8.8 Properties of colloids
8.8.1 Optical property of colloids
Out

class reading:
Levine pp. 402

405
colloidal systems
lyophilic colloids
lyophobic colloids
sedimentation
Emulsion
Gels
1857
,
Faraday
first
observed
the
optical
properties
of
Au
sol
8.8.1 Tyndall effect and its applications
sol
solution
Dyndall
Effect
:
particles
of
the
colloidal
size
can
scatter
light
.
(1) Tyndall effect
1871
,
Tyndall
found
that
when
an
intense
beam
of
light
is
passed
through
the
sol,
the
scattered
light
is
observed
at
right
angles
to
the
beam
.
(2) Rayleigh scattering equation:
The
greater
the
size
(
V
)
and
the
particle
number
(
v
)
per
unit
volume,
the
stronger
the
scattering
intensity
.
light with shorter wave length
scatters more intensively.
cos
1
2
2
9
2
2
1
2
2
2
1
2
2
2
4
2
2
0
n
n
n
n
r
vV
I
I
4
2
cV
K
I
Applications
1.
Colors
of
scattering
light
and
transition
light
:
blue
sky
and
colorful
sunset
2.
Intensity
of
scattering
light
:
wavelength,
particle
size
.
Homogeneous
solution?
3.
Scattering
light
of
macromolecular
solution?
4.
Determine
particle
size
and
concentration?
Distinguishing true solutions from sols
1925
Noble
Prize
Germany,
Austria,
1865

04

01

1929

09

29
Colloid
chemistry
(ultramicroscope)
Richard A. Zsigmondy
(3) Ultramicroscope
principle of ultramicroscope
1
)
:
Particle
size
For
particles
less
than
0
.
1
m
in
diameter
which
are
too
small
to
be
truly
resolved
by
the
light
microscope,
under
the
ultramicroscope,
they
look
like
stars
in
the
dark
sky
.
Their
differences
in
size
are
indicated
by
differences
in
brightness
.
The pictures are reproduced from the Nobel Prize report.
Filament, rod, lath, disk, ellipsoid
2)
Particle number
: can be determined by counting the bright
dot in the field of version;
3
)
Particle
shape
:
is
decided
by
the
brightness
change
when
the
sol
was
passing
through
a
slit
.
Slit

ultramicroscope
For two colloids with the same
concentration:
2
2
2
1
2
1
V
V
I
I
For two colloids with the same
diameter:
2
1
2
1
c
c
I
I
4) Concentration and size of the particles
From:
Nobel Lecture, December, 11, 1926
4
2
cV
K
I
8.8.2 Dynamic properties of colloids
(1) Brownian Motion:
1827
,
Robert
Brown
observed
that
pollen
grains
executed
a
ceaseless
random
motion
and
traveled
a
zig

zag
path
.
Vitality?
In
1903
,
Zsigmondy
studied
Brownian
motion
using
ultramicroscopy
and
found
that
the
motion
of
the
colloidal
particles
is
in
direct
proportion
to
Temperature
,
in
reverse
proportion
to
viscosity
of
the
medium,
but
independent
of
the
chemical
nature
of
the
particles
.
For
particle
with
diameter
>
5
洬
湯
Brownian
motion
can
be
observed
.
Wiener
suggested
that
the
Brownian
motion
arose
from
molecular
motion
.
Although
motion
of
molecules
can
not
be
observed
directly,
the
Brownian
motion
gave
indirect
evidence
for
it
.
Unbalanced collision from
medium molecules
(2) Diffusion and osmotic pressure
x
Fickian first law for diffusion
dx
dc
DA
dt
dm
Concentration gradient
D
iffusion coefficient
Concentration gradient
1905 Einstein proposed that:
Lf
RT
f
T
k
D
B
For spheric colloidal particles,
r
f
6
Stokes’ law
f
= frictional coefficient
r
L
RT
D
6
1
Einstein first law for diffusion
F
A
B
C
D
E
c
1
c
2
½
x
½
x
x
c
c
dx
dc
)
(
2
1
)
(
2
1
2
1
2
1
2
1
2
1
c
c
x
c
x
c
x
m
x
c
c
D
dx
dc
D
)
(
2
1
)
(
2
1
)
(
2
1
2
1
c
c
x
t
x
c
c
D
Dt
x
2
r
t
L
RT
x
3
Einstein

Brownian motion equation
The
above
equation
suggests
that
if
x
was
determined
using
ultramicroscope,
the
diameter
of
the
colloidal
particle
can
be
calculated
.
The
mean
molar
weight
of
colloidal
particle
can
also
be
determined
according
to
:
L
r
M
3
3
4
r
t
L
RT
x
3
Perrin
calculated
Avgadro’s
constant
from
the
above
equation
using
gamboge
sol
with
diameter
of
0
.
212
m,
=
0
.
0011
Pa
s
.
After
30
s
of
diffusion,
the
mean
diffusion
distance
is
7
.
09
cm
s

1
L
= 6.5
23
Because
of
the
Brownian
motion,
osmotic
pressure
also
originates
RT
V
n
Which confirm the validity of Einstein

Brownian motion equation
(3) Sedimentation and sedimentation equilibrium
diffusion
1) sedimentation equilibrium
Gravitational
force
Buoyant
force
a
a’
b
b’
c
d
h
Mean concentration:
(
c

½ d
c
)
The number of colloidal
particles:
AdhL
dc
c
)
2
(
Diffusion force:
cRT
RTdc
d
The diffusion force exerting on each colloidal particle
cdhL
RTdc
AdhL
dc
c
Ad
f
d
)
2
(
The gravitational force exerting on each particle:
g
r
f
g
)
(
3
4
0
3
d
g
f
f
g
h
h
RT
LV
c
c
)
)(
(
ln
1
2
0
2
1
Altitude distribution
systems
Particle diameter / nm
h
O
2
0.27
5 km
Highly dispersed Au sol
1.86
2.15 m
Micro

dispersed Au sol
8.53
2.5 cm
Coarsely dispersed Au sol
186
0.2
m
Heights needed for half

change of concentration
This
suggests
that
Brownian
motion
is
one
of
the
important
reasons
for
the
stability
of
colloidal
system
.
g
h
h
RT
LV
c
c
)
)(
(
ln
1
2
0
2
1
2) Velocity of sedimentation
Gravitational force exerting on a particle:
g
r
f
g
)
(
3
4
0
3
When the particle sediments at velocity
v
, the resistance force is:
rv
fv
f
F
6
When the particle sediments at a constant velocity
g
F
f
f
g
r
v
)
(
9
2
0
2
radius
time
10
m
5.9 s
1
m
9.8 s
100 nm
16 h
10 nm
68 d
1 nm
19 y
Times needed for particles to settle 1 cm
For
particles
with
radius
less
than
100
nm,
sedimentation
is
impossible
due
to
convection
and
vibration
of
the
medium
.
g
r
v
)
(
9
2
0
2
3) ultracentrifuge:
Sedimentation
for
colloids
is
usually
a
very
slow
process
.
The
use
of
a
centrifuge
can
greatly
speed
up
the
process
by
increasing
the
force
on
the
particle
far
above
that
due
to
gravitation
alone
.
1924,
Svedberg
invented
ultracentrifuge
, the r.p.m of which can attain
100 ~ 160 thousand and produce accelerations of the order of 10
6
g
.
Centrifuge acceleration:
x
a
2
revolutions per minute
r
2
xM
F
c
r
2
xM
F
c
x
v
M
xM
F
b
2
0
r
0
2
dt
dx
Lf
F
d
For sedimentation with constant velocity
dx
v
RT
x
M
c
dc
)
1
(
0
2
r
)
(
)
1
(
ln
2
2
1
2
2
2
0
1
2
r
x
x
v
c
c
RT
M
Therefore,
ultracentrifuge
can
be
used
for
determination
of
the
molar
weight
of
colloidal
particle
and
macromolecules
and
for
separation
of
proteins
with
different
molecular
weights
.
light
Quartz
window
balance
cell
bearing
To optical
system
rotor
Sample
cell
1926
Noble
Prize
Sweden
1884

08

30

1971

02

26
Disperse systems
(ultracentrifuge)
Theodor Svedberg
The
first
ultracentrifuge,
completed
in
1924
,
was
capable
of
generating
a
centrifugal
force
up
to
5
,
000
times
the
force
of
gravity
.
Svedberg
found
that
the
size
and
weight
of
the
particles
determined
their
rate
of
sedimentation,
and
he
used
this
fact
to
measure
their
size
.
With
an
ultracentrifuge,
he
determined
precisely
the
molecular
weights
of
highly
complex
proteins
such
as
hemoglobin
(
血色素
)
.
Why
does
Ag
sol
with
different
particle
sizes
show
different
color?
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