aem lect12

Advanced Electronic Ceramics I (2004)http://www.zeta-meter.com/

DLVO theory: General

DLVO (Derjaguin, Landau, Verwey, Overbeek)

♦ Electric Double Layer begins to interfere- electrostatic repulsion becomes significant

♦ Van der Waals Attraction

In order to agglomerate, two particles on a collisioncourse must have sufficient kinetic energy due to their velocity and mass to “jump over” the energybarrier

Steric Stabilization- adsorption of polymer on particle surface prevent

the particles from coming close enough for van derWaals attraction to cause flocculation

For flocculation- mechanical bridging by long chain polymer

enables flocculation in spite of the electrostatic forces that would normally make them repel each other.

Advanced Electronic Ceramics I (2004)

DLVO theory: GeneralPotential Energy Curve

Φtot = ΦR + ΦARepulsion Born repulsion for atoms

Double layer for colloidsAttraction x-6 Van Der Waals for atoms

D-2 for platesR/D for spheres

Intermolecular force1) Strong Bonding ionic bonding

covalent bondingmetallic bonding

2) Weak Bonding Van Der Waals Bonding1. Debye (permanent dipole-induced dipole)2. Keesom (permanent dipole-permanent dipole)3. London (induced dipole-induced dipole)


Van Der Waals Bonding for atoms

1. Debye (permanent dipole-induced dipole)

2. Keesom (permanent dipole-permanent dipole)

3. London (induced dipole-induced dipole)

ΦVDWA = -βx-6 β: various interaction parameters(Jm6)

α1, α2: polarizability µ1: permanent dipole

momentµ2: induced dipole momentx: distance from dipole


Van Der Waals Attraction for plates

ρNA/M : number of molecule per cubic centimeter(M= molecular weight)A: Hamaker constant (energy unit): Typical range : 10-20 ~ 10-19 J - a materials constant that depends on the dielectric properties of twomaterials and the intervening medium

Dδ δ

As δ → ∞

ΦR = [64nokTγo2/(κ)] exp (-κD)

where γo = [exp(Zeϕo/2kT)-1]/[exp(Zeϕo/2kT)+1](assumption D >> κ-1)


Van Der Waals Attraction for spheres

As R >> s

s 2R2R

ΦR = [64πRnokTγo2/(κ2)] exp (-κs)

where γo = [exp(Zeϕo/2kT)-1]/[exp(Zeϕo/2kT)+1]assumption: D>> κ-1


Van der Waals Attraction and Surface Tension

- Evaluation of Hamaker constant via surface tension

WLL

L

L

L

WLL: work of cohesion

- The difficulties of calculating β due to the lack of the informationabout the polarizability, permanent dipole orientation, chemical homogeneity of the surface


Van der Waals Attraction and Surface Tension

WLL = 2γL = ΦD=∞ - ΦD=do

2γL = A/(12πdo2)

A=24πγLdo2

when additional interaction besides London forces operates betweenthe moleculeA = 4πγddo

2/(1.2)

The estimation of Hamaker constant via the direct measurement of VDW forces as a function of separation using the displacement ofsensitive spring and also from capacitance type measurement is not easy due to the external vibration and surface roughness

Do: intermolecular spacingγd: dispersion component of surface

tension


Hamaker constant 1

When the materials interact across a liquid, their Hamaker constants decreases but remains high.


Hamaker constant 2

2 1 2 1 2 12 1

particle solvent

Flocculationoccur+ +

Change in potential energy in above reaction∆Φ = Φ11 + Φ22 -2Φ12

ΦA∝ AA212 = A11 + A22 -2A12 (A12 = (A11A22)1/2 : geometric mixing rule)∴ A212 = (A11

1/2 - A221/2)2

1. Effective Hamaker constant A212 always >0( identical particles exert a net attraction due to van der Waals forcesin a medium as well as under vacuum)

2. Embedding a particles in a medium generally diminishes the VDWA.3. No interaction at A11=A22

- can be used to evaluate the A11 and A22


Repulsive and Attractive Potentials

Both mode of interaction become weakeras the separation becomes larger.At sufficiently large spacing the particles exert no influence each other.

For spherical particle

s 2R2R

r


Repulsive and Attractive Potentials

Metastable: possessing a degree of kinetic stability eventhough it lacks thermodynamic stability

Kinetic of flocculation offer some clues as to the height of the maximum


DLVO: Hamaker constant

For platesΦtot = [64nokTγo

2/(κ)] exp (-κd) -A/(12πd2)where γo = [exp(Zeϕo/2kT)-1]/[exp(Zeϕo/2kT)+1](assumption D >> κ-1)

A212↑ → VDWA [-A/(12πd2)]↓


DLVO: ϕo

For platesΦtot = [64nokTγo

2/(κ)] exp (-κD) -A/(12πd2)where γo = [exp(Zeϕo/2kT)-1]/[exp(Zeϕo/2kT)+1](assumption D >> κ-1)

ϕo ↑ → γo ≈ 1 → ΦR ↑

sensitivity of the ΦR to the ϕo values decreases as ϕo values increases.For some system, ϕo values is adjustable by varying the concentration of potential determining ions. (remember Nernst equation)


DLVO: κ

For spheresΦtot = [64πRnokTγo

2/(κ2)] exp (-κs)-AR/(12s)

where γo = [exp(Zeϕo/2kT)-1][exp(Zeϕo/2kT)+1]

assumption: D>> κ-1

κ ↑ → ΦR ↓


DLVO and CFC


DLVO : summary

For spheres: Φtot = [64πRnokTγo2/(κ2)] exp (-κs) -AR/(12s)

For plates: Φtot = [64nokTγo2/(κ)] exp (-κD) -A/(12πd2)

where γo = [exp(Zeϕo/2kT)-1]/[exp(Zeϕo/2kT)+1](assumption D >> κ-1)

1. The higher the potential at the surface of particle(ϕo) - and therefore throughout the double layer - the larger repulsion(ΦR) between the particles will be.

2. The lower concentration of indifferent electrolyte, the longer is the distance from the surface before the repulsion drops significantly.(κ)

3. The larger Hamaker constant(A), the larger is the attraction between macroscopic bodies.(ΦA)

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