Transcript Document 7363260

Structure and Properties of
Non-Metallic Materials
Lecture 4:
Colloids
Professor Darran Cairns
[email protected]
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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 the5
number of steps and thus is proportional to time.
Einstein-Smoluchowski
If the displacement vector after time t is R then
R(t )2
 t
Where  is related to the diffusion constant and can be
determined following Einstein and Smoluchowski’s argument
d2R
dR
m 2 
 FRandom
dt
dt
Equation of motion of particle
  6a
Drag coefficient for
spherical particle of radius a
If the motion of the particle is truly random then
<x2>=<y2>=<z2> and therefore <R2>=3<x2>
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Einstein-Smoluchowski II
Multiplying equation of motion by x and rearranging and
useing the identity d(x2)/dt=2x(dx/dt)
 d (x2 )
2
dt
d 2x
 xFRandom  mx 2
dt
but
d 2 x d  dx   dx 
x 2  x  
dt
dt  dt   dt 
2
Rewriting again using the above identity and taking averages
2
 d (x )
2
dt
 xFRandom
Not correlated
d
dx
 dx 
m
x
m  
dt
dt
 dt 
Not correlated
2
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Einstein-Smoluchowski III
2
 d (x )
2
dt
 dx 
 m  
 dt 
2
But from the equipartition of energy for any object in thermal
equilibrium at temperature T we can write (m(vx)2)/2=kBT/2
d (x2 )
dt
2
k BT

Giving us a total mean squared displacement
R 2

6 k BT

t
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Einstein-Smoluchowski IV
The motion of the particle is diffusive, with a diffusion
coefficient D given by the Einstein formula
D
k BT

For a sphere diffusing in a liquid   6a and therefore
DSE 
k BT
6a
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
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from this.
Electrostatic double-layer forces
Form of potential due to double layer can be found by
solving
 ze 
d 2 2 zen0


sinh 
2
dx
0
 k BT 
If the potential is small sinh(x) ~ x (the Debye-Huckel
approximation) the form of the potential is
 x   0 exp  x 
Where κ-1 is the Debye screening length
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 2e 2 n0 z 2 

  
 0 k BT 
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 Φ 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 nonadsorbing 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
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stick on the outside of the cluster, as access to its interior is blocked, resulting in
much more open aggregates with a fractal structure.
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.
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The fractal dimension of this pattern is D=log 5/ log 3=1.465
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,
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triangles are polystyrene spheres of radii between 54 and 90 nm in water.
Viscosity versus shear rate
Relative viscosity as a function of shear rate for model hard-sphere lattices. The
shear rate γ is plotted as the dimensionless combination, the Peclet number Pe=6π
η0a3γ/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
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diamonds 55nm polystyrene spheres in a meta-cresol.
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
The percolation model. We start with array of points, to which bonds are added at
random (left). As more bonds are added clusters of points are formed (middle), which
ultimately join to form a cluster which spans the entire system (right).
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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
N  f  z  1
n
Below some critical value of f finite clusters (sols) are formed. Above fc an
infinite cluster (gel) forms.
1
fc 
z  1
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Gel fraction versus fraction of reacted
bonds
The gel fraction in the
classical model of gelation for
a coordination number z=3.
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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
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pHs above about 7).
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
Model for the structure
of a casein micelle.
Casein protein subunits
are linked by colloidal
calcium phosphate to
produce a raspberrylike structure
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.
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Ice Cream
Typical structure of icecream 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)]
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