Structure and Properties of Non-Metallic Materials Lecture 4:Colloids

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Structure and Properties of Non-Metallic
MaterialsLecture 4 Colloids

• Professor Darran Cairns
• drcairns_at_mmm.com

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Colloids
Disperse Phase Dispersion Medium Name Examples
Liquid Gas Liquid aerosol Fog
Solid Gas Solid aerosol Smoke
Gas Liquid Foam Foams
Liquid Liquid Emulsion Milk
Solid Liquid Sol, colloidal dispersion or suspension paste Silver iodide in photographic film, paints, toothpaste
Gas Solid Solid foam Polyurethane foam, expanded polystyrene
Liquid Solid Solid emulsion Asphalt, ice cream
Solid Solid Solid suspension Opal, pearl, pigmented plastic
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Shapes of Colloid Particles
Typical shapes of colloid particles (a)
spherical particles of polystyrene latex, (b)
fibres of chrysotile asbestos, (c) thin plates of
kaolininite.
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Monodispersed Colloids
Monodisperse inorganic colloids. (a) Zinc
sulphide (spherulite) (b) cadmium carbonate
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Brownian Motion
If you look at a dilute suspension of colloidal
particles (for example plant pollen in water)
under a microscope each particle moves in a
random jiggling motion. This motion is known as
Brownian Motion after Botanist Robert Brown who
reported the phenomenon in 1827.
In addition to his Nobel Prize winning work on
the photoelectric effect and his celebrated work
on special and general relativity Albert Einstein
found time to characterize Brownian motion.
The movement of a colloidal particle in
suspension has the characteristics of a random
walk. In a random walk the mean of the total
displacement is always zero, but the mean value
of the square of the displacement is
proportional to the number of steps and thus is
proportional to time.
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Einstein-Smoluchowski
If the displacement vector after time t is R then
Where a is related to the diffusion constant and
can be determined following Einstein and
Smoluchowskis argument
Equation of motion of particle
Drag coefficient for spherical particle of radius
a
If the motion of the particle is truly random
then ltx2gtlty2gtltz2gt and therefore ltR2gt3ltx2gt
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Einstein-Smoluchowski II
Multiplying equation of motion by x and
rearranging and useing the identity
d(x2)/dt2x(dx/dt)
but
Rewriting again using the above identity and
taking averages
Not correlated
Not correlated
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Einstein-Smoluchowski III
But from the equipartition of energy for any
object in thermal equilibrium at temperature T we
can write (m(vx)2)/2kBT/2
Giving us a total mean squared displacement
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Einstein-Smoluchowski IV
The motion of the particle is diffusive, with a
diffusion coefficient D given by the Einstein
formula
For a sphere diffusing in a liquid and therefore
Stokes-Einstein
This relationship is often used to determine the
size of unknown colloidal particles using dynamic
light scattering. Dynamic light scattering can
be used to measure the diffucion coefficients and
the radius of the particles can be calculated
from this.
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Electrostatic double-layer forces
Form of potential due to double layer can be
found by solving
If the potential is small sinh(x) x (the
Debye-Huckel approximation) the form of the
potential is
Where ?-1 is the Debye screening length
Models for the electric double layer around a
charged colloid particle (a) diffuse double
layer model, (b) Stern model
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Electrostatic double-layer forces
Distribution of ions near a charged surface,
according to Debye-Huckel theory. The dotted line
illustrates the form of the potential near the
surface.
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Polymer stabilisation of colloids
Stabilisation of colloids with grafted polymers.
When the particles come close enough for the
grafted polymers to overlap, a local increase in
polymer concentration leads to a repulsive force
of osmotic origin.
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Depletion reaction
The depletion interaction. Polymer coils are
excluded from a depletion zone near the surface
of the colloidal particles when the depletion
zones of two particles overlap there is a net
attractive force between the particles arising
from unbalanced osmotic pressures.
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ESEM of waterborne latex
A water-borne latex suspension imaged by
environmental scanning electron microscopy,
showing the formation of ordered regions.
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Close packed structures
A single close-packed layer, illustrating that
there are two sites on which a second
close-packed layer can be placed b and c.
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Charged spheres of polyelectrolyte
Phase diagram for charged spheres in a
polyelectrolyte solution as a function of the
volume fraction of spheres F and the
concentration of salt as calculated for spheres
of radius 0.1 mm with surface charge 5000e.
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Phase diagram of colloidal spheres
Calculated phase diagram for a colloid of hard
spheres with non-adsorbing polymer added to the
solution. The ratio of the sizes of the
colloidal spheres to the radii of the polymer
molecules is 0.57
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Aggregation and rearrangement
Aggregation with and without rearrangement. In
(a) the attraction is weak enough to allow the
particles to rearrange following aggregation
this produces relatively compact aggregates. In
(b) the attractive energy is so strong that once
particles make contact, they remain stuck in this
position. Particles arriving later tend to stick
on the outside of the cluster, as access to its
interior is blocked, resulting in much more open
aggregates with a fractal structure.
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Fractal model for aggregates
Four stages in the construction of a simple
deterministic fractal model for particle
aggregates. In (a) five particles are formed in
the shape of a cross. In (b) five of these
crosses are joined together to form a larger
cross. The process is extended in (c) and (d) in
two dimensions. Each time the mass is increased
by a factor of 5, the lateral extension is
increased by a factor of 3. The fractal
dimension of this pattern is Dlog 5/ log 31.465
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Viscosity versus volume fraction
Relative viscosity as a function of volume
fraction for model hard sphere lattices, in the
limit of low shear rates (filled symbols) and
high shear rates (open symbols). The solid lines
are fitting functions and the dashed line is the
Einstein prediction for the dilute limit.
Squares are 76 nm silica spheres in cyclohexane,
triangles are polystyrene spheres of radii
between 54 and 90 nm in water.
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Viscosity versus shear rate
Relative viscosity as a function of shear rate
for model hard-sphere lattices. The shear rate ?
is plotted as the dimensionless combination, the
Peclet number Pe6p ?0a3?/kBT. The solid line is
for polystyrene lattices of radii between 54 and
90 nm in water the circles are 38 nm polystyrene
lattices in benzyl alcohol, and the diamonds 55nm
polystyrene spheres in a meta-cresol.
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Gels

• Chemical Gels
• Thermosetting resins
• Sol-gel glasses
• Vulcanized rubbers
• Physical gels
• Microcrystalline regions
• Microphase seperation

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Thermosetting gel
Schematic of a thermosetting gel. The system
consists of a mixture of short chains with
reactive groups at each end, and cross-linker
molecules, each with four functional groups
capable of reacting with the ends of the chains.
As the reaction proceeds the chains are linked
together by the cross-linker to form an infinite
network.
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Vulcanization
Schematic of a vulcanization reaction. The
system consists of a mixture of long chains.
Initially, the chains are entangled but not
covalently linked. The reaction proceeds by
chemically linking adjacent chains, leading to
the formation of an infinite network.
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Physical gels
Thermoreversible gelation by the formation of
microcrystals. At low temperatures (bottom)
adjacent chains form small crystalline regions
which act as cross-links. Above the melting
temperature, the crosslinks disappear (top).
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Thermoplastic elastomers
Butadiene
A triblock copolymer (SBS) can form a
thermoplastic elastomer. The end blocks
microphase separate to form small, spherical
domains. When these domains are glassy they act
as cross-links for the rubbery centre blocks the
rubber can be returned to the melt state by
heating above the glass transition of the end
blocks.
Styrene
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Percolation model

• Gels show a discontinuous change in properties at
  the gel point
• Simple model which captures this change is the
  percolation model
• Bonds added at random to a lattice
• gelation occurs when a continuous cluster forms
  that spans the whole lattice
• Numerical simulation not analytical solution

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Percolation model
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Cayley trees
Three generations of a Cayley tree
Definitions of branches and neighbours on a
Cayley tree
Number of bonds N out to nth generation of a
Cayley tree with a coordination number z and a
probability of bond formation f is given by
Below some critical value of f finite clusters
(sols) are formed. Above fc an infinite cluster
(gel) forms.
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Gel fraction versus fraction of reacted bonds
The gel fraction in the classical model of
gelation for a coordination number z3.
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Dangling ends and gels
The effect of dangling ends on the shear modulus
of a gel near the gel point. The bonds shown
with dashed lines are part of the infinite
network, but do not contribute to the elastic
modulus.
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Clay

• Clay minerals one of oldest materials known to
  man.
• In agriculture any soil particles of radius less
  than 2 mm
• In ceramics generally mean aluminosilicates
• Silicon can bond to oxygen to form thin flat
  sheets
• Silica sheets bond to flat sheets of aluminum
  oxide
• Impurities lead to ve charge on sheet surface

Card-house structure of kaolinite due to ve
charge on edge and ve charge on surface. Occurs
at low pH.
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Kaolinite
(a) A sketch of the ideal kaolinite layer
structure (Al(OH)2)2O(SiO2)2. One hydoxyl ion is
situated within the hexagonal ring of apical,
tetrahedral oxygens and there are three others in
the uppermost plane of the octahedral sheet. The
two sheets combined make up the kaolinite layer.
(b) simplified schematic diagram of a kaolinite
crystal. Note that the upper and lower cleavage
faces of the perfect crystal would be different.
A typical crystal would contain a 100 or so such
layers. (c) A typical kaolinite crystal of
aspect ratio (a/c) about 10. Note the negative
charges on the cleavage faces or basal planes and
positive charges around the edges (these are
eliminated at pHs above about 7).
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Printing ink
Simplified model of ink impression and
absorption. (1) The ink is hydraulically pressed
into the pores. As the roller pulls away, the
ink film splits by cavitation and rupture and the
surface is thoroughly wet. (2) the paper relaxes
and draws ink into the larger pores. (3) The
capillary forces take over and draw liquid into
the smaller pores, leaving most of the pigment
behind. (4) The ink continues to spread slowly
over all the surfaces
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Bread Dough
Scanning electron microscope studies of bread
dough morphology. (a) Dried dough showing the
starch granules embedded in the gluten matrix.
(b) Environmental SEM (ESEM) of fresh dough
showing hydrated starch granules and the thick
gluten matrix that holds the dough together
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Milk
Milk is a classic food colloid. It is basically
an oil-in-water emulsion, stabilized by protein
particles. Fresh unskimmed cows milk contains
86 water, 5 lactose, 4 fat, 4 proteins and 1
salt. The milky appearance is due to large
colloidal particles called casein micelles.
Casein micelles are polydisperse associates of
proteins bound together with colloidal calcium
phosphate. The fat globules are dispersed in
water and are stabilized by a membrane of
proteins and phospholipids at the oil/water
interface.
Model for the structure of a casein micelle.
Casein protein subunits are linked by colloidal
calcium phosphate to produce a raspberry-like
structure
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Ice Cream
Typical structure of ice-cream revealed in an
electron micrograph. (a) Ice crystals, average
size 50 µm, (b) air cells, average size 100-200
µm, (c) unfrozen material. From W.S. Arbuckle,
Ice Cream, 2nd Edition, Avi Publishing Company
(1972)