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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

Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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Page 1: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 2: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 3: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 4: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 5: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 6: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 7: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory 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

Page 8: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 9: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 10: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 11: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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)

Page 12: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 13: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 14: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 15: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 16: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 17: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 18: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

−− ⋅=

Page 19: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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 =−+=∑

Page 20: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

Debye length

Other expressions for k-1 [nm]

Page 21: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

Debye length

k-1 = f(salt conc., type of salt)

k-1 for salt conc.

k-1 for x:1 salt

Page 22: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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)

Page 23: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 24: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 25: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

Molecular factors affecting the electric forces

Page 26: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 27: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 28: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

Critical Coagulation Concentration (CCC)

Critical coagulation concentration (CCC)

minimum concentration ofminimum concentration ofan inert electrolyte

� coagulate a dispersion

� coagulation → visible changein the dispersion appearence

Page 29: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 30: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

Critical Coagulation Concentration (CCC)

CCC → values for various(nano)particles / electrolyte

Page 31: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

ψ

γwhere:

for aqueous dispersions at 25 °C

Page 32: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

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.

Page 33: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

Critical Coagulation Concentration (CCC)

the vanlency of counter-ions !!

the influence of co-ions is very low.

the influence of ion type ?

Page 34: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 35: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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.

Page 36: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 37: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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).

Page 38: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 39: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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

Page 40: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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.

Page 41: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

� 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.

Page 42: Stability of colloidal systems - unibas.chpcsp/2017/PCSP-2017-4FcursS.pdf · Stability of colloidal systems Colloidal stability DLVO theory Electric double layer in colloidal systems

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