Colloid stability.Lyophobic sols. Stabilization of

colloids.

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 wetted)– Thermodynamically stable

● Lyophobic: little or no interactions between the parti-cles and the solvent (partially wetted or unwetted parti-cles)– Thermodynamically unstable– Can be kinetically stable or unstable

● Mixing is spontaneous.● Mixing is reversible.● Thermodynamically stable.● Inhomogeneities on molecular levels.

● Mixing is non-spontaneous (requires mechan-ical energy).

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

lizing agent) and unmix spontaneously.

● Inhomogeneities on large length scales com-pared to molecular dimensions.

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 and dispersions

=

Thermodynamical stability

● Solutions are thermodynamically stable

● Gibbs energy of the components before mixing is higher than after 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 settle out under the influence of gravity. An ini-tially formed aggregate is called a floc and the process of its formation floccula-tion. The floc may or may not separate out. If the aggregate changes to a much denser form, it is said to undergo co-agulation. An aggregate usually sepa-rates out either by sedimentation (if it is more dense than the medium) or by creaming (if it less dense than the medium). The term’s flocculation and co-agulation have often been used inter-changeably. Usually coagulation is ir-reversible whereas flocculation can be reversed by the process of defloccula-tion.

Kinetic stability

Coagulation or flocculation

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

b)The suspended particles form light, fluffy agglomerates held together by strong van der Waals forces. The flocculated particles settle 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.

a floc

loosely adher-ing mass, it can be reversed by deflocculation

a) coagulated, b) flocculated particles

Much denser form, irreversible

a cake

Strength of interparticle forces

Encounters between particles occur as a result of Brownian motion and stability of a suspension is determined by the inter-action between particles during these en-counters

There is no repulsion

There is repulsion

Stability depends on the balance of at-tractive and repulsive interactions

Attraction comes from van der Waals forces between particles.

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

Stability of lyophobic sols

● Lyophobic sols are thermodynamically unstable● However there are stabilizing factors → kinetical sta-

bility can be attained● Whether aggregation does or does not occur depend

of the balance of attractive and repulsive forces

● For stabilization to occur, the repulsive forces must dominate

F⃗ =F⃗ A+F⃗ R

VR VS

Electrostatic and steric stabilization

There is Attraction between atoms/molecules even in vacuum (VA: at-traction potential)

Dispersion attraction between atoms / molecules is additive so it effects in case of macroscopic bodies too.

x

x

The attraction depends on the geometry of the particles

x

A is the Hamaker constant (or attraction parameter)

Molecular origin of Van der Waals attraction

V A (r )=const

x 6

V A (x )=−A r12 x

V A (x )=−A

12 πx 2

r

Molecules inparticle 1

Molecules inparticle 2

● The attraction of bodies arises from London (dispersion) attraction of molecules (all molecules act independently).

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

● An attractive energy curve is used to indicate the variation in van der Waals force with distance (x) between the particles.

The Hamaker model

x

x

The Hamaker constant (A) in vacuum depends on material properties: den-sity, polarizability

x

An attractive energy or attractive potential curve is used to indicate the variation in van der Waals force with distance between the particles.

The effective Hamaker constant Aeff also depends on the dispersion medium

Effective Hamaker constant

V A(x )=−A r12 x

VA(x)

Particles of the same charge

Ψ=ΨSt e−κ(x−x OHP)

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

ζ ≈ ΨStOHP: outer Helmholtz plane = Stern plane

The loosely held countercharges form “electric double layers”. The electrostatic repulsion re-sults from the interpenetration of the diffuse 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 & Attraction (DLVO 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 r12 x

V R (x )=r (kT )2 γ2 z−2 e−κ x

x

γ=e

ze ΨSt

2kT −1

eze ΨSt

2kT +1

VT = VA + VR

(large sediment height or gel)

Van der Waals attraction will predominate at small and at large interparticle distances. At intermediate distances double layer repulsion may predominate, depending on the actual values of the forces. In order to agglomerate, two particles on a collision course must have sufficient kinetic energy due to their velocity and mass, to “jump over” this barrier.

The height of the energy barrier depends upon the zeta potential and 1/

Precipitate, or cake

sol

In the secondary minimum there is a reversible floccula-tion: sol- gel transformation

coagulation

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

Electrostatic stability of dispersions

An increase in electrolyte concentration leads to a compression of the double layer (κ increase) and so the energy bar-rier to coagulation decreases or disap-pears. If the barrier is cleared, then the net interaction is all attractive, and as a result the particles coagulate. This inner region is after 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 (n0) eliminates the repulsive barrier?

If the potential energy maximum is large compared with the thermal en-ergy, kT of the particles, the system should be stable; otherwise, the sys-tem should coagulate.

Counterion valen-cy c.c.c (in mol/l) ~z-6

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 con-centration (c.c.c.) inversely depends on the sixth power of the charge on the ions.

c.c.c (in mol/l) ~ 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 collisions is unsuccessful, so the rate of coagulation slower, ks.

Rates of coagulation can be mea-sured by the change in the num-ber of particles, Smoluchowski equation:

2 28 d

dNDaN k N

dtπ− = =

kd is the rate of the diffusion limited ag-gregation or rapid coagulation (no barrier, Vmax=0)

The stability ratio: d

s

kW

k=

The stability of dispersion is increased by: increase in particle radius, increase in electrokinetic poten-tial (ζ >25mV), decrease in Hamaker constant, de-crease in the ionic strength, decrease in tempera-ture.

maxexpV

kTα −≈

t: time, Np: number of single particles per unit volume, D: diffusion coefficient, kD: rate constant, kB: Boltzman constant, T: temperature, Vmax: maximal rate of aggregation

Strength of interparticle forces –Rates of coagulation

N/N0

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

2dNk N

dt− =

0

1 1k t

N N− =

If all flocculation rate constants are the same

00

1/

1 / 2N N

kN t=

+

N decreases with time, while their size increases.

Elementary acts of coagulation:

initial act 00

1/

1 / 2N N

kN t=

+

0 0constant ~ 1/VN V N V N= =

Rate can be measured through decreasing the total number -dN/dt or increasing the average volume, dV/dt for example by turbidity as a function of time.Turbidity~ V2N~ V (VN) ~V constant

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

VR VS

Steric stabilization

Protective action of adsorbed macro-molecules (natural or synthetic)

Two effects

MV

VRV

S M VRV V V= +

Polymer thickness

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

Entropic repulsion

Lyophilic macromolecules as stabilizers

Steric stability

Steric repulsion

Steric + attractive interaction

One factor of steric stabilization is the tail size

VS+VA

Short tail

Long tail

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 difficult to prepare.

VT = VA + VS VR=0

How to avoid coagulation

The stabilizing polymer must be in a good solvent environ-ment

S M VRV V V= +

VT = VA + VS

Effect of the temperature!

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

• Sterically stabilized dispersions are stable when the polymer is soluble – the one phase regions.

• The worse the solvent, the more unstable the colloidal dispersion. Cross-over from stabilization to flocculation: theta solvent, theta temperature

Chemical adsorption

Configuration of adsorbed polymers

Steric + electrostatic stabilizationIt can be achieved by polyelectrolytes, gelatin, protein... or by charged surface + neutral polymers (caution about zeta potential)

VT = VA + VR + VSVT = VA + VR

Plane of shear is pushed out, farther

Good adsorbent, good solvent, (very) low polymer density, (very) long polymers

The long polymers ‘bind’ the colloids together in open flocs. Application: water purification (in practice, a few ppm of cationic polyelectrolyte is added, since most natural colloid surfaces are negative)

Bridging flocculation

The isoelectric point of casein is 4.6.

Lyophilic sols’ stability comes from solvation + charge. If solvation interaction alone is strong enough the colloids stay stable at its iso-electric pH if it is not they coagulate at their isoelectric pH.Gelatin is stable at its isoelectric condition so called isostable colloids, but it can be precipi-tated with much more salt or dehydration agent (acetone, alcohol).Casein is unstable at this isoelectric pH where there is no charge, this is an isolabile protein. Casein precipitates at iep where there is no re-pulsion.

lyophilic colloids: isostableno precipitation at iep

isolabileprecipitation at iep

The fermentation of milk sugar (lactose) produces lactic acid, which acts on milk protein to give yoghurt its gel-like texture

Stability of lyophilic colloids