colloid polymer
Mechanism 3 – Entrapped by complex mesh
• 表面官能基解離表面官能基解離• 特定離子吸附特定離子吸附• 離子結晶體溶解離子結晶體溶解• 同型置換作用同型置換作用
HH
HH++
HHHHHH++
- --COOH
AgAg++
-
AgISiSi+4+4
AlAl+3+3
Clay
Stability of a Colloidal Dispersion
Origin of surface chargeOrigin of surface charge