Soft Condensed Matter
Physics
colloids; foams and gels;
Poly-electrolytes
colloids
What do the following have in common: fog; water-based paints, milk and
Mayonnaise?
They are all colloidal states!
Colloid is derived from ”kolla”; Greek for glue
The term colloid was first used in 1861, but with a different meaning from the
present.
Colloids should not be considered a special class of chemical substances;
instead matter can artificially or naturally adopt a colloidal state. The size
of objects is taken as the relevant parameter in defining the colloidal state.
Colloids
Colloid: a microscopically heterogeneous system where one component
has dimensions between those of molecules and those of sand
Typical particle size: 1nm to 1 µm
Surface to volume ratio is large
Colloid particles in dispersions undergo Brownian motion
When they encounter one another, the balance of attractive and repulsive
forces determine whether the dispersion is stable. If the repulsive forces
are sufficient to balance the attractive Van der Waals interactions the
colloidal suspension is said to be stable.
Flocculation: reversible aggregation
Coagulation: irreversible aggregation
Lyophilic and lyophobic colloids
Lyophilic colloids form systems called gels (solvent-loving colloid)
Lyophobic colloids form systems called sols (solvent-hating colloid)
Examples of lyophobic colloids: colloidal gold; droplets of liquid in aqueous solvent
The particles prefer not to associate with the solvent and, if conditions are right will
associate with each other.
Types of Colloids
Many colloids are two-phase dispersions. Systems where a dispersed phase
is distributed within a continuous dispersion medium are called simple colloids
or collodial dispersions
Disperse
phase
Dispersion
medium
Liquid
Gas
Solid
Gas
Name
Examples
Liquid aerosol
Fog, liquid sprays
Gas
Liquid
Solid aerosol
Foam
Smoke
Foams and froths
Liquid
Liquid
Emulsion
Milk, mayonnaise
Solid
Liquid
Sol, colloidal dispersion
Paints, toothpaste
Colloidal suspension
Paste (high solid content)
Gas
Solid
Solid foam
Polyurethane foam
Expanded polystyrene
Liquid
Solid
Solid emulsion
Tarmac, Ice cream
Solid
Solid
Solid suspension
Opal, pearl
pigmented plastic
Other types of Colloids
Association colloids: amphiphiles in solution
Macromolecular colloids: macromolecules forming particles of 1 nm or larger
dispersed in a liquid
Network colloids: e.g. porous solid
Multiple colloids: colloids where three or more phases co-exist (e.g. oil bearing
porous rock)
The collodial system: a delicate balance of
opposing forces
Brownian motion (thermal agitation)
The kinetic energy Ek transferred to a particle depends on the temperature
Ek = 3kT / 2
K = Plank's constant; T = absolute temperature
If the particles are small enough, diffusion due to thermal agitation opposes
sedimentation or creaming, and an equilibrium state is set up
C (h) = C 0e − mgh / kt
C(h) is the particle concentration at height h; C0 is the concentration
at the bottom of the tube; g is acceleration due to gravity; and
m is the effective mass of each particle.
4 3
m = πr ∆ρ
3
∆ρ is the difference in density between the dispersed phase and the
suspension fluid
Balance of forces
The general expretion for C(h) shows that if the thermal agitation kT is large
compared with mgH the concentrations at the top and bottom of the tube will
be more or less the same (C(h) = Co). On the other hand, when kT is much
smaller than mgH, a phase separation occurs, either through sedimentation or
creaming.
Example
Small spheres of density 2000 kg/m3 in water (so that ∆ρ = 2000 kg/m3), at room
temperature (T= 300 K), in a container of height 10 cm (H= 0.1 m).
Case 1: the ratio between the particle concentration near the surface and that
near the bottom of the container is of order zero for particles of diameter
100 nm (eventual sedimentation)
Case 2: the ratio between the particle concentration near the surface and that
near the bottom of the container is 0.88 for particles of diameter
10 nm (almost no sedimentation occurs)
Rate of sedimentation
The example illustrates the effect of particle size on phase separation, but it gives
no idea of the rate at which it happens. The sedimentation speed V can be
estimated by formulating the fact that it is the limiting speed at which the force of
gravity is balanced by frictional forces with the suspension liquid.
mg = 6πηrV
implying that
2∆ρgr
mg
V=
=
6πηr
9η
2
where m is the effective mass of the particle, r its radius and η the viscosity
of the suspension fluid.
Even though Boltzmann's law predicts a phase separation, the above relation
implies that it may take very long time when the viscosity is high.
Colloidal particles: van der Waals forces
Van der Waals radius (distances of the order 0.2-0.4 nm)
Consider the forces exerted by two particles (or more generally, several particles), we
can assume that the van der Waals forces are additive. Within a given particle, each
atom or molecule is thus subject to attractive forces from all the atoms of the
neighboring particles. Hence, two identical spherical objects of radius r are coupled
with energy:
Ar
Evdw = −
12s
where s is the inter-particle distance (defining zero energy when the particles are
infinitely far apart), and A is a physical constant, Hamaker’s constant, characterizing
the material.
When the particles are immersed in a fluid M, the same formula applies but the
Constant changes, and is denoted AM rather than A
Hamaker constant
Material
A [10-20 J]
AM[10-20J] (in water)
n-pentane
3.7
0.34
polystyrene
6.6
1.0
4.1
-
30-50
20-40
acetone
metals
In the case of polystyrene particles in water, the Hamaker constant is 10-20J.
Calculating the energy of attraction we find that, for a radius of 100 nm, the
Inter-particle energy is 8.3x10-20J at a distance of 1 nm, and 0.8x10-20J at a
distance of 10 nm. Expressed in multiples of kT (kT = 0.4x10-20J at rt) these
energy values become 20 kT and 2 kT, respectively. Both greater than the energy
of thermal motion.
Consequently, even if gravitational effects can be neglected, the combined effect
Of Brownian motion and van der Waals forces would cause attractive collisions
Between the particles, leading to the rapid formation of aggregates.
There has to be repulsive forces, capable of counterbalancing the the attractive forces!
Forces of electrostatic origin
In most natural colloidal systems, and in particular the aqueous solutions,
the repulsive interparticle forces are related to the presence of ionized species
on the surface of the particles.
Despite the fact that there are surface charges, the colloidal medium remains
electrically neutral globally. However, positive and negative ions are not
distributed homogeneously throughout the continuous medium.
The electrical energy Ee of a multi-particle system can be worked out for simple
geometrical arrangements. The repulsive force between two identical spherical
particles of radius r, separated by a distance s, is given by:
Ee = 2πrεκψ e
2
0
−κs
Stability of colloids
The long-term colloidal stability of a dispersion will be of great
importance in a number of industries such as pharmaceutical,
ceramic, paints and pigments. The term “stability” can have
different connotations to different applications. When applied to
colloids, a stable colloidal system is one in which the particles
resist flocculation or aggregation and exhibits a long shelf-life.
This will depend upon the balance of the repulsive and attractive
forces that exist between particles as they approach one another.
If all the particles have a mutual repulsion then the dispersion
will remain stable. However, if the particles have little or no
repulsive force then some instability mechanism will eventually
take place e.g. flocculation, aggregation etc.
In certain circumstances, the particles in a colloidal dispersion may adhere to one another
and form aggregates of successively increasing size that may settle out under the
influence of gravity. An initially formed aggregate is called a floc and the process of its
formation flocculation. The floc may or may not separate out. If the aggregate changes to
a much denser form, it is said to undergo coagulation. 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). The term’s flocculation and coagulation have often been used
interchangeably. Usually coagulation is irreversible whereas flocculation can be reversed
by the process of deflocculation. The following figure schematically represents some of
these processes.
Derjaguin, Landau, Verwey and Overbeek theory
(DLVO theory)
DLVO theory suggests that the stability of a particle in solution is dependent upon
its total potential energy function VT.
VT = VA + VR + VS
VS = potential energy due to the solvent
VA = attractive potential
VR = repulsive potential
Derjaguin, Landau, Verwey and Overbeek theory
(DLVO theory)
DLVO theory suggests that the stability of a colloidal system is determined by the sum
of van der Waals attractive forces (VA) and electrical double layer repulsive (VR) forces
that exist between particles as they approach each other due to the Brownian motion
they are undergoing.
This theory proposes that an energy barrier resulting from the repulsive force prevents
two particles approaching one another and adhering together (figure 1). But if the
particles collide with sufficient energy to overcome that barrier, the attractive force will
pull them into contact where they adhere strongly and irreversibly together. Therefore if
the particles have a sufficiently high repulsion, the dispersion will resist flocculation and
the colloidal system will be stable. However if a repulsion mechanism does not exist
then flocculation or coagulation will eventually take place.
Stabilization of colloids
Steric repulsion - this involves polymers added to the system adsorbing onto the particle
surface and preventing the particle surfaces coming into close contact. If enough polymer
adsorbs, the thickness of the coating is sufficient to keep particles separated by steric
repulsions between the polymer layers, and at those separations the van der Waals
forces are too weak to cause the particles to adhere.
Electrostatic or charge stabilization - this is the effect on particle interaction due to the
distribution of charged species in the system.
Steric stabilization
Steric stabilization is achieved by attaching long chain molecules to colloidal
Particles. Then, when colloidal particles approach one another (for example,
due to Brownian motion), the limited interpenetration of the polymer chains
Leads to an effective repulsion which stabilizes the dispersion against flocculation.
Advantages of steric stabilization relative charge stabilization:
a) The interparticle repulsion does not depend on electrolyte concentration
b) Effective in both aqueous and non-aqueous media
c) Effective over a wide range of colloid concentration, whereas charge stabilization
is most effective at low concentrations
Flocculation and stabilization by polymers
Molecular weight of polymer
polymer concentration
Poly-electrolytes
Addition of electrolyte
Poly-electrolytes
Polyelectrolytes are polymers whose repeating units bear an electrolyte group
+ Cl
H3N
Cl O
+
O
H3N
OH
OH
n
n
O
O S O
+
O
Na
-
O
O
OH
S
*
S
S
n
*
Examples of poly-electrolytes
The electrolyte groups will dissociate in aqueous solutions, making the polymers
charged. Polyelectrolyte properties are thus similar to both electrolytes and polymers.
Note: many biopolymers are poly-electrolytes (proteins; DNA)
Gels
Definition of a gel: a coherent mass consisting of a liquid in which particles are either
dispersed or arranged in a fine network throughout the mass. A gel may be notably
elastic and jellylike (as gelatin or fruit jelly), or quite solid and rigid (as silica gel)
A colloidal gel is formed by association of colloid particles or molecules in a
liquid such that the solvent is immobile. A gel is thus a low density disordered arrested
state which does not flow but possess solid-like properties such as a yield stress.
Similarly to glasses, the gel structure
does not show any significant order and,
in this respect, it is similar to that of
a liquid.
Association of sol particles can occur
through bridging flocculation, if the
bridges are extensive enough to form
a continuous network through the sample
Gels can form in concentrated polymer
solutions due to network formation
Gels can also form by association
of sol particles
Swelling of gels; syneresis
Gels formed by polymers in aqueous solutions can often be swollen to a substantial
extent. In contact with water such gels will take up water, because of an osmotic
effect. The water can diffuse into the polymer network, but the polymer chains can
not diffuse out. Thus the network acts as a kind of semi-permeable membrane.
If the gel is strong enough, swelling stops when the internal pressure in the gel
is equal to the osmotic pressure. If the gel is weak, the internal pressure will cause
the gel to break up, and the polymer will dissolve in solution
The process of syneresis in gels results from the kinetics of gel formation. The
initially formed gel structure may not be the most stable. The diffusion of polymer
chains, which is a slow process, may slowly lead to the formation of a more stable
compact structure. An increased pressure may then be exerted on the water in the
gel, leading to its slow expulsion; a process termed syneresis
Gelatin
Gelatin is an example of a network colloid, that is formed from denatured collagen
in water.
Gelatin is a protein produced by partial hydrolysis of collagen extracted from the bones,
connective tissues, organs, and some intestines of animals. Gelatin melts when heated
and solidifies when cooled again. Together with water, it forms a semi-solid colloid gel.
The cross-linking in gelatin is by non-covalent hydrogen bonding and electrostatic
Interactions. Thus the gelation process is thermo-reversible
Gels
Poly(methylmethacrylate) = PMMA
Foams
A foam is defined as a coarse dispersion of a gas in a liquid, where the volume
fraction of gas is greater than that of the liquid.
Note: solid foams are also possible
Liquid foams are always formed by mixtures of liquids (usually containing a soap
or surfactant) and never by a pure liquid
Foams are not thermodynamically stable due to their large interfacial area, and
thus surface free energy. However, some foams, particularly those formed by
addition of small amounts of foaming agents such as soaps or surfactants,
can be metastable. Foams formed by other liquids such as alcohols or short
chain fatty acids are unstable, and the foam collapses rapidly.
Foams: why are they unstable?
Drainage: drainage of the liquid due to gravity leads to thinning of the liquid film
Rupture: rupture results from random disturbances (mechanical, thermal,
evaporation, impurities)
The lifetime of a foam is controlled by three major factors:
(1) drainage: gravitational force causes most of the liquid to drain out of the foam,
resulting in the separation of liquid from foam. Drainage is a main limiting factor
for foam stability; (2) bubble coarsening: due to size difference, the pressure in
small bubbles is higher than that in relatively bigger bubbles. Driven by pressure
difference, gas molecules would diffuse from small bubbles to bigger bubbles through
liquid films, causing the big bubbles to become bigger and the small bubbles smaller,
and thus the average bubble diameter keeps growing. (3) film rupture: in dry foams,
the film is rather thin. Once the thickness is around the average gap among liquid
molecules, a local void in thin film would appear due to molecular thermal fluctuations,
and the whole film would break irreversibly, resulting in previous bubbles separated
by the film merging into one bigger bubble.
Relationship among factors limiting the
stability of liquid foam