Colloid stability.Lyophobic sols. Stabilization of

colloids.

Levente NovákIstván BányaiZoltán Nagy

Department of Physical Chemistry

Lyophilic and lyophobic sols

● Sols (lyosols) are dispersed colloidal size particles in a liquid medium (=solid/liquid dispersions)

● These sols can be● Lyophilic : strong interactions exist between the parti-

cles and the solvent (the particles are weted)– Thermodynamically stable

● Lyophobic: weak interactions between the particles and the solvent (partially weted or unweted particles)– Thermodynamically always unstable (→ aggregation)– Can be kinetically stable or unstable

● Mixing is spontaneous.● Mixing is reversible.● The mixture is thermodynamically sta-

ble.● Inhomogeneities are on molecular scale.

● Mixing is non-spontaneous (requires mechani-cal energy).

● Mixing is irreversible.● Thermodynamically unstable (requires a stabi-

lizing agent) and unmix spontaneously.

● Inhomogeneities on colloidal scale.

Properties of the real solutions are inde-pendent on the way these solutions are prepared.

Properties of the colloidal dispersions are strongly dependent on the way they are pre-pared → for repeatability, empirical prepara-tion procedures are followed

Solutions versus dispersions

=

Thermodynamical stability

● Solutions are thermodynamically stable● Gibbs energy of the components before mixing is higher than afer

mixing (ΔG<0)

● Dispersions are thermodynamically unstable● The Gibbs energy increases by mixing (ΔG>0)● But if unmixing is slow enough → kinetically stable dispersions

● In an unstable system the particles may adhere to one another and form aggre-gates of increasing size that may setle or “cream” out under the influence of grav-ity. An initially formed aggregate is called a floc or flocculate and the process is flocculation. The floc may or may not separate out.

● If the aggregate changes to a much denser form, it is said to undergo coagula-tion. An aggregate usually separates out either by sedimentation (if it is more dense than the medium) or by creaming (if it less dense than the medium).

● Usually coagulation is irreversible whereas flocculation can be reversed by the process of deflocculation.

Kinetic stability

Coagulation or flocculation

a)The suspended particles setle out and form a firm, dense mass (cake). The coagulate can not be redispersed by gentle agitation.

b)The suspended particles form light, flufy agglomerates held together by strong van der Waals forces. The flocculated particles setle rapidly forming a loosely adhering mass with a large sediment height. Gentle agitation will easily resuspend the particles. Weak flocculation requires strong adhesion and a zeta potential of almost zero.

Loosely adher-ing mass, it can be reversed by deflocculation→ floc or floc-culate

a) coagulated, b) flocculated particles

Dense mass, irreversible aggregation→ cake or coagulate

Strength of interparticle forces

Encounters between particles occur as a re-sult of Brownian motion and stability of a suspension is determined by the interac-tion between particles during these en-counters.

Stability depends on the balance of atrac-tive and repulsive interactions.

Atraction comes from van der Waals forces between particles.

Repulsion is a consequence of interaction between similarly charged electric double layers and/or particle-solvent afinity. Re-pulsion prevents particles to get close enough and atach.

There is no repulsion

There is repulsion

Stability of lyophobic sols (summary)

● Lyophobic sols are thermodynamically unstable.● However there are stabilizing factors (e.g. repul-

sion) → kinetical stability can be atained.● Whether aggregation does or does not occur de-

pend of the balance of atractive and repulsive forces.

● For obtention of a stable lyosol, repulsive forces must dominate

F⃗ T=F⃗ A+F⃗ R

VR VS

Electrostatic and steric stabilization

There is atraction between atoms or mol-ecules even in vacuum.

VA: atraction potential (J).

Dispersion atraction between atoms or molecules is additive so it also acts in case of macroscopic bodies too.

l

x

The atraction depends on the geometry of the particles (composed of atoms)

x

A is the Hamaker constant or atraction parameter (unit: J).

Molecular origin of the van der Waals atraction

V A(l )=const

l 6

V A(x )=−A r6 x

V A(x )=−A

12 π x 2 ×area

r

Molecules inparticle 1

Molecules inparticle 2

● The atraction of bodies arises from London (dispersion) atraction of molecules (all mole-cules act independently).

● The efect is additive: one molecule of the first colloid has a van der Waals atraction to each molecule in the second colloid, the total force is the sum of all forces.

● An atractive energy curve is used to indicate the variation in van der Waals force with dis-tance (x) between the particles.

The Hamaker model

xA=π2 C ρ1ρ2

C : interaction energy constant (J·m-6 for van der Waals interactions)ρ1 : number density of the surface 1 (m-3)ρ2 : number density of the surface 2 (m-3)

x

● The Hamaker constant (A) in vac-uum depends on material proper-ties: density, polarizability

● The efective Hamaker constant Aef

also depends on the dispersion medium

An atractive energy or atractive po-tential curve is used to indicate the variation in van der Waals force with distance between the particles.

Efective Hamaker constant

V A(x )=−A r6 x

VA(x)

1 1x

x1 1x

2

Aef =(√A12−√A22 )2

V A(x )=−Aef r

6 xOrder of magnitude: Aef ≈ 10-20 – 10-21 J

x

Repulsion: particles of the same charge

Ψ =Ψ St e−κ(x−x St )

Most of the time the shear plane is close enough to the Stern plane, so we can consider

ζ ≈ ΨSt St: outer Helmholtz plane = Stern plane

The loosely held countercharges form “electric double layers”. The electrostatic repulsion re-sults from the interpenetration of the difuse part of the double layer around each charged particle.

VR

x: distance between the sur-faces

Repulsion between overlapping double layers

V R (x )=Ψ02 e−κx

An electrostatic repulsion curve is used to in-dicate the energy that must be overcome if the particles are to be forced together.

The Balance of Repulsion & Atraction (DLVOa theory)

Notice the secondary minimum. The system flocculates, but the aggregates are weak → this may imply reversible flocculation.

The point of maximum repulsive energy is called the energy barrier. Energy is required to overcome this repulsion. The height of the barrier indicates how stable the system is. The electrostatic stabilization is highly sensitive with respect to sur-face charge (ζ ~ Ψ ~ pH) and salt concentration (κ, z).

VT = VA + VR

V A(x )=−A r6 x

V R (x )=r (kT )2γ

2 z−2 e−κx

x

γ =e

ze ΨSt

2 kT−1

eze ΨSt

2kT+1

VT = VA + VR

(large sediment height or gel)

• VOan der Waals atraction will predominate at small and at large interparticle distances.• At intermediate distances double layer repulsion may predominate, depending on the ac-

tual values of the forces.• In order to agglomerate, two particles on a collision course must have suficient kinetic

energy due to their velocity and mass, to “jump over” this barrier.

The height of the energy barrier depends upon ζ and 1/κ.

Precipitate, or cake

sol

In the secondary minimum there is a reversible floccula-tion or sol-gel transforma-tion.

VT ,VA, VR (J) the total, atractive and repulsive energy of two spherical particles at distance d (m).

Primary minimum, irreversible coagulation

Secondary minimum, “weak” flocculation

(large sediment height or gel)

gel

Electrostatic stability of dispersions

● An increase in electrolyte concentra-tion leads to a compression of the double layer (κ increase) → the en-ergy barrier to coagulation decreases or disappears.

● If the barrier is cleared, then the net interaction is all atractive → the particles coagulate. This inner region is afer referred to as an “energy trap” since the colloids can be considered to be trapped together by van der Waals forces.

Ionic strength: I1 < I2 < I3 < I4 < I5

Inverse Debye length: κ1 < κ

2 < κ

3 < κ

4 < κ

5

What concentration of salt (c =c.c.c.) eliminates the repulsive barrier completely?

If the potential energy maximum is large compared to the thermal energy, kBT of the particles, the system should be stable; otherwise, the system should coagulate.

Counterion va-lency c.c.c. (in mol/l) ~ z -6

The c.c.c. is the concentration of salt that just eliminates the repulsive barrier.

Critical coagulation concentration

Schulze–Hardy Rule

The Schulze–Hardy rule states:the critical coagulation concen-tration (c.c.c.) inversely de-pends on the sixth power of the charge on the ions.

c.c.c. (in mol/dm3) ~ z -6

cmonovalent : cdivalent : ctrivalent

1 : 2-6 : 3-6 = 1 : 0.015 : 0.0014

If there is an energy barrier, Vmax to coagulate then a fraction (α) of col-lisions is unsuccessful, so the rate of coagulation ks is slower.

Rates of coagulation can be mea-sured by the change in the number of particles, Smoluchowski equa-tion:

kd is the rate of the difusion limited aggregation or rapid coagulation (no barrier, Vmax=0)

The stability ratio: d

s

kW

k

The stability of dispersion is increased by: in-crease in particle radius, increase in electrokinetic potential (|ζ| > 25 mVO), decrease in the Hamaker constant, decrease in the ionic strength, decrease in temperature.

t : time (s), N: number of single particles per volume (dm-3), D : difusion coeficient (m2 s-1), ks: relative number of successful collisions (s-1), kd: number of total collisions (s-1), kB: Boltzman constant (J K-1), T: temperature (K), Vmax: maximal rate of aggregation (mol s-1)

Rates of coagulation

−dNdt

=8 πD αN 2=k d N 2

α ∼ e−V max

k B T

Elementary steps of coagulation:

initial step

htp://apricot.polyu.edu.hk/~lam/dla/

V × N =constant=V 0× N 0 V ∼1N

−dNdt

=k N 2→

1N

−1

N 0

=k t

NN 0

=1

1+k N 0 t /2

If all flocculation rate constants are the same:

N decreases with time, while the size of the resulting particles increases:

N/N

0 NN 0

=1

1+k N 0 t /2

The decrease in the normalized number of total particles, singlets, doublets, and triplets according to the Smoluchowski theory as a function of time.

Rate can be measured through the decrease of the total number (-dN/dt)or the increase of the average volume (dV/dt) for example by turbidity as a function of time:Turbidity ~ V 2 N = V (V×N ) ~ V×constant

VR VS

Steric stabilization

Protective action of adsorbed macromolecules (natural or synthetic)

Two efects

Polymer thickness

Work is required to push the particles closer together than their polymer layers keep them apart.

Entropic repulsion

Lyophilic macromolecules as stabilizers

V S=V M+V VR

VVOR

VM

Loos

e la

yers

Den

se la

yers

Steric stabilization

Steric repulsion

Steric + atractive interaction

ane factor of steric stabilization is the tail size

Short tail

Long tail

VT = V

S+VA

Steric stabilization

Steric stabilization by surface bound polymers:● is not sensitive to surface charge

and salt concentration● works also in non-aqueous media● works also in concentrated

dispersionsDisadvantage: more dificult to prepare.

VT = VA + VS VR=0

How to avoid coagulation

The stabilizing polymer must be in a good solvent environment

Efect of the temperature:

Segments in the tail can move freely or not, the interaction between segments themselves is stronger or smaller than than the interaction between the segments and the solvent.

V S=V M+V VR

V T=V A+V S

Configuration of adsorbed polymers

• Sterically stabilized dispersions are stable when the stabilizing polymer is soluble in the solvent – or at least it has one such part.

• The worse the solvent, the more unstable the colloidal dispersion.

• Cross-over from stabilization to flocculation: theta solvent at theta temperature (theta solvent: interactions between polymer segments are of the same strength than between a segment and the solvent).Chemical adsorption

(chemisorption)

Combined steric and electrostatic stabilization

It can be achieved by polyelectrolytes (like proteins) or by the combination of charged surface and neutral polymers

VT = VA + VR + VSVT = VA + VR

Plane of shear is pushed out farther

Steric stabilization makes the potential minimum disappear (no net atraction)

Electrostaticrepulsion

Electrostaticrepulsion

Stericrepulsion

van der Waalsatraction

van der Waalsatraction

Conditions:● good adsorbent● good solvent● (very) low polymer density● (very) long chain polymers

Long polymers ‘bind’ the colloids together in open flocs.

Application: water purification (a few ppm of cationic polyelectrolyte is added to the dispersion → flocculation, since most natural colloid surfaces are negative).

Bridging flocculation

Stability of lyophilic colloids

Lyophilic colloids

Isostable:no precipitation at

IEP

Isolabile:precipitation at

IEP

Stability of lyophilic sols comes from sol-vation and charge. If solvation interaction alone is strong enough the colloids stay stable at their isoelectric pH. If it is not, colloids coagulate at their isoelectric pH.

Gelatin is stable at its isoelectric point so it is an isostable colloid, but it can be pre-cipitated with much more salt or a dehy-drating agent (acetone, alcohol).

Casein is unstable at its isoelectric pH where it is uncharged, this is an isolabile protein. Casein precipitates at its IEP where there is no repulsion.

Stability of lyophilic colloids

The fermentation of milk sugar (lactose) produces lactic acid, which acts on milk protein casein → coagulation and denaturation → yoghurt (gel-like texture)

The isoelectric point of casein is 4.6.

Repulsiondisappearsat pH=4.6