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Bentonite Erosion and Colloid Transport Mats Jansson 1

The DLVO theory

Electro-Osmotic

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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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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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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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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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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.pdf

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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)