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7/28/2019 Dlvo Theory - Kth
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Bentonite Erosion and Colloid Transport Mats Jansson 1
The DLVO theory
Electro-Osmotic
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Bentonite Erosion and Colloid Transport Mats Jansson 2
The Stern Layer
The Stern layer
Ions are firmly attached(immobilized) to colloid surface
The potential drops from thesurface potential almost linearlythrough the Stern layer
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Bentonite Erosion and Colloid Transport Mats Jansson 3
The Diffuse Double Layer
The Stern layer
The Diffuse layer
The DiffuseDouble Layer
Potential
Distance from Colloid
Surface Potential
Stern Layer
Zeta PotentialDiffuse Layer
Zeta Potential(Low Concentration)
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The Repulsive Energy
x
(x)
()=0
d
Distance between Stern layers
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Bentonite Erosion and Colloid Transport Mats Jansson 5
The Repulsive Energy
x
(x)
()=0
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The Repulsive Energy
x
(x)
()=0
d/2
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The Repulsive Energy
(x)
d/2
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The Repulsive Energy
(x)
d/2
Excess of total ion concentration at d/2=> Osmotic pressure
p = pd/2 - p= RT [c+d/2 + c
-d/2 - 2c]
The osmotic pressure becomes
p = RT 2c (cosh (z d/2) 1)
(d/2 = F d/2 / (RT)
Together with the Bolzmann equation
(F = Faradays constant)
RT
Fz-
i,xi,
xi
ecc
=
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The Repulsive Energy
(x)
d/2
p = RT 2c (cosh (z d/2) 1)
(d/2 = F d/2 / (RT)
Cut the system in two at x=d/2. Look at the point x=d/2As the electrical field strength is zero,the electrical force exerted on either half of the system is zero
The remaining force is due to the osmotic pressure difference(described by the equation below)
The repulsive force is electro-osmotic in nature, not electrostatic in the proper sense!
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The Repulsive Energy
p = RT 2c (cosh (z d/2) 1)
The repulsive force can be calculated ifd/2 is known
Evaluating d/2 is very difficult
Approximation d/2 1 is useful (fulfilled when dis suff. large)
d/2 can be obtained from superposition the potentials of the isolated platesand approximated/2 = (8/z) 0 e-d/2
0 = surface charge density
d/2 = (8/z) 0 e-d/2
lengthDebye1
,
22
==
RT
czF ii
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The Repulsive Energy
p = RT 2c (cosh (z d/2) 1)
d/2 = (8/z) 0 e-d/2
Sinced/2 1cosh (x) = 1 + x2/2
p = 64 RT c 02 e-d
The electro-osmotic energy per surface area is then
el = - d p dx
el
= 64 RT c
0
2 (1/) e-d
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The Attractive Energy
The most important interaction energy besides the electro-osmoticis the van der Waals energy (dispersion energy)
For our system the van der Waals energy per surface area is
vdW = - A / (12 d2
)
A is the Hamaker constant (typically about 10-20 J)A is very difficult to determine experimentally
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DLVO theory
Derjaguin-Landau-Verwey-Oberbeek
= 64 RT c 02 (1/) e-d A / (12 d2)
=el +vdW
Repulsion (electro-osmotic)
Attraction (van der Waal)
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DLVO theory
= 64 RT c 02 (1/) e-d A / (12 d2)
Increase c
222
2
0 1264
22
d
A
eczF
RT
cRT
dRT
czF
=
=> Repulsion decreases
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Repulsion c varied
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10
c=1
c=0.1
c=0.01
222
20
12
64
22
d
Ae
czF
RTcRT
dRT
czF
=
dce
c
cy
=
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Secondary minimum
Secondary minimum
If the surface area of the particle is largeEnergy in secondary minimum > kT
=> Causes a stabilization (reversible coagulation)
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DLVO summary
Electro-osmotic repulsion
van der Waal attraction(difficult to obtain a correct Hamaker constant)
At long and short distances vdW > Electro-osmotic
Electro-osmotic barrier
When surface are is large reversible coagulation mayoccur at secondary minimum
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Extended DLVO theory
Hydration forces
Hydrophobic forces
Oscillatory forces
Membrane fluctuations
Water structure forces
When the DLVO theory fails to explain experimental results,an extra term is often added, such as
The theory is then called the Extended DLVO theory
d d h h d
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Bentonite Erosion and Colloid Transport Mats Jansson 19
DLVO extended with hydration
DLVO theory fails to describe systems withvery hydrophobic or very hydrophilic particles
or in other words
DLVO theory is only applicable for lyophobic colloidswith advancing contact angle a between 15 and 64
(a for Na-montmorillonite = 17)
Small Large
DLVO d d i h h d i
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Bentonite Erosion and Colloid Transport Mats Jansson 20
DLVO extended with hydration
Small Large
The DLVO expression can be extendedwith a hydration component:
=el +vdW + H
H = a/2 (C1 e-d/D1 + C2 e
-d/D2)
C1, C2 constants, D1, D2 decay lengths
E t d d DLVO DLVO
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Extended DLVO vs DLVO
Silica particles (r = 6 nm) in 0.01M NaCl
Shu
kun
Chen
Thesis
200
7
DLVO th D b k
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DLVO theory: Drawbacks
Lifschitz theory of attractive forces
Ion fluctuation forces
Charge regulations in the double layer
Specific ion effects
The DLVO theory does not account for
DLVO th D b k
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DLVO theory: Drawbacks
Proper description of vdW force
Surface charge density
Surface potentials
Debye length, etc.
Even so, an extended term is often needed to
explain the behaviour of a system
The DLVO theory has a numberof (adjustable) parameters
Forces can vary in magnitude by a factor of 50 or moreby simply changing the counter-ion from e.g. bromide to acetateBostrm et alPhys Rev Lett 87, (16) 8103 (2001) (click here to read)
Pashley et alJ Phys Chem 90 1637 (1986)
Concluding remarks
http://www.kemi.kth.se/nuchem/colloid/bostrom.pdfhttp://www.kemi.kth.se/nuchem/colloid/bostrom.pdf7/28/2019 Dlvo Theory - Kth
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Concluding remarks
The DLVO theory has been established since 1945
It can often describe trends and tendencies, but
In many articles I found the DLVO theory fails to
quantitatively explain/(predict) experimental results
(without parameter fitting or extended theories)
"... DLVO-theory is completely inadequate (to put it gently)
in almost every system so far investigated".
Christiansen J Dispersion Sci Technol. 9: 171 (1988)