Transcript Document

Electrostatic Forces &
The Electrical Double Layer
Dry Clay
Swollen Clay
Repulsive electrostatics control swelling of clays in
water
Liquid-Solid Interface; Colloids
 Separation techniques such as :
 column chromatography, HPLC, Paper
Chromatography, TLC
 They are examples of the adsorption of
solutes at the liquid solid interface.
 Liquid solid interfaces can be found
everywhere and in any form and size, from
electrode surfaces to ship hulls.
Liquid-Solid Interface; Colloids
 Not so obvious examples for a solid-liquid
interface is a colloid particle.
 Colloids are widely spread in daily use:
 Paint
 Blood
 Air pollution
Liquid-Solid Interface; Colloids
 A very sensitive method to measure the
amount of adsorbed material is by using a
QCM (quartz crystal microbalance)
Liquid-Solid Interface; Colloids
 Adsorption at low solute concentration:
 These isotherms can be either fitted by the
langmuir isotherm
 Or the freundlich isotherm
Liquid-Solid Interface; Colloids
 Stearic acid is adsorbed onto carbon black
differently in different solvents:
Liquid-Solid Interface; Colloids
 Different chain lengthes will show
differences in adsorption behaviour:
Liquid-Solid Interface; Colloids
 Traube´s rule:
Liquid-Solid Interface; Colloids
 Composite adsorption isotherms:
Intermolecular Forces
Interaction Force/Radius (mN/m)
6
van der Waals
Electrostatic
Steric
Depletion
Hydrophobic
Solvation
5
4
3
2
Repulsive Forces
(Above X-axis)
1
0
Attractive Forces
(Below X-axis)
-1
-2
0
10
20
30
40
Separation Distance (nm)
50
Electrostatic Forces &
The Electrical Double Layer
Flagella
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.
Electrostatic Forces & van der Waals Forces
jointly influence Flocculation / Coagulation
Suspension of Al2O3 at
different solution pH
Critical for Water Treatment Processes
Electrostatic Forces &
The Electrical Double Layer
1)
2)
3)
4)
Sources of interfacial charge
Electrostatic theory: The electrical double layer
Electro-kinetic Phenomena
Electrostatic forces
SOURCES OF INTERFACIAL CHARGE
• Immersion of some materials in an electrolyte
solution. Two mechanisms can operate.
(1) Direct Ionization of surface groups.
H
O
H
M
O O O
O
H
H
O
M
H
O O O
O
M
+ H2O
O O O
(2) Specific ion adsorption
OH
M
+
+
+
O O O
SURFACE CHARGE GENERATION (cont.)
(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
HO
O O O OH
Si Al Si Si
HO O O O OH
ELECTRICAL DOUBLE LAYERS
+
Ψ0
-
x
SOLVENT MOLECULES
-
-
+
+
+
+
-
COUNTER IONS
OHP
CO IONS
Helmholtz (100+ years ago) proposed that surface charge
is balanced by a layer of oppositely charged ions
Gouy-Chapman Model (1910-1913)
Ψ0 -
x
+
+
-
+
+
+
+
-
-
Diffusion plane
• 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
Stern (1924) / Grahame (1947) Model
Gouy/Chapman diffuse double layer and layer of adsorbed charge.
Linear decay until the Stern plane.
x
Ψζ Ψ0 -
Difusion layer
+
-
+
+
+
+
-
+
-
-
+
Stern Plane Shear Plane
Gouy Plane
Bulk Solution
Stern (1924) / Grahame (1947) Model
In 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.
x
Ψζ Ψ0 -
Difusion layer
-
+
+
+
+
+
+
-
+
+
+
-
-
OHP
Shear Plane Gouy Plane
Bulk Solution
POISSON-BOLTZMANN DISTRIBUTION
1st 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”
→ →
E 
 r 
 0 r
Definitions
E: Electric filed
Electric field is the differential of the electric potential
Ψ: Electric potential
E→
(r )    
→r 
ρ: Charge density
EQ: Energy of the ion
Combining the two equations we get:
 (r )
x, r : Distance
 2  r   
 0 r
Boltzmann ion distribution
Which for one dimension becomes:
d 2 x 
 x 


dx2
 0
 x   0 e

EQ
kT

 n0 Zee
Assuming Boltzmann ion distribution:
d 2  x 
 x 
1 n
Zen Ze kT Ze kT
 Z i e kT


Zi nee

e
e

2
dx
 0
 0 i
 0


eZ
kT
POISSON-BOLTZMANN DISTRIBUTION
d 2 2Zen
Ze 


sinh

2
 r 0
 kT 
dx
Z = electrolyte valence,
e = elementary charge (C)
n = electrolyte concentration(#/m3)
r = dielectric constant of medium
0 = permittivity of a vacuum (F/m)
k = Boltzmann constant (J/K)
T = temperature (K)
•
•
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 DISTRIBUTION
Debye-Hückel approximation
Ze
1 then:
For
kT
2


d 2 2Zen
Ze

2
Zen
Ze

2
n
Ze


2



sinh



x


 x 


2
dx
 r 0
 r 0 kT
 kT   r  0 kT

The solution is a simple exponential decay (assuming Ψ(0)=Ψ0 and
Ψ(∞)=0):
x  0ex
Debye-Hückel parameter () describes the decay length


2nZe 
 r  0 kT
2
DOUBLE LAYER FOR MULTIVALENT
ELECTROLYTE: DEBYE LENGTH
Debye-Hückel parameter () describes the decay length
1/ 2
2
n
 e
2
  
Ci Z i 

  r  0 kT i 1

Zi
e
Ci
n
r
0
k
T
= electrolyte valence
= elementary charge (C)
= ion concentration (#/m3)
= number of ions
= dielectric constant of medium
= permittivity of a vacuum (F/m)
= Boltzmann constant (J/K)
= temperature (K)
-1 (Debye length) has units of length
POISSON-BOLTZMANN DISTRIBUTION
Exact Solution
Surface Potential (mV)
Surface Potential (mV)
For 0.001 M 1-1 electrolyte
Ze
<1
kT
Ze
>1
kT
DEBYE LENGTH AND VALENCY
Debye Length -1, (nm)
100
1-1 electrolyte
90
2-2 electrolyte
80
3-3 electrolyte
70
60
50
40
30
20
10
0
10-5 10-4 10-3 10-2 10-1 100 101
Electrolyte Concentration (M)
• Ions of higher valence are more effective in screening
surface charge.
ZETA POTENTIAL
Point of Zero Charge (PZC) - pH at which surface potential = 0
Isoelectric Point (IEP) - pH at which zeta potential = 0
Question: 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 --
Zeta Potential (mV)
50
40
30
20
10
0
-1 0
-2 0
-3 0
-4 0
-5 0
Increasing
I.S.
A lu m in a
1
2
3
4
5
6
pH
7
8
9
10
11
SPECIFIC ADSORPTION
•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
+
+
+
+
+
+
+2
+
-
-
+
+
-
+
+
+
+
-
+
-
SPECIFIC ADSORPTION
Ca2+
PO43-
pH
Multivalent cations shift IEP to right (calcite supernatant)
Multivalent anions shift IEP to left (apatite supernatant)
Amankonah and Somasundaran, Colloids and Surfaces, 15, 335 (1985).
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
ZETA POTENTIAL MEASUREMENT
• 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
Electrophoresis
Smoluchowski Formula (1921)
assumed a >> 1
 = Debye parameter
a = particle radius
- electrical double layer thickness much smaller than
particle
 r 0
v


 r 0
 

v = velocity,
r = media dielectric constant
0 = permittivity of free space
 = zeta potential, E = electric field
 = medium viscosity
E = electrophoretic mobility
ZETA POTENTIAL MEASUREMENT
Electrophoresis
Henry Formula (1931)
expanded for arbitrary a, assumed E field does not
alter surface charge
- low 0
v = velocity
2 r  0 
v
f1 ( a ) 
r = media dielectric constant
3
0 = permittivity of free space
2 r  0 
 
f1 ( a )
 = zeta potential
3
 = medium viscosity
E = electric field
E = electrophoretic mobility
Hunter, Foundations of Colloid Science, p. 560
ZETA POTENTIAL MEASUREMENT
Streaming Potential
 = Debye parameter
exp(Ze  / 2 kT )
 1 a = particle radius
a
 = zeta potential
 = Potential over capillary (V)
r = media dielectric constant
0 = permittivity of free space (F/m)
 = medium viscosity (Pa·s)
KE= solution conductivity (S/m)
p = pressure drop across capillary (Pa)
 r 0
E 
p
K E
Combined Effects of van der Waals and
Electrostatic Forces
DLVO Theory
DLVO – Derjaguin, Landau, Verwey and Overbeek
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:
AR 64kTRn 2
U ( x)  

exp x 
2
12x

Van der Waals
(Attractive force)
Electrostatics
(Repulsive force)
DLVO Theory
AR 64kTRn 2
U ( x)  

exp x 
2
12x

A = Hamakar’s constant
R = Radius of particle
x = Distance of Separation
k = Boltzmann’s constant
T = Temperature
n = bulk ion concentration
= Debye parameter
 ze 
  tanh

 4kT 
z = valency of ion
e = Charge of electron
Ψ = Surface potential
DLVO Theory
100 nm Alumina, 0.01 M NaCl, zeta=-20 mV
For short distances of separation between particles
DLVO Theory
Hard Sphere Repulsion
(< 0.5 nm)
J/m
No Salt added
Energy Barrier
x (distance)
Secondary Minimum
(Flocculation)
Primary Minimum
(Coagulation)
Discussion: Flocculation vs. Coagulation
The 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
Effect of Salt
Hard Sphere Repulsion
(< 0.5 nm)
J/m
No Salt added
Upon Salt addition
Energy Barrier
x (distance)
Secondary Minimum
(Flocculation)
Primary Minimum
(Coagulation)
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
Reduces the energy barrier (may induce coagulation)
Also increases the distance at which secondary minimum
occurs (aids flocculation)
Since increased salt concentration decreases -1 (or
decreases electrostatics), at the Critical Salt Concentration
U(x) = 0
Effect of Salt Concentration and Type
AR 64kTRn 2


exp H   0
2
12H

H: Distance of separation at critical salt concentration
At critical salt concentration, H = 1.
Upon simplification, we get:
1
n 6
z
n: Concentration
Z: Valence
Schultz – Hardy Rule:
Concentration to induce rapid coagulation varies
inversely with charge on cation
Effect of Salt Concentration and Type
For As2S3 sol, KCl: MgCl2: AlCl3 required to induce
flocculation and coagulation varies by a simple
proportion 1: 0.014: 0.0018
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 Effect
Agglomerate
Dispersion
Dispersion
Stability
diagram for
Si3N4(M11)
particles as
produced from
calculations
(IEP 4.4)
assuming 90%
probability of
coagulation for
solid formation.
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.