CHAPTER
5
AGGREGATION OF SMALL PARTICLES
Page No.
5.1 Introduction
67
5.1.1
Van der Waals attraction
69
5.1.2
Electrostatic repulsion
69
5.1.3 Diffusion limited aggregation
71
5.1.4
Reaction limited aggregation
72
5.1.5 Characterisation of the aggregates
73
5.1.6 Work included in this chapter
73
5.2 Aggregation of microclusters of sulphur
5.2.1
Introduction
5.2.2 Experiment and Observation
5.2.3
Discussion
5.3 Aggregation of microclusters of silver
5.3.1
Introduction
5.3.2 Experiment and Observation
5.3.3 Discussion
5.4 Aggregation of microclusters of silver
iodide and mercuric iodide
5.4.1
Introduction
5.4.2 Experiment and Observation
5.4.3
Discussion
5.5 Conclusion
References
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5.1 Introduction
Understanding
kinetic
aggregation
of
small
particles to form clusters and the study of the structure of
these
clusters
colloid
was
has
been the prime goal in
the
field
physics for many years. The interest in this
aroused
aggregation
not
only
represents
due
to
the
fact
one of the major
that
of
field
colloid
applications and
experimental tests of modern statistical theories of kinetic
growth,
but
simulations
characterize
recent
developments
including
(1,2) have made it feasible to
computer
quantitatively
the aggregates despite their very
random
and
disordered appearance. The random, tenuous clusters that are
produced when colloids aggregate, exhibit dilation
symmetry
and can be termed as fractals ( 3 ) . Since cluster aggregation
is a kinetic non-equlibrium growth process, the structure of
the
aggregates
is
inherently
related
to
dynamics
of
aggregation.
The
particles dispersed in a liquid phase will
be
undergoing Brownian notion and will be continually colliding
with one another. There should be a protective mechanism
prevent
aggregation and to retain the individuality of
particles.
The
protection
may
be
achieved
to
the
through
electrostatic stabilization or through steric stabilization.
In
the case of electrostatic stabilization
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the
electrical
protection
may
be
electrolyte
content
destroyed
of
by
an
the solution
increase
at
a
in
fairly
the
sharp
concentration. All electrolytes have this effect but counter
ions
of
those
high charge numbers are much more
of low valence. This valance effect is known
of Schulze (4) and Hardy ( 5 ) . A
rule
effective
sterically
than
as
the
protected
suspension may be caused to flocculate by the addition of
non-solvent
for the protecting molecules. These
a
protective
mechanisms can only slow down the process of aggregation but
cannot prevent it. The structure of the aggregates depends
on the mechanism of aggregation. If the
strongly
between
particles
particles
so
in
a
suspension
is
significant, the
will coagulate only very slowly but when they
they are observed to form very compact
little
repulsion
entrapped
solvent.
When
the
do
structures with
repulsion
significant, the clusters stick to one another
is
not
immediately
and irreversibly upon collision and the aggregation rate
is
determined by the diffusion of the clusters. The key to
the
traditional
and
understanding
of both colloid
stability
aggregation of small particles dispersed in a liquid
medium
is in the determination of the energy of interaction between
two
colloid
centre
particles as a function
separation
particles
(6). The energy of
of
their
center-to-
interaction
may arise due to van der Waals attraction
electrostatic repulsion.
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between
or
by
5.1.1
Van der Waals attraction
The
approaching
overall
The
by
van der Waals forces between the atoms in
particles are to some extent additive
and
effect is an attractive force of quite long
idea has been worked out by De Boer (7) and
Hamaker
(8). According to the widely used
two
the
range.
especially
DLVO
theory
(9,10,11), The attractive van der Waals interaction between
two spherical particles is
where A is the Hamaker constant, r is the separation of
the
centres and a is the sphere radius
5.1.2
Electrostatic Repulsion
Suspensions of a solid phase in a liquid medium can
be stable over a long period of time if the particles
repel
one
Waals
another strongly enough to overcome the van
der
attraction. Electrostatic repulsion if exists can be
enough
the
and can have a long enough range to do the
case
of
electrostatic
stabilization
screened coulomb forces is
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the
strong
job.
In
repulsive
constant
where Z is the charge per sphere, €the dielectric
of
the solvent K is the inverse screening length and n
the
total number of ions in solution
The potential energy due to van der
between
two
colloidal
particles
of
the
Waal's
same
effect
material
immersed in a fluid is negative. The repulsive force due
Coulombic interactions between particles lead to a
potential
positive
energy. There is a primary and secondary minimum
due to the attraction with a steep barrier between them.
is well established that the height of the barrier and
depth
of
the
secondary minimum play a
determining the
energy
to
critical
the
in
Thus
the
barrier height Eb of width K-l is the origin of
the
stability
of
diffusion
induced collision, two particles will approach
K- 1 , and will overcome the energy barrier and
to
within
stick
is
This
a
extent of particle aggregation.
role
It
dispersion
aganist
aggregation.
together with a probability P+exp(-Eb/kBT)
the
Boltzmann
type
initial
of
clusters
and
T
an approach can be
rate
aggregation
constant
of
kinetics
used
aggregation.
are
themselves also
more
diffuse
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is
the
to
The
In
where
a
kg
temperature.
determine
the
subsequent
complicated
as
the
and grow. The mechanism
of
aggregation observed in fresh and aged suspensions will
therefore be different and fall into two universal
namely
diffusion
limited
aggregation(DLA)
regimes,
and
reaction
limited aggregation(RLA).
5.1.3
the
Diffusion Limited Aggregation
When Eb << kBT where kB is the Boltzmann constant,
aggregation rate is maximum and particles stick to one
another
quickly
and
irreversibly upon
collisions.
The
aggregation is limited only by the diffusion of particles or
small clusters of particles and this regime
named diffusion
limited aggregation (6,121 forms the first universal
of
kinetic aggregation. A general feature of this
regime
kind
of
aggregation appears to be the dilation symmetry exhibited by
the resultant clusters, whether they are formed by accretion
of
single particles or by cluster-cluster aggregation.
The
tenuous, highly disordered structures of the clusters can be
quantitatively
characterized
as
fractals.
The
fractal
dimension of the cluster aggregates is experimentally
- 0.05, which is in excellent
( 6 ) to be df = 1.75+
with
the
simulations
fractal
dimension
obtained
from
agreement
computer
of the cluster-cluster aggregation models
The fractal dimension remains the same when the
mass(l3).
fractal dimension is also not sensitive to the form
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(6).
diffusivity
of the clusters is taken to be independant of the
The
found
of
cluster
mass distribution, remaining unchanged whether
the
aggregation occurs in a system of equal sized clusters
or
in polydisperse distributions (15).
structural
reorganisations
configuration
after
to
(14)
Furthermore,
form
a
the clusters stick do
more
not
small
stable
appear
to
change the fractal dimension significantly (6).
Reaction Limited Aggregation
5.1.4
When
>
Eb
KBT the rate of
aggregation
is many
orders of magnitude less than that for DLA. In this case the
rate
of
limiting step in the kinetics is the actual
a
bond
and
aggregation
clusters,
we
(6).
as
label
this
rpgime
formation
reaction
limited
In the RLA regime, the structure of
determined by their
fractal
the
dimension,
the
aggregation dynamics, and the cluster mass distributions all
change
dramatically
clusters
from
the
DLA
behaviour.
The
formed by RLA have a much more dense
and
large
compact
appearance than that of the clusters formed by DLA. This may
be
due
to
the reason that the clusters will
be
able
to
interpenetrate one another to a greater degree than for DLA,
leading to an increased fractal dimension (df=2.05+0.1)
for
clusters (6). The bonds once they are formed, are
very
the
strong
and
geometry
are
rigid.
This rigidity along
with
of the clusters, will ensure that
the
the
still quite tenuous and that their structure
fractal.
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complex
aggregates
is
still
Thus
to
the two universl regimes-DLA and RLA-
be sufficient to describe the mechanisms
of
appear
homogenous
aggregation of a large number of colloidal systems
Characterisation of the Aggregates
5.1.5
The best way to study the structure of the highly
dispersed
colloidal aggregates would be to observe then
in
three dimensions. The very small size of the particles makes
it necessary to use transmission electron microscope(TEM) to
attain
to
sufficient resolution to measure the structure down
length scales of the order of the
individual particles
(6).
Analyses of aggregates using'TEM has the
that
the TEN image is a two dimensional projection of
three
disadvantage
dimensional cluster and that the cluster have
to
the
be
removed from the liquid phase and dried, a process that may
distort the structure. Still TEM imaging is the most
and
convenient method
to actually
see
and
direct
analyse the
structure
of aggregates and it has been shown that
dimension
obtained by TEM analysis corresponds to
fractal
that
of
the cluster in solution (6).
5.1.6
Work Included in this Chapter
In
this
chapter, the
study
of
microclusters of certain materials using TEN
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aggregation of
and
electron
diffraction are discussed. Section 1 deals with the study of
aggregation
of microclusters of sulphur dispersed in
water
methanol mixture, Section 2 consists of the investigation of
the mechanism of aggregation observed in Ag colloids in
of a stabiliser and in Section 3, the
presence
the
aggregation
found in fresh and aged samples of microclusters of AgI
and
HgIZ are discussed.
SECTION 1
5.2 Aggregation of Microclusters of Sulphur
5.2.1
Introduction
The
form
larger
process
clusters
of agregation of small
and the structure
particles
that
result are
important technologically and scientifically. All
knowledge of
computer
the growth of these clusters
to
has
of
our
come
from
simulations (1,2,14,15) which have suggested
that
the resultant structures exhibit scale invariance and can be
termed
of
as fractals. Despite the accumulation of the
theoretical results
experimental
theories
have
Weitz
work
that
on the
kinetics of
can test the
aggregation,
validity
have been rather sparse. Forrest and
analysed aggregation of metallic smoke
of
colloids
(16)
particles
and
of gold by TEM. Schafer et a1
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modern
Witten
and Oliveria (17) investigated aggregates of
aqueous
wealth
uniform
(18) have
reported
formed
TEM analyses of silica particles.
in
these cases were highly
The
ramified
structures
exhibiting
a
scale invariance and are described as fractals.
This section consists of a study of aggregation
colloidal
suspension of
sulphur particles
by
TEM
and
electron diffraction. The aggregates formed have been
to
of
found
be random, tenuous and could be termed as fractals.
The
electron diffraction patterns of the aggregates are found to
be
spotty
indicating that the
crystalline
aggregating
(21,221. The electron
particles
diffraction
are
photographs
have been used to study the mechanism of aggregation.
5.2.2
Experiment and Observation
Suspensions of small particles of sulphur used
this work were prepared by quickly adding measured
quantity
of a saturated solution of flours of sulphur in methanol
constant temperature
Suspensions
distilled
of
two
water
to
in to doubly
different
distilled
water
concentrations
sulphur solution) were
at
(23).
(ratio
used
in
for
of
the
present study. The suspension of 2:1 concentration contained
0.113
gm
of sulphur per litre and
the
4:l
concentration
contained 0.056 gm of sulphur per litre of the suspension. A
drop
placed
of
the freshly prepared suspension
of
sulphur
on the TEM grid and the liquid phase was allowed
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was
to
evaporate.
examined
area
The
structure of
the
sulphur
clusters were
using a PHILIPS EM 301 TEM. By examining the
full
of the TEM grid, clusters of widely varying degree
aggregation
could
be
found
and
photographed.
The
of
same
microscope but now in the electron diffraction mode was used
for
the
determination of
crystallinity
of the
sulphur
particles and selected area electron diffraction photographs
were
taken.
temperature
The samples were allowed to
age
at
for 24 hours and these were also
constant
subjected
to
TEM and electron diffraction studies to determine the effect
of
aging
on the extent of aggregation
Electron micrographs of fresh (Figs.5.1
(Figs.5.2
and
5.4)
samples are
of
the
particles.
and 5.3)
reproduced
to
and
aged
show the
structure of the aggregates. Figures 5.5,5.7 and 5.6,5.8 are
the electron diffraction photographs of aggregates in
fresh
and aged samples respectively.
5.2.3
Discussion
The
random,
tenuous
clusters that
are
produced
when colloids aggregate can be quantitatively characterised
as
has
DLA or RLA despite their very
been
disordered
shown that the aggregates
appearance-It
produced
through
the
reaction limited and diffusion limited process show dilation
symmetry
and
can
be termed as fractals
(6).
The
random
aggregates of sulphur particles produced in fresh as well as
aged samples in the present study must also be self
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similar
Figure Captions
Fig.5.1
-
5.4
Electron rn-icrography of suspensions of
small particles of sulphur.
Fig.5.1
Fresh sample (Con. 2:l)
Fig.5.2
Aged sample
Fig.5.3
Fresh sample (Con. 4:l)
Pig.5.4
Aged sample
(Con. 2:l)
(Con. 4:l)
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Figure Captions
Fig.5.5
-
5.8
Electron diffraction photographs of
suspensions of small particles of sulphur.
Fig.5.5
Fresh sample (con. 2:l)
Fig.5.6
Aged sample
Fig.5.7
Fresh sample (Con. 4:l)
Fig.5.8
Aged sample
(Con. 2:l)
(Con. 4:l)
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'
and
could
be termed fractals since aggregation
well shown to be describable by DLA and
amply
has
RLA
been
regimes
(6).
Theoretical
and experimental studies
the literature indicate that
diffuse
via
clusters
Brownian
aggregate.
(6) are
models
the clusters themseleves
motion and growth
These
better
reported
occurs
cluster-cluster
representation
of
when
the
one on a growing aggregate. Also in the RLA
which
model
Each
up of
of
the
(20).
two
actual
regime
one
in
bond formation is the rate limiting step, this
may even lead to chemical reaction upon
aggregation.
tiny cluster getting added to a growing cluster, made
crystalline particles
the particles
the
may
aggregation
experimental situation than the attachment of particles
by
in
formation
forming
and
a tiny
the crystalline
nature
cluster may
hamper
of aggregates exhibiting
not
fractal
structure
The TEM micrographs (Figs.5.1 to 5.4) show irregularly
shaped, ramified
structures for fresh and aged samples
of
suspensions
sulphur particles.
of
aggregates
of
The
structure
of sulphur observed in fresh samples
should
be
more open and must fall in the DLA regime while structure of
aggregates of aged samples should be more dense
fall
in
the
RLA
regime.
The
electron
and
should
diffraction
photographs of the structures formed in fresh samples of low
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concentrations show
indicating only
there
by
(Fig.5.7)
limited
thin packing
of
indicating a role of
number
of
crystalline
DLA.
spots
particles,
Electron
diffraction
photographs for aged samples (Fig.5.8) of low concentrations
show much larger number of spots (almost rings)
indicating
close packing of crystalline particles. This indicates
that
aggregates formed in aged samples of low concentration must
be
more dense and must be formed through RLA mechanism.
high
concentrations
initially
hours
(-?:I)
open
structures are
by DLA (Fig.5.5) and structures formed
indicate an
extreme
case
of
close
mass with a limited
evident
formed
after
packing
particles, resulting in the formation of a poly
At
24
of
crystalline
number of crystallites (21,22). This is
from the very limited number of
diffraction
spots
(Fig.5. 6).
SECTION 2
5.3 Aggregation of Small Particles of Silver
5.3.1
Introduction
Metal colloids have been known for a long time
and
are of great interest due to their technological, industrial
and
medicinal
applications.
traditional and
least
as
far
Colloidal gold
is the
widely studied colloid and was
back
as
the
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twelth
century.
known
most
at
Faraday's
scientific studies of colloidal gold was instrumental in the
establishment of the discipline of colloid science. Many
of
the concepts of colloid science, especially the stability of
colloids, were tested using colloidal gold. Colloidal silver
also
have
methods
silver
been
been
known long ago
(24-261, of
colloid
and
prepared
which the preparation
These
of
dates back to 1889. Colloidal
studied mainly for their optical
colloids are
also of
by
Carey
in
Lea
silver
properties
interest
various
have
(27-30).
the
areas
of
catalysis, especially when free organic radicles in solution
are
involved. More recently they gained interest with
surface
enhanced Raman scattering technique(SERS1
study of
molecules adsorbed at the
particles.
properties
These
surface of
studies emphasized
that
of small particles of silver are
the
for
the
colloidal
the
various
influenced
the size and shape of particles and more specially by
their
aggregation state. In this work an attempt has been made
characterise
through
electron
microscopy
the
aggregation observed in silver colloids produced by
by
to
cluster
Bredigs
method.
5.3.2
Experiment and Observation
Silver
suspension used for the present study
prepared by Bredis's method (23,31) as discribed in
2
of
chapter 4. The resulting suspension was
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were
section
filtered
to
remove
for
coarser particles and kept undisturbed for two
the
particles
suspension were
to
then
aggregate.
subjected
The
to
particles
TEM
in
and
days
the
electron
diffraction studies to determine the effect of aging on
the
extent of aggre~ation.The TEN micrographs of the aggregates
(see Fig.4.2 of chapter 4) exhibits
appearance
characteristically
aggregates.
4.3
of
the
tenuous
observed
ramified
for
fractal
The electron diffraction photographs
(see Fig
4) show characterstic diffraction rings
chapter
observed for crystalline material.
5.3.3
Discussion
The
show
the
electron micrographs of aggregates of
random
aggregates.
The
tenuous
nature
aggregates formed
exhibited
when
by
silver
silver
fractal
particles
flocculate, can be due to DLA or RLA just as in the case
sulphur
clusters
discussed in section 1 of
this
of
chapter.
Since no electrolyte is added to initiate aggregation in the
silver
suspension, the
necessary cocdition
for
DLA,
ie
Eb<<kgT may not be satisfied and the aggregation mechanism
may
not in general be DLA. Even though the
probability
formation of clusters through DLA are small the chance
the
presence
of aggregates formed through
DLA
cannot
discarded, since at the time of prepar~tionof the
the formation of clusters through DLA are probable.
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of
for
be
colloid
In the case of silver colloid, the surface adsorbed
ions
cause
the
the silver particles to be highly
ionic strength of the solution creates
screening
double
length of
layer
charged
a
few atomic distances.
Debye-Huckel
The
interaction between the particles
suspension very
stable against
resulting
makes
aggregation.
clusters will not stick to one another
collision, but
bond.
Thus
aggregation
the
(Eb>kgT),
immediately
they may do so through the formation
the
rate
limiting step
in
the
Since
repulsive double layer interaction is very strong
the
and
the
on
of
kinetics
is the actual formation of a bond and we
a
of
label
this
regime of aggregation as reaction limited
(6).
The electron diffraction pattern of the aggregates of
silver
aggregation
show the characteristic diffraction rings
(see Fig
4.3 of chapter 4). This indicates that the particles forming
the
aggregates are crystalline and they are packed
and
are much dense. It is established through
observations
closely
experimental
that the large clusters formed by RLA
have
a
much more dense compact appearance ( 6 ) . This result together
with
the
results
aggregation
of
produced
the
present
in aged silver
under the RLA regime.
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study
shoe
that
suspension may
the
fall
SECTION 3
5.4
Aggregation of Microclusters of AgI and Hg12
5.4.1
Introduction
Though the aggregation of metal clusters have
been
studied widely (16-la), the investigation of aggregation of
clusters of inorganic compounds are rather few (32).
of
the dynamics of aggregation in inorganic
Study
colloids will
provide a better understanding of the physical properties of
the
aggregates.
The importance of silver
iodide
(32) in
photographic processes has led to extensive investigation of
their
properties and intense interest in the mechanism
aggregation.
industrial
Colloidal
Hg12 is also a
material
applications. In this section, the
of
of
wide
aggregation
dynamics observed in fresh and aged samples of colloidal AgI
and Hg12 are discussed.
5.4.2
Experilnent and Observation
Aqueous
present
work
chapter 4.
and
Hg12
studies.
suspensions of AgI and Hg12 used
were prepared as discussed in
section
2
the
of
Fresh and aged samples of the suspensions of AgI
were subjected to TEM
A
in
well
defined
and
electron
continuous ring
diffraction
structure was
observed in the electron diffraction pattern of aged samples
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of Hg12 (see Fig.4.8)
while fresh samples indicate a spotty
pattern
).
fresh
(see Fig.4.7
Electron
diffraction
suspensions of AgI indicates a spotty
behavieur
while
aged
samples show rings
pattern
of
(see Fig.4.9)
with
a
limited
number of bright spots (see Fig.4.10).
Discussion
5.4.3
TEM micrographs of clusters of AgI
The
(see Figs.4.5
these
are
Hg12
and 4.6) indicate the state of aqgregation
clusters. The stability of AgI and
found
and
HgIg
in
suspensions
to be different. AgI suspension is found
to
be
stable while the suspension of Hg12
flocculates
within a very short time after preparation. The
aggregation
dynamics observed in fresh samples of the above
suspensions
moderately
falls in the DLA regime, since the probability of
formation
of
tine
of
established
by
clusters
preparation
through
of
the
DLA
is
suspension.
large
It
at
is
the
experimental observations that the aggregates formed through
DLA
are
less densly packed ( 6 ) . The
electron
diffraction
pattern of fresh samples of AgI (see Fig.4.9) indicate
packing
of
crytalline material
and
suggests
that
thin
the
aggregation dynamics observed falls in the DLA regime.
In
the
case of aged samples of
AgI,
the
energy
barrier between particles is significant and particles stick
to each other only by the formation of a bond. The
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electron
diffraction pattern of aged samples of AgI
shows
almost
continuous diffraction
(see Fig.4.10)
rings
indicating a
close packing of crystalline particles in the aggregates and
thereby
indicating that the mechanism of aggregation
falls
in the RLA regime.
Hg12
The
aggregates
suspension which
within
electrolyte is
Eb<<kBT
diffusion of
case
is
a short time after the
very
unstable
preparation.
required to initiate aggregation.
and the aggregation is limited
particles.
Thus
in
Hg12.
In
only
the
by
No
this
the
aggregation
observed in fresh and aged samples are the same and falls in
the
5.5
regime
DLA
(see Figs.4.7
and
4.8).
Conclusion
The
been
process
analysed
aggregates
mechanism
by
formed
of
of aggregation of
TEM
and
exhibit
electron
a
microclusters
has
diffraction.
The
behaviour.
The
fractal
aggregation observed
in
fresh
and
suspensions may fall under the regimes of diffusion
aged
limited
aggregation or reaction limited aggregation according as the
energy of interaction between the clusters.
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