Post on 11-Jul-2018
Stability of colloidal systems
� Colloidal stability
� DLVO theory
� Electric double layer in colloidal systems
� Processes to induce charges at surfaces
� Key parameters for electric forces (ζ-potential, Debye length)
� Molecular factors affecting the electric forces
� Colloid stability (CCC, coagulation)
� Kinetics of aggregation
o Colloidal stability = dispersion of colloidal particles, which do notaggregate (in the desired time limits)
o Mechanic stability = dispersion of colloidal particles, which do not sediment
Colloidal stability:
Colloidal stability
( )HfV =
� Minima: instability aggregation (attraction forces dominate)
� Maxima: stability (repulsion forces dominate)
∫∞
−=H
FdHV
o DLVO theory (Derjaguin-Landau-Verwey-Overbeek) = the effect of theforces is simply additive between van der Waals and electrostatic forces(double layer energy)
DLVO theory
AR VVV +≅
V(1)= stable colloidal dispersion
V(2)= instable colloidal dispersion
o Forces in colloidal systems are longer range than the intermolecular forces
DLVO theory
o Critical coagulation concentration = concentration of the disperse phasefor which:
0=V
0=dH
dV
( )H
ARkHRV
12exp2 2
00 −−Ψ= εεπ
dH
Example: spherical particles, equalradius, aprox. neutral (< 25mV for 1:1electrolytes)
= zeta potential
R = radius of particles
k = Debye length
0ΨRV
AVStability: balance betweenrepulsion and attraction
Electric double layer in colloidal systems
o Almost all particles are charged in H2O/polar liquids.
o Most surfaces have negative charge - typically cations are more hydrated than the anions
Change = f( pH, nature of the surface groups, salt concentration)
- typically cations are more hydrated than the anions- anions adsorb at the surface
o Hydration number = number of water molecules an ion can bind
- divalent and trivalent cations are more solvated than monovalent cations.- monovalent cations are only weakly solvated
-The charge at the interface is compensated by counter-ions
o Double layer model = two regions are present at tha interface between asurface (planar, spherical) and the medium:
- Stern layer = one short counter-ions plane (interaction with the interface)
- Diffuse layer = counter-ions with a concentration that gradually decreasesuntil an electroneutral solution
Electric double layer in colloidal systems
Net change:
- Stern layer + diffuse layer + surface = 0
- If the double layer of two particlesoverlap > the change of the Stern layermakes the particles to repel each-other
Electric double layer in colloidal systems
Formation of osmotic pressure in themid plane of the overalping layer
Processes to induce charges at surfaces
a) Differential ions solubility
b) Direct ionization ofsurface groups
c) Isomorphous substitution
d) Specific ions adsorption
e) Anisotropic crystals
Processes to induce charges at surfaces
Determine IEP:( )pHf=ζ
o Isoelectric point, IEP = point in the interface region (around theparticle/in front of the surface) where the charge is zero.
o There are colloidal systems with more than one IEP (liquid crystals).
- Zeta potential
- IEP for surfaces
f(surface treatment)
( )pHf=ζ
Key parameters for electric forces
Electrical forces between nanoparticles
Overlap of the diffuse double layer
o DLVO Theory → the repulsion potential: ( )kHRVR −⋅Ψ= exp2 200εεπo DLVO Theory → the repulsion potential:
o Key parameters:
- ζ potential, Ψ0
- Debye length, k-1
( )kHRVR −⋅Ψ= exp2 00εεπ
ζ - potential
Electrical double → traverse with the nanoparticles
Nanoparticles have counter-ions & solvent molecules attached
ζ potential → potential where the centre of the first layer of solvated ionsζ potential → potential where the centre of the first layer of solvated ions
moving relative to the surface is located
ζ potential → located at ∼ 0.5nmfrom the surface
ζ > 30 mV→ stability (exceptions exist)
ζ - potential
Various „surface“ potentials
Ψ0 – surface potential
Ψd – Stern potential
ζ potentialζ potential
ζ potential → indicate the extent to which the ions from the solution are
adsorbed into the stem layer
Stern layer → few Å→ the finite size of the charged groups / ions
asociated with the surface
ζ - potential
ζ << Stern Potential : Ψd – when exist high salt concentrations
in practice:
How to measure ? → electrophoresis
0Ψ≡Ψ= dζ
How to measure ? → electrophoresis
E
v=µ [ ] 112 −−= sVmµ
[ ] 1−= msv [ ] 1−= VmE
ζ - potential
o Small nanoparticles (Hückel model):
00 2
3
εεµη=Ψ
o Large nanoparticles (Smoluchowski model):
o Any size nanoparticles (Henry model): :
00 εε
µη=Ψ
( )kRf00
5.1
εεµη=Ψ
ζ - potential
µ < 0 ⇒ Ψ0 < 0
ζ = f(pH, salt conc.)
o Nanoparticles → aggregate close to the pH for
IEP (VR → 0)
o nanoparticles (+) at pH < IEP
o nanoparticles (-) at pH > IEP
ζ when salt conc. salt enhance instability
ζ - potential
ζ = f(ionic strength)
High salt conc. ⇒ compression of the double layer
ζ to stabilize the nanoparticlesζ to stabilize the nanoparticles
o addition of small charged particles
→ adsorb to the surface
o change pH to be far from IEP
flocculation → (ζ ≅ 0) ⇒ IEP should be avoided
Debye length
Debye length → thickness of the double layer (varying potential ∼ 3/k – 4/k)
Stern layer << diffuse layer:
INe
Tk
zcNe
Tkk
A
B
BiA
B
i22
02
)(2
01 εεεε ==∑
−
iz22 +=+Ca
224 −=−SO
o few nm → high salt conc.
o few 102nm→ low salt conc
1−k
Csalt k-1 repulsion
Debye length
Simpler formula
Example: H2O solution – 25°C
[ ] ( )−− ⋅= Lmolnm
nmk1
1 429.0[ ] ( )∑
− ⋅=
iii zc
Lmolnmnmk
2
1 429.0
∑=i
ii zcI 2
2
1
[ ] ( )I
Lmolnmnmk
2
429.0 11
−− ⋅=
Debye length
Important: what type of electrolyte is involved !
Example:
−+ +→ 2442 12 SONaSONa ( )( ) ( )( ) CCCzc ii 6212 222 =−+=∑
−+ +→ ClCaCaCl 21 22 ( )( ) ( )( ) CCCzc ii 61221 222 =−+=∑
−+ +→ 24
24 11 SOMgMgSO ( )( ) ( )( ) CCCzc ii 82121 222 =−+=∑
−+ +→ ClAlAlCl 31 33 ( )( ) ( )( ) CCCzc ii 121331 222 =−+=∑
−+ +→ ClNaNaCl 11 ( )( ) ( )( ) CCCzc ii 21111 222 =−+=∑
Debye length
Other expressions for k-1 [nm]
Debye length
k-1 = f(salt conc., type of salt)
k-1 for salt conc.
k-1 for x:1 salt
Molecular factors affecting the electric forces
2 nanoparticles approach → double layers overlap
� nanoparticles repel each other
Electrostatic double layer interactions
↓
decrease exponentialy with H
≅ 0→ after a few k-1
(thickness of the double layer)
Molecular factors affecting the electric forces
Monodisperse nanoparticles → kR < 5
(Debye-Hückel approximation)
( )kHRVR −⋅Ψ= exp2 200εεπ
� valid for single , symmetric electrolyte
(1:1 or 2:2) → present in the medium Approximation valid whenconditions → more complex
( )kHRVR −⋅Ψ= exp2 00εεπ
Molecular factors affecting the electric forces
Effect of nanoparticles in a dispersionVR for H
VR for k-1
concentration of nanoparticles
⇓
Faster decay of electrostatic repulsion
↓
� aggregationThe electrolyte
↓
Not „particle-free“ solution
Molecular factors affecting the electric forces
Molecular factors affecting the electric forces
Effect of salts (counter-ions) on stability
Addition of electrolyte
Decrease the double layer → instability → coagulation
� Repulsive forces
⇓
� Van der Waals forces dominate
⇓
Nanoparticles → coagulate
� Compression of the diffusepart of the double layer
� Possible ion adsorbtion intothe Stern layer
Addition of electrolyte
V
Colloid stability – a kinetic view
Effect of salt concentration on the energy1: The repulsive force dominates and the colloid remains stable.
2: The secondary minimum starts appearing but the energy barrier is still very high, so the colloid is kinetically stable.
3: If the barrier is sufficiently low, the particles may Energy barriers
salt concentration 1
5
H (nm)
3: If the barrier is sufficiently low, the particles may even be able to cross it due to their thermal energy.
4: Energy barrier has become zero , and fast coagulation is possible. The concentration at this point is called ‘Critical Coagulation Concentration (CCC)’ at which coagulation can occur spontaneously. Hence, the colloid becomes unstable.
5: There is a large attractive Van-der Waals force, due to which there is no barrier and very fast coagulation takes place.
Energy barriers
Critical Coagulation Concentration (CCC)
Critical coagulation concentration (CCC)
minimum concentration ofminimum concentration ofan inert electrolyte
⇓
� coagulate a dispersion
� coagulation → visible changein the dispersion appearence
Critical Coagulation Concentration (CCC)
Schulze-Hardy rule → role of salt in colloidal
stability
� Strongly dependent on the valency of the
6
1
zCCC ≈
� Strongly dependent on the valency of thecounter-ions
CCC depends weakly on:
� Concentration of nanoparticles
� Nature of nanoparticles
� Charge number of counter-ions
Critical Coagulation Concentration (CCC)
CCC → values for various(nano)particles / electrolyte
Critical Coagulation Concentration (CCC)
Schulze-Hardy rule:
DLVO theory: ( )H
ARHRV
12exp2 2
00 −−⋅Ψ= κεεπ 0=V
6
6)()(
1
=⇒∝
IIzzsaltICCCsaltIICCC
zCCC I
0=dH
dV
626
455330
41085.9
zAeN
TkCCC
A
B γεε×=
LmolzJA
CCC /)/(
1084.362
439γ−×=
1
1
2
2
+
−=Tk
ze
Tk
ze
B
o
B
o
e
eψ
ψ
γwhere:
for aqueous dispersions at 25 °C
Critical Coagulation Concentration (CCC)
626
455330
41085.9
zAeN
TkCCC
A
B γεε×=From:
6
1
zCCC∝High potential 1→γ agree with Schulze-Hardy rule
1
1
2
2
+
−=Tk
ze
Tk
ze
B
o
B
o
e
eψ
ψ
γ
z
low potentialTk
ze
B40ψγ →
2
40
zCCC
ψ∝z
10 ∝ψ
6
1
zCCC∝
3ε∝CCC CCC independent with particle size
The vanlency of counter-ions is very important to t he collioid stability.
Critical Coagulation Concentration (CCC)
the vanlency of counter-ions !!
the influence of co-ions is very low.
the influence of ion type ?
Hofmeister series – effectiveness of coagulation
effectiveness of coagulationeffectiveness of coagulation
Precipitation at very high electrolyte concentration(salting-out effect)
Hydration of ions
dehydration of hydrophilic colloids
precipitation
Purification of proteins with different
hydrophobicity
Kinetics of aggregation
Slow (potential-limited) coagulation
TkV B15max ≤
H (nm)
V
Vmax Thermal energy overcomes the repulsive potential energy barrier (curve 3)
+
Second order
Smoluchowski model for slow coagulation:
tknn
nkdt
dn2
0
22
11 =−⇒=−
n = number of particles per volume at some time t (m-3)k2 = reaction constant (m3 number-1 s-1)n0 = number of particles at start (t = 0) per unit volume (m-3)
obtain k2 by ploting 1/nas a funtion of t.
H (nm)
V
Kinetics of aggregation
Fast (diffusion-controlled) coagulation
zero electrostatic barrier (by ion adsorption or by adding electrolyte)
See curve 5
The rate is limited only by the diffusion rate of particles towards one another and all of particles towards one another and all collisions lead to adhesion
medium
BTkk
η3
402 =
Smoluchowski model for fast coagulation:
depend on temperature and viscosity of medium but not the particle size
0022
1
2
102
00 4
311
5.0
1
Tnknkttk
nn B
mediumη==⇒=−
t1/2 is generally in the order of seconds to minutes
Kinetics of aggregation
Stability ratio W
2
02
k
kW = the total collisions between particles divided by
the collisions of particles which result in a coagulation
W is directly related to the maximum (barrier) of the potential energy function
Reerink-Overbeek equation: Fuchs equation:
Tk
V
BeR
Wmax
2
1
κ= dH
H
Tk
V
RWR
B∫∞
=2
2
)exp(2
R = particle radiusrequire numerical solutions
→≥ 510W
→= 910W
easily obtained with modest potentials, about 15 kBT , debye length above 20 nm (curve 3).
corresponds to a V of about 25 kBT (very slow coagulation, rather stable dispersion, curve 2).
Stability ratio W
Kinetics of aggregation
Theoretical repationships between W and electrolyte (1-1, 2-2) concentration obtained by Fuchs equation
cz
aW d log1006.2log
2
29
×−= γψ
a = effective ratius of particles slow cogulation (potential-limited coagulation)
a = effective ratius of particles
fast cogulation (diffusion-controlled coagulation)
linear relationship
CCC!W = 1
Stability ratio W
Kinetics of aggregation
W is able to be measured directly by estimating the apparent rates from static light scattering (SLS) or dynamic light scattering (DLS) with the relation:
∆∆
==∑∑ fastfastW
∆∑
aggregation of particles with a radius of 135 nm is induced with KCl
Fast coagulation
dt
dDk H=0
From coagulation to sedimentation
coagulation distabilized by electrolytes
reach to a equilibrum state as a
irreversible
water treatment
reach to a equilibrum state as a consequence of the height of the repusion energy barrier increasing with increasing particle size
flocculationreversible clumped by polymers
sendimentation sedimentation velocity see Lecture 2.
� G. M. Kontogeorgis, S. Kill, Introduction to applied colloid and
References:
� G. M. Kontogeorgis, S. Kill, Introduction to applied colloid andsurface chemistry, Wiley-VCH, 2016
�D. F. Evans, H. Wennerstrom, The colloidal domain, Wiley-VCH, second edition, 2014.
Stability of colloidal systems
� Colloidal stability
� DLVO theory
� Electric double layer in colloidal systems
� Processes to induce charges at surfaces
� Key parameters for electric forces (ζ-potential, Debye length)
� Molecular factors affecting the electric forces
� Colloid stability (CCC, coagulation)
� Kinetics of aggregation