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.

cos1

22

92

21

22

21

22

24

22

0

nn

nn

r

vVII

4

2

cV

KI

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 PrizeGermany, 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 i

n diameter which are too small

to be truly resolved by the ligh

t microscope, under the ultram

icroscope, they look like stars i

n the dark sky. Their differenc

es in size are indicated by diffe

rences 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:

22

21

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

KI

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 m, no 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

dcDA

dt

dm

Concentration gradient

Diffusion coefficient

Concentration gradient

1905 Einstein proposed that:

Lf

RT

f

TkD B

For spheric colloidal particles,

rf 6 Stokes’ law

f = frictional coefficient

rL

RTD

6

1 Einstein first law for diffusion

F

A

B

C

D

Ec1 c2

½ x ½ x

x

cc

dx

dc )( 21

)(

2

1

2

1

2

12121 ccxcxcxm

x

ccD

dx

dcD

)( 21

)(

2

1)(21

21 ccxtx

ccD

Dtx 2

r

t

L

RTx

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:

LrM 3

3

4

r

t

L

RTx

3

Perrin calculated Avgadro’s constant from the above equ

ation using gamboge sol with diameter of 0.212 m, = 0.0

011 Pas. After 30 s of diffusion, the mean diffusion distanc

e is 7.09 cm s-1

L = 6.5 1023

Because of the Brownian motion, osmotic pressure also originates

RTV

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

dh

Mean concentration:

(c - ½ dc)

The number of colloidal particles:

AdhLdc

c )2

(

Diffusion force: cRT RTdcd The diffusion force exerting on each colloidal particle

cdhL

RTdc

AdhLdc

c

Adfd

)2

(

The gravitational force exerting on each particle:

grf g )(3

40

3

dg ff

ghhRT

LV

c

c))((ln 12

0

2

1 Altitude distribution

systems Particle diameter / nm h

O2 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.

ghhRT

LV

c

c))((ln 12

0

2

1

2) Velocity of sedimentation

Gravitational force exerting on a particle:

grf g )(3

40

3

When the particle sediments at velocity v, the resistance force is:

rvfvfF 6

When the particle sediments at a constant velocitygF ff

gr

v)(

9

2 02

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.

gr

v)(

9

2 02

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 106 g.

Centrifuge acceleration: xa 2

revolutions per minute

r2xMFc

r2xMFc

xvMxMFb2

0r02

dt

dxLfFd

For sedimentation with constant velocity

dxvRT

xM

c

dc)1( 0

2r

)()1(

ln2

21

22

20

1

2

r xxv

cc

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?