8.8 Properties of colloids

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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






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?