electrostatic forces & the electrical double layer repulsive electrostatics control swelling of...

Electrostatic Forces &The Electrical Double Layer

Repulsive electrostatics control swelling of clays in water

Dry Clay Swollen Clay

Liquid-Solid Interface; ColloidsLiquid-Solid Interface; Colloids

Separation techniques such as :Separation techniques such as : column chromatography, HPLC, Paper column chromatography, HPLC, Paper

Chromatography, TLCChromatography, TLC They are examples of the adsorption of They are examples of the adsorption of

solutes at the liquid solid interface.solutes at the liquid solid interface. Liquid solid interfaces can be found Liquid solid interfaces can be found

everywhere and in any form and size, from everywhere and in any form and size, from electrode surfaces to ship hulls.electrode surfaces to ship hulls.


Not so obvious examples for a solid-liquid Not so obvious examples for a solid-liquid interface is a colloid particle.interface is a colloid particle.

Colloids are widely spread in daily use:Colloids are widely spread in daily use: PaintPaint BloodBlood Air pollutionAir pollution


A very sensitive method to measure the A very sensitive method to measure the amount of adsorbed material is by using a amount of adsorbed material is by using a QCM (quartz crystal microbalance)QCM (quartz crystal microbalance)


Adsorption at low solute concentration:Adsorption at low solute concentration: These isotherms can be either fitted by the These isotherms can be either fitted by the

langmuir isothermlangmuir isotherm Or the freundlich isothermOr the freundlich isotherm


Stearic acid is adsorbed onto carbon black Stearic acid is adsorbed onto carbon black differently in different solvents:differently in different solvents:


Different chain lengthes will show Different chain lengthes will show differences in adsorption behaviour:differences in adsorption behaviour:


Traube´s rule:Traube´s rule:


Composite adsorption isotherms:Composite adsorption isotherms:

Intermolecular Forces

Repulsive Forces (Above X-axis)

Attractive Forces (Below X-axis)


E-Coli demonstrate tumbling & locomotive modes of motion in the cell to align themselves with the cell’s rear portion

Flagella motion is propelled by a molecular motor made of proteins – Influencing proton release through protein is a key molecular approach to prevent E-Coli induced diarrhea

Mingming Wu, Cornell University (animation)Berg, Howard, C. Nature 249: 78-79, 1974.

Flagella

Electrostatic Forces & van der Waals Forces jointly influence Flocculation / Coagulation

Suspension of Al2O3 at different solution pH

Critical for Water Treatment Processes


1) Sources of interfacial charge2) Electrostatic theory: The electrical double layer3) Electro-kinetic Phenomena4) Electrostatic forces

• Immersion of some materials in an electrolyte solution. Two mechanisms can operate.

(1) Direct Ionization of surface groups.

(2) Specific ion adsorption

M

OH

OO O+ + +

SOURCES OF INTERFACIAL CHARGE

O

M

H HO

M

HO

MO O O OO O OO O

H HO-

+ H2O

(3) Differential ion solubility Some ionic crystals have a slight imbalance in number of lattice cations or anions on surface, eg. AgI, BaSO4, CaF2, NaCl, KCl

(4) Substitution of surface ions eg. lattice substitution in kaolin

HOSi

HO

O

OAl

O

OSi

O

OSi

OH

OH

SURFACE CHARGE GENERATION (cont.)

ELECTRICAL DOUBLE LAYERS

Helmholtz (100+ years ago) proposed that surface charge is balanced by a layer of oppositely charged ions

COUNTER IONS

+

+

+

+

-

-

-

+

-

CO IONSOHP

--------

SOLVENT MOLECULES

Ψ0

x

Gouy-Chapman Model (1910-1913)

• Assumed Poisson-Boltzmann distribution of ions from surface • ions are point charges• ions do not interact with each other

• Assumed that diffuse layer begins at some distance from the surface

+

+ +

++

-

-

-

+

-

Diffusion plane

Ψ0

x---------

Stern (1924) / Grahame (1947) Model Gouy/Chapman diffuse double layer and layer of adsorbed charge.Linear decay until the Stern plane.

+

+

+

+

+

Shear Plane Gouy Plane

Difusion layer

+

-

-

-

+-

Bulk SolutionStern Plane

-------------

-

-Ψ0

x

Ψζ

Stern (1924) / Grahame (1947) ModelIn different approaches the linear decay is assumed to be until the shear plane, since there is the barrier where the charges considered static. In this courese however we will assume that the decay is linear until the Stern plane.

+

+

+

+

+

Shear Plane Gouy Plane

Difusion layer

+

-

-

-

+-

Bulk SolutionOHP

-----------

-

-

+

+

Ψ0

Ψζ

x

POISSON-BOLTZMANN DISTRIBUTION1st Maxwell law (Gauss law): “The total of the electric flux out of a

closed surface is equal to the charge enclosed divided by the permittivity”

r

rE

0

rrE )(Electric field is the differential of the electric potential

→ →

→→

Combining the two equations we get:

r

rr

0

2 )(

Which for one dimension becomes:

0

2

2

x

dx

xd

Assuming Boltzmann ion distribution:

kTeZkTeZn

i

kTeZi ee

ZenneeZ

x

dx

xdi

000

2

2 1

kT

eZ

kT

E

ZeenexQ

00

Boltzmann ion distribution

DefinitionsE: Electric filedΨ: Electric potentialρ: Charge densityEQ: Energy of the ionx, r : Distance

POISSON-BOLTZMANN DISTRIBUTION

Z = electrolyte valence, e = elementary charge (C)n = electrolyte concentration(#/m3)r = dielectric constant of medium0 = permittivity of a vacuum (F/m)k = Boltzmann constant (J/K)T = temperature (K)

kTZe

sinhZen2

dx

d

0r2

2

• Poisson-Boltzmann distribution describes the EDL• Defines potential as a function of distance from a surface

• ions are point charges• ions do not interact with each other

POISSON-BOLTZMANN DISTRIBUTIONDebye-Hückel approximation

For then:

The solution is a simple exponential decay (assuming Ψ(0)=Ψ0 and Ψ(∞)=0):

Debye-Hückel parameter () describes the decay length

ZekT

1

x 0e x

xxkT

Zen

kT

ZeZen

kT

ZeZen

dx

d

rrr

2

0

2

002

2 22sinh

2

kT

Zen

r 0

22

DOUBLE LAYER FOR MULTIVALENTELECTROLYTE: DEBYE LENGTH

Debye-Hückel parameter () describes the decay length

Zi = electrolyte valencee = elementary charge (C)Ci = ion concentration (#/m3)n = number of ionsr = dielectric constant of medium0 = permittivity of a vacuum (F/m)k = Boltzmann constant (J/K)T = temperature (K)

-1 (Debye length) has units of length

2/1

1

2

0

2

n

iii

r

ZCkT

e

POISSON-BOLTZMANN DISTRIBUTIONExact Solution

For 0.001 M 1-1 electrolyte

ZekT

< 1

ZekT

> 1

Surf

ace

Pote

ntia

l (m

V)

Surf

ace

Pote

ntia

l (m

V)

Electrolyte Concentration (M)10-5 10-4 10-3 10-2 10-1 100 101

Debye L

ength -1, (nm

)

0

10

20

30

40

50

60

70

80

90

1001-1 electrolyte2-2 electrolyte3-3 electrolyte

DEBYE LENGTH AND VALENCY

• Ions of higher valence are more effective in screening surface charge.

ZETA POTENTIAL

Point of Zero Charge (PZC) - pH at which surface potential = 0Isoelectric Point (IEP) - pH at which zeta potential = 0Question: What will happen to a mixed suspension of Alumina and Si3N4 particles in water at pH 4, 7 and 9?

ZETA POTENTIAL-- Effect of Ionic Strength --

p H

1 2 3 4 5 6 7 8 9 1 0 1 1

Zeta P

otential (mV

)

- 5 0

- 4 0

- 3 0

- 2 0

- 1 0

0

1 0

2 0

3 0

4 0

5 0

A l u m i n a

IncreasingI.S.

•Free energy decrease upon adsorption greater than predicted by electrostatics

• Have the ability to shift the isoelectric point v and reverse zeta potential

• Multivalent ions: Ca+2, Mg+2, La+3, hexametaphosphate, sodium silicate

• Self-assembling organic molecules: surfactants, polyelectrolytes

SPECIFIC ADSORPTION

+2+

- - - - -

+

+

+

+

+

+ +

+

+

++

+ +

SPECIFIC ADSORPTION

Multivalent cations shift IEP to right (calcite supernatant)Multivalent anions shift IEP to left (apatite supernatant)

pH

Amankonah and Somasundaran, Colloids and Surfaces, 15, 335 (1985).

PO43-

Ca2+

ELECTROKINETIC PHENOMENA

• Electrophoresis - Movement of particle in a stationary fluid by an applied electric field.

• Electro-osmosis - Movement of liquid past a surface by an applied electric field

• Streaming Potential - Creation of an electric field as a liquid moves past a stationary charged surface

• Sedimentation Potential - Creation of an electric field

when a charged particle moves relative to stationary fluid

• Electrophoresis - determined by the rate of diffusion (electrophoretic mobility) of a charged particle in an applied DC electric field.

• PCS - determined by diffusion of particles as measured by

photon correlation spectroscopy (PCS) in applied field

• Acoustophoresis - determined by the potential created by a

particle vibrating in its double layer due to an acoustic wave

• Streaming Potential - determined by measuring the potential

created as a fluid moves past macroscopic surfaces or a porous plug

ZETA POTENTIAL MEASUREMENT

ZETA POTENTIAL MEASUREMENTElectrophoresis

Smoluchowski Formula (1921) assumed a >> 1 = Debye parameter

a = particle radius - electrical double layer thickness much smaller than particle

v = velocity, r = media dielectric constant0 = permittivity of free space = zeta potential, E = electric field = medium viscosityE = electrophoretic mobility

0r

0rv

ZETA POTENTIAL MEASUREMENTElectrophoresis

Henry Formula (1931) expanded for arbitrary a, assumed E field does not alter surface charge

- low 0

v = velocityr = media dielectric constant

0 = permittivity of free space = zeta potential = medium viscosityE = electric fieldE = electrophoretic mobility

)a(f3

2

)a(f3

2v

10r

10r

Hunter, Foundations of Colloid Science, p. 560

ZETA POTENTIAL MEASUREMENTStreaming Potential

= Debye parameter a = particle radius

= zeta potential

= Potential over capillary (V)r = media dielectric constant0 = permittivity of free space (F/m) = medium viscosity (Pa·s)KE= solution conductivity (S/m)p = pressure drop across capillary (Pa)

pK

EE

0r

1a

)kT2/Zeexp(

DLVO Theory

DLVO – Derjaguin, Landau, Verwey and Overbeek

Combined Effects of van der Waals and Electrostatic Forces

Based on the sum of van der Waals attractive potential and a screened electrostatic repulsion potential arising between the “double layer potential” screened by ions in solution. The total interaction energy U of the system is:

xkTRn

x

ARxU

exp64

12)(

2

2

Van der Waals (Attractive force)

Electrostatics (Repulsive force)

xkTRn

x

ARxU

exp64

12)(

2

2

DLVO Theory

A = Hamakar’s constant

R = Radius of particle

x = Distance of Separation

k = Boltzmann’s constant

T = Temperature

n = bulk ion concentration

= Debye parameter

z = valency of ion

e = Charge of electron

Ψ = Surface potential

kT

ze

4tanh

DLVO Theory

For short distances of separation between particles

100 nm Alumina, 0.01 M NaCl, zeta=-20 mV

Primary Minimum

Secondary Minimum

Energy Barrier

Hard Sphere Repulsion (< 0.5 nm)

J/m

x (distance)

DLVO Theory

(Flocculation)

(Coagulation)

No Salt added

Discussion: Flocculation vs. CoagulationThe DLVO theory defines formally (and distinctly), the often

inter-used terms flocculation and coagulation

Flocculation:

• Corresponds to the secondary energy minimum at large distances of separation

• The energy minimum is shallow (weak attractions, 1-2 kT units)

• Attraction forces may be overcome by simple shaking

Coagulation:

• Corresponds to the primary energy minimum at short distances of separation upon overcoming the energy barrier

• The energy minimum is deep (strong attractions)

• Once coagulated, particle separation is almost impossible

Primary Minimum

Secondary Minimum

Energy Barrier

Hard Sphere Repulsion (< 0.5 nm)

J/m

x (distance)

Effect of Salt

(Flocculation)

(Coagulation)

No Salt added

Upon Salt addition

Addition of salt reduces the energy barrier of repulsion. How?

Secondary Minimum: Real System

100 nm Alumina, zeta=-30 mV

Discussion on the Effect of Salt

The salt reduces the EDL thickness by charge screening

Also increases the distance at which secondary minimum occurs (aids flocculation)

Reduces the energy barrier (may induce coagulation)

Since increased salt concentration decreases -1 (or decreases electrostatics), at the Critical Salt Concentration U(x) = 0

Effect of Salt Concentration and Type

0exp64

12 2

2

HkTRn

H

AR

H: Distance of separation at critical salt concentration

At critical salt concentration, H = 1.

Upon simplification, we get:

6

1

zn Schultz – Hardy Rule:

Concentration to induce rapid coagulation varies inversely with charge on cation

n: ConcentrationZ: Valence

For As2S3 sol, KCl: MgCl2: AlCl3 required to induce flocculation and coagulation varies by a simple proportion 1: 0.014: 0.0018

Effect of Salt Concentration and Type

The DLVO theory thus explains why alum (AlCl3) and polymers are effective (functionality and cost wise) to induce flocculation and coagulation

pH and Salt Concentration EffectpH and Salt Concentration Effect

Stability diagram for Si3N4(M11) particles as produced from calculations (IEP 4.4) assuming 90% probability of coagulation for solid formation.

Dispersion

Dispersion

Agglomerate

REMARKS-- hydrophobic and solvation forces --

• Due to the number of fitting parameters (0, A132, spring constant, I.S.) and uncertainty in force laws (C.C. vs C.P., retardation) hydrophobic forces often invoked to explain differences between theory and experiment.

• Because hydrophobic forces involve the structure of the solvent, the number of molecules to be considered in the interaction is large and computer simulation has only begun to approach this problem.

• Widely accepted phenomenological models of hydrophobic forces still need to be developed.

electrostatic forces & the electrical double layer repulsive electrostatics control swelling of...

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