colloidal stability introduction interparticle repulsion interparticle attraction hamaker constant...
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CCoollllooiiddaal l SSttaabbiilliittyy Introduction Interparticle Repulsion Interparticle Attraction
Hamaker constantMeasurement techniquesSolvent Effects
Electrostatic StabilisationCritical Coagulation
Concentration Kinetics of Coagulation
IntroductionIntroductionColloid stability: ability of a colloidal dispersion to avoid coagulation.
KineticKinetic vs thermodynamicthermodynamic parameters.
Two kinds of induced stability:
(1) ElectrostaticElectrostatic induced stability:• (like) charges, repel• van der Waal’s forces, attract
V
+verepulsive
stable
-veattractiveunstable
0
H=particle separation
(2) Polymer induced or Steric StabilitySteric Stability:
Stability is a result of a steric effect,where the two polymer layers on interacting particles overlap and
repel one another.
Interparticle RepulsionInterparticle Repulsion
Goal is to calculate repulsive potentialVR between two particles
H
d
Two possibilities for :
Due to adsorption of charged species remains constant, decreases
Due to intrinsic charge on the particles constrained to remain constant,
increases as overlap increases
o
Derjaguin ApproximationDerjaguin Approximation
•Approximate sphere by a set of “rings”•Assumes:
•Constant potential case.•Sphere radius much larger than
double layer thickness, a>10.•NO assumptions on potentials.
Ha1
dH
a2
1
1
2kTze
2kTze
d
d
e
e H
dR
H
R
eaV
ezeaa
TkaaV
2
22
21
21
22
21
2
64
low potentials (D-H approx.)both particles the same.
SummarySummary
Simplest form of repulsive interaction: spherical like particles low potentials large interparticle distances.
As increases, repulsion decreases, destabilisation occurs:
increase in electrolyte concentration increase in counter-ion charge.
Like charged particles stabilise, unlike charges destabilise.
H2dR ea2V
Interparticle AttractionInterparticle Attraction
Van der Waal’s forces: exist for all particlesatom-sized and up.
permanent dipole-permanent dipole KeesomKeesom interaction
permanent dipole-induced dipole DebyeDebye interaction
induced dipole-induced dipole LondonLondon or dispersion interaction ALWAYS PRESENT
always attractive (?) long range (0.2 - 10 nm)
6rV
Form of van der Waal’s InteractionsForm of van der Waal’s Interactions
includes contributions from London,Keesom and Debye forces.
= f(polarizability, dipole moment)
Relative contributions:
CCl4 0 10.7 4.41 0 0 100Ethanol 1.73 5.49 3.4 42.6 9.7 47.6Benzene 0 10.5 4.29 0 0 100Phenol 1.55 11.6 6.48 14.5 8.6 76.9Toluene 0.43 11.8 5.16 0.1 0.9 99Water 1.82 1.44 2.1 84.8 4.5 10.5
Compound % % % Debye x1030 m3 x1077 Jm6Keesom Debye London
(single particle)
Van der Waal’s interactions betweenVan der Waal’s interactions betweentwo particlestwo particles
Must sum over each volume elementof a large particle -- introduces error!
For two spheres close together (H<<a):
2
21
21
)(6
12
MN
A
aaHaAa
V
HAa
V
A
A
A Equal Spheres
Unequal Spheres
Hamaker Constant!
where...
units of Joules
Hamaker constant determined by bothpolarizability and dipole moment ofmaterial in question...
Acetone 4.2Alumina 15.4Gold 45.3Magnesia 10.5Metals 16-45Rubber 8.58polystyrene 7.8-9.8Silver 39.8Toulene 5.4Water 4.35
Material A (x 1020 J)
Means of measuring
determine from and (approximate and not always possible to get values)
Measure using bulk properties:
Surface tension is an obvious one
224 odA
Direct Measurement of forces
This is a difficult thing to do...
Insert Fig. 1.27 here
Solvent EffectsSolvent Effects
Previous results were in vacuum.
Presence of a solvent between particleswill affect the overall Hamaker constant:
3solvent
3solvent
3solvent
3solvent1
1 2
2
AVR
13233312132
132
AAAAA
AAAA initialfinaleffective
...,2/1
221112 etcAAA
22/1
33
2/1
11131
2/1
33
2/1
22
2/1
33
2/1
11132
AAA
AAAAA
Net result:
If particles are the same reduces to...
If particles are the same… Aeff is always positive -- i.e attractive. If A’s are similar, attraction is weak.
If particles are different… Aeff is positive if A33>A11,A22 or A33<
A11,A22 attractive. Aeff is negative if A11<A33<A22 i.e.
repulsive interaction if the solvent Hamaker constant is intermediate to those of the particles.
Electrostatic StabilisationElectrostatic Stabilisation
We may combine the two expressions forthe potential experienced as follows…
HAa
ezeTak
VVV H
ar 1232
22
222
0 20 40 60 80 100120140
-40
-20
0
20
40
Vne
t/kT
H (nm)
= 100 mV= 1x108 m-1
a = 100 nm
A=2x10-20 J
5x10-20 J
1x10-19 J2x10-19 J
Effects of changing AEffects of changing A
Least control, setby system.
Effective over long range.
Effects of changing Effects of changing (i.e. (i.e. ):):
HAa
ezeTak
VVV H
ar 1232
22
222
Much shorter rangeeffect.
More effective at lowvalues of
Experimentally,we measure thezeta potential.
0 20 40 60 80 100120140
0
200
400
= 50 mV
= 75 mV
= 150 mV
= 200 mV
Vne
t/kT
H (nm)A = 2x10-19 J= 1x108 m-1
a = 100 nm
Effects of changing Effects of changing (i.e. electrolyte (i.e. electrolyteconcentration):concentration):
0 20 40 60 80 100120140-40
-20
0
20
40
= 1 x 107m-1
3 x 107m-1
1 x 108m-1
3 x 108m-1
Vne
t/kT
H (nm)
A = 2x10-19 J= 25 mVa = 100 nm
This is the itemwe have mostcontrol over!
Affects potentialsat short distances.
For a 1:1 electro-lyte, the transitionis about 10-2 - 10-3
molar.
HAa
ezeTak
VVV H
ar 1232
22
222
22
A ecz2NkT 1
Critical Coagulation ConcentrationCritical Coagulation ConcentrationThe Schulze-Hardy RuleThe Schulze-Hardy Rule
C.C.C. is fairly ill-defined:
The concentration of electrolyte which is just sufficient to coagulate a dispersion to an arbitrarily chosen extent in an arbitrarily defined time.
0
V
H
At the C.C.C:
dV/dH = 0 at V= 0
012
32
012
32
222
222
22
222
HAa
ezeTak
HAa
ezeTak
H
H
Assuming a symmetrical electrolyte(i.e. z+ = z-):
626
455329980...
zAeNTk
cccA
As becomes large 1 small ze /4kT
Thus:
c.c.c.c.c.c. 1/z 1/z66 at high potentials
c.c.c. c.c.c. 1/z 1/z22 at low potentials
Effect is independent of particle size!Strongly dependent on temperature!
As2S3 (negative) AgI (negative) Al2O3 (positive)
LiCl 58 LiNO3 165 NaCl 43.5NaCl 51 NaNO3 140 KCl 46KCl 49.5 KNO3 136 KNO3 60KNO3 50 RbNO3 126KC2H3O2 110 AgNO3 0.01
CaCl2 0.65 Ca(NO3)2 2.40 K2SO4 0.30MgCl2 0.72 Mg(NO3)2 2.60 K2Cr2O7 0.63MgSO4 0.81 Pb(NO3)2 2.43 K2oxalate 0.69
AlCl3 0.093 Al(NO3)3 0.067 K3[Fe(CN)6] 0.08Al2(SO4)3 0.096 La(NO3)3 0.069Al(NO3)3 0.095 Ce(NO3)3 0.69
Stronger dependency is typical ofadsorption in the Stern layer: softerspecies tend to adsorb better (morepolarizable) so have a slightlystronger effect.
Any potential determining ion willhave a significant effect.
Critical Coagulation ConcentrationsCritical Coagulation Concentrations(mmol/L)
Kinetics of CoagulationKinetics of Coagulation No dispersion is stable thermodynamically. Always a potential well.
Two steps in mechanism:
(1) Colloids approach one another diffusion controlled: perikinetic. externally imposed velocity
gradient: orthokinetic (e.g. sedimentation, stirring, etc.).
(2) Colloids stick to one another (assume probability of unity).
Two forces then controlling approach:
(1) Rapid diffusion controlled.(2) Interaction-force controlled (potential barrier, slows approach).
The Stability RatioThe Stability Ratio
W= Rate of diffusion-controlled collision Rate of interaction-force controlled collision
W = large : particles are relatively stable.
W = 1 : rate unhindered, particles unstable.
Diffusion-controlled (Rapid) Rate:Diffusion-controlled (Rapid) Rate:
RR1
R2
R1+R2
2
2
drNd
DdtdN
Fick’s Second law can now be used:
Which can be used to show that foridentical particles, the collision rate:
DRNZ 16
Since 2 particles are involved, the reactionfollows second order kinetics:
2
2Nk
dtdN
Thus, the rate constant is given by:
34
82
kT
DRk o
•Only binary collisionsoccur (dilute solution).•Neglect solvent flow outof gap.•For second relationshipStokes-Einstein is used.
slow
o
kk
W 2
The stability ratio can thus be given by:
kslow will depend upon the potentialaround the particles.
Can acquire an expression for kslow bymodifying Fick’s second law with an“activation energy”, V(R), where V(R)is the potential barrier previously dicussed.
dRRe
aWa
kTV
2
2
/
2
Assume a (very simple) barrier suchas the following...
V
Vmax
2a -10
particlestouch
Then…
kTVea
W /max
21
Critical Coagulation ConcentrationCritical Coagulation Concentration
Can solve previous simple expressionfor W in terms of Vmax, determined fromwhen dV/dH = 0
For water as dispersion medium
cza
xKW log1006.2log2
29
AgI Particle CoagulationAgI Particle Coagulation
Plot is linear
When log W =0 we are at the CCC, breaks in the curve appear as coagulation occurs at a rapid rate.
Coagulation rates cannot be measured in this system beyond about log W = 4. Corresponds to an energy barrier of about 15 kT.
Can use the slopes to analyze for o, if the particle size is known.
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