Transcript 幻灯片 1

8.8 Properties of colloids
8.8.1 Optical property of colloids
Out-class reading:
Levine pp. 402-405 13.6 Colloids
8.8.1 Tyndall effect and its applications
(1) Tyndall effect
1857, Faraday first observed the optical properties of Au sol
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.
sol
solution
Dyndall Effect:
particles of the colloidal
size can scatter light.
(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.
9 vV
I  I0
24 r 2
2
2
2
 n n 

 1  cos  
 n  2n 
2
2
2
2
2
1
2
1

I K
cV 2
4
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
(3) Ultramicroscope
Richard A. Zsigmondy
1925 Noble Prize
Germany, Austria,
1865-04-01 - 1929-09-29
Colloid chemistry
(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.
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
Filament, rod, lath, disk, ellipsoid
4) Concentration and size of the particles
I K
cV 2
4
For two colloids with the same
concentration:
I1
V12
 2
I2
V2
For two colloids with the same
diameter:
I1
c1

I2
c2
From: Nobel Lecture, December, 11, 1926
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.
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.
Vitality?
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
Indirect evidence for thermal motion of molecules
(2) Diffusion and osmotic pressure
Fickian first law for diffusion
 dc 
dn
 
 DA  
dt
 dx 
x
Concentration gradient
Concentration gradient
Diffusion coefficient
1905 Einstein proposed that:
kBT RT
D

f
Lf
f = frictional coefficient
For spheric colloidal particles,
f  6r
RT 1
D
L 6r
Stokes’ law
Einstein first law for diffusion
1
C
c1
A
c2
E
D
½x
B
½x
F
1

1

n   xc1  xc2    x(c1  c2 )
2
2

2

(c1  c2 )
 dc 
D   D
x
 dx 
 dc  (c1  c2 )
 
x
 dx 
(c1  c2 )
1
D
t   x(c1  c2 )
2
x
x  2 Dt
x
RT t
L 3r
Einstein-Brownian motion equation
x
RT t
L 3r
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:
4 3
M  r L
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  1023
Which confirm the validity of Einstein-Brownian motion equation
Because of the Brownian motion, osmotic pressure also originates
n
  RT
V
(3) Sedimentation and sedimentation equilibrium
1) sedimentation equilibrium
diffusion
Buoyant
force
Mean concentration:
(c - ½ dc)
Gravitational
force
b’
b
a
dh
c
The number of colloidal
particles:
a’
dc
(c 
) AdhL
2
Diffusion force:
  cRT d  RTdc
The diffusion force exerting on each colloidal particle
Ad
RTdc
fd 

dc
cdhL
(c 
) AdhL
2
The gravitational force exerting on each particle:
fg 
4 3
r (    0 ) g
3
f g  fd
c1 LV
ln

(    0 )( h2  h1 ) g
c2 RT
Altitude distribution
c1 LV
ln

(    0 )( h2  h1 ) g
c2 RT
Heights needed for half-change of concentration
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
This suggests that Brownian motion is one of the important
reasons for the stability of colloidal system.
2) Velocity of sedimentation
Gravitational force exerting on a particle:
4 3
f g  r (    0 ) g
3
When the particle sediments at velocity v, the resistance force is:
f F  fv  6rv
When the particle sediments at a constant velocity
2 r 2 (   0 )g
v
9

fF  fg
2 r 2 (   0 )g
v
9

Times needed for particles to settle 1 cm
radius
time
10 m
5.9 s
1 m
9.8 s
100 nm
16 h
10 nm
68 d
1 nm
19 y
For particles with radius less than 100 nm, sedimentation is
impossible due to convection and vibration of the medium.
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.
revolutions per minute
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:
a  x
2
Fc   2 xM r
Fc   xM r
2
Fb   xM 0  M r v 0 x
2
2
dx
Fd  Lf
dt
For sedimentation with constant velocity
c2
dc M r x
c1

(1  v 0 )dx M 
r
c
RT
(1  v 0 ) 2 ( x22  x12 )
2
2 RT ln
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.
rotor
light
Quartz
window
balance
cell
Sample
cell
bearing To optical
system
The first ultracentrifuge, completed in
1924, was capable of generating a
centrifugal force up to 5,000 times the force
of gravity.
Theodor Svedberg
1926 Noble Prize
Sweden
1884-08-30 - 1971-02-26
Disperse systems
(ultracentrifuge)
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).