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Mechanical and optical
properties of colloidal solutions
1. Kinetic properties of the dispersed systems
2. Investigation methods of the dispersed systems
according to their kinetic properties.
3. Optical properties
4. Optical investigation methods of the dispersed systems
Assistant Kozachok S.S. prepared
PROPERTIES OF COLLOIDAL SOLUTIONS
The main characteristic properties of colloidal solutions are:
Brownian motion
The motion of
colloidal particle in
dispersed medium
Direction
of the
particle
Average
Brownian displacement
x 
RT


;
N a 3r
2 RTt
x 
Na f
x  2 Dt
2
• 1. Fick's first law of diffusion (analogous with
the equation of heat conduction) states that
the mass of substance dm diffusing in the x
direction in a time dt across an area S is
proportional to the concentration gradient
dc/dx at the plane in question:
dm
dC
  DS
dt
dx
• (The minus sign denotes that diffusion takes
place in the direction of decreasing
concentration.)
The proportionality factor D is called the diffusion
coefficient.
If – dc/dx = 1, S = 1 and dt = 1 D = dm, diffusion
coefficient equals to the mass of substance diffusing in
a time dt across an area S at the concentration gradient
equals to 1.
[D] = m2/s
Einstein equation for spherical particles of the
dispersed systems
D = kT/6πηr
diffusion coefficient is inversely proportsiynyry to
particle radius
2. The rate of change of concentration at any
given point is given by an exactly equivalent
expression, Fick's second law:
Osmotic pressure
of colloid solutions:
1. Osmotic pressure is
very low:
 RT
  
V Na
2. Osmotic pressure is inversely proportional to
the cube of radius of particles and is directly
proportional to raise to the cube (third)
power of its dispersion in the same dispersed
medium:
3
3
1
r2
D1
 3  3
2
r1
D2
Hepp-Skatchard’s osmometr
Colloidal
solution
Capillary
with toluol
2.53 10 C

M
5
where 2.53·105 –
constant at 25ºС
manometer
π=
[cm of water
shaft]
Sedimentation
equilibrium
Sedimentation rate
(Stock’s equation):
2 r (   0 ) g
 
9

2
Sedimentation analysis
It consists of the obtaining sedimentation curve, that
shows the dependence of the sediment mass m of the
dispersed phases, which is settled down till certain
time t. For monodispersed systems (with the same
particles size) this dependence is line:
m = Qυt/H
where Q – general mass of the dispersed phases; H –
initial height of column of the dispersed system.
But all real dispersed systems are polydispersed and
that’s why the sedimentation rate for different fraction
is different: large particles settle down faster, smaller –
slowly. Therefore sedimentation curve is bent to the
axis of ordinates.
Tangent of the slope in specific point adjacents to the
sedimentation determines the sedimentation velocity
for the corresponding particles.
Knowing the sedimentation rate of the corresponding
particles of separated fractions can be determined the
particle’s size (radius)
9hH / t1
r1 
2(   0 ) g
Sedimentation curves mono- and
poly-disperced systems
9hm
r
2Q(   0 ) g
Content of separated
fraction
Q
Distribution curve of the particles of the
dispersed phase according to the size
r
Sedimentometers:
а) Phygorovski’
b) Vagner’
h
hm

Q
, where m – mass settled down fraction, Q–
general mass of powders
The scheme, which explains the
color of the atmosphere
Sky blue
Sun
Observation
point
Rayleigh equation:
I 0 nV 2
I k 4

Sunset
(Sunrise )
red
The intensity of the transmitted light beam is defined
according to Rayleigh equation:
I t  I 0 24
V
n1  n 0 2
( 2
)
2
4
 n1  2n 0
2
3
2
2
where I0 is the intensity of the incident light beam, It is the intensity of
the transmitted light beam, n1 and n0 – the refractive indices of the
particles and the dispersion medium. λ - wavelength
Optical properties
Optical microscopy
Colloidal particles are often too small to permit direct microscopic
observation. The resolving power of an optical microscope (i.e. The
smallest distance by which two objects may be separated and yet remain
distinguishable from each other) is limited mainly by the wavelength λ of
the light used for illumination.
The numerical aperture of an optical microscope is generally less than
unity. With oil-immersion objectives numerical apertures up to about 1.5
are attainable, so that, for light of wavelength 600 nm, this would permit
a resolution limit of about 200 nm (0.2 μ.m). Since the human eye can
readily distinguish objects some 0.2 mm (200 μm) apart, there is little
advantage in using an optical microscope, however well constructed,
which magnifies more than about 1000
times. Further magnification increases the size but not the definition of
the image.
• Particle sizes as measured by optical
microscopy are likely to be in serious error for
diameters less than c. 200 nm.
• Two techniques for overcoming the limitations
of optical microscopy are of particular value in
the study of colloidal systems. They are
electron microscopy and dark-field
microscopy – the ultramicroscope
The transmission electron microscope
To increase the resolving power of a microscope so that matter
of colloidal (and smaller) dimensions may be observed
directly, the wavelength of the radiation used must be reduced
considerably below that of visible light. Electron beams can be
produced with wavelengths of the order of 0.01 nm and
focused by electric or magnetic fields, which act as the
equivalent of lenses. The resolution of an electron microscope
is limited not so much by wavelength as by the technical
difficulties of stabilising high-tension supplies and correcting
lens aberrations.
The useful range of the transmission electron microscope for
particle size measurement is c. 1 nm-5 μm diameter.
The use of the electron microscope for studying colloidal systems is
limited by the fact that electrons can only travel unhindered in high
vacuum, so that any system having a significant vapour pressure must
be thoroughly dried before it can be observed.
A small amount of the material under investigation is deposited on
an electron-transparent plastic or carbon film (10-20 nm thick)
supported on a fine copper mesh grid. The sample scatters electrons
out of the field of view, and the final image can be made visible on a
fluorescent screen.
Dark-field microscopy-the ultramicroscope
Dark-field illumination is a particularly useful technique for
detecting the presence of, counting and investigating the
motion of suspended colloidal particles. It is obtained by
arranging the illumination system of an ordinary microscope
so that light does not enter the objective unless scattered by
the sample under investigation.
Lyophobic particles as small as 5-10 nm can be made
indirectly visible in this way.
The two principal techniques of dark-field illumination are the
slit and the cardioid methods.
1) In the slit ultramicroscope of Siedentopf and Zsigmondy
(1903) the sample is illuminated from the side by an intense
narrow beam of light from a carbon-arc source
Scheme ultramicroscope
Light
source
Lens
Lens
2) The cardioid condenser (a standard microscope accessory)
is an optical device for producing a hollow cone of
illuminating light; the sample is located at the apex of the
cone, where the light intensity is high (Figure 3.4).
Dark-field microscopy is, nevertheless, an extremely useful
technique for studying colloidal dispersions and obtaining
information concerning:
1. Brownian motion.
2. Sedimentation equilibrium.
3. Electrophoretic mobility.
4. The progress of particle aggregation.
5. Number-average particle size (from counting experiments
and a knowledge of the concentration of dispersed phase).
6. Polydispersity (the larger particles scatter more light and
therefore appear to be brighter).
7. Asymmetry (asymmetric particles give a flashing effect,
owing to different scattering intensities for different
orientations).
Light scattering
When a beam of light is directed at a colloidal solution or
dispersion, some of the light may be absorbed (colour is
produced when light of certain wavelengths is selectively
absorbed), some is scattered and the remainder is transmitted
undisturbed through the sample.
The Tyndall effect-turbidity
All materials are capable of scattering light (Tyndall effect) to some
extent. The noticeable turbidity associated with many colloidal
dispersions is a consequence of intense light scattering. A beam of
sunlight is often visible from the side because of light scattered by
dust particles. Solutions of certain macromolecular materials may
appear to be clear, but in fact they are slightly turbid because of
weak light scattering. Only a perfectly homogeneous system would
not scatter light; therefore, even pure liquids and dust-free gases are
very slightly turbid.
The turbidity of a material is defined by the expression
where I0 is the intensity of the incident light beam, It is the
intensity of the transmitted light beam, l is the length of the
sample and τ is the turbidity.
This expression is used in Turbidimetry. It is based on the
measuring of the intensity of the transmitted light beam.
Measurement of scattered light
As we shall see, the intensity, polarisation and angular
distribution of the light scattered from a colloidal system
depend on the size and shape of the scattering particles, the
interactions between them, and the difference between the
refractive indices of the particles and the dispersion medium.
Light-scattering measurements are, therefore, of great
value for estimating particle size, shape and interactions, and
have found wide application in the study of colloidal
dispersions, association colloids, and solutions of natural and
synthetic macromolecules.
The intensity of the light scattered by colloidal solutions
or dispersions of low turbidity is measured directly. A
detecting photocell is mounted on a rotating arm to permit
measurement of the light scattered at several angles, and fitted
with a polaroid for observing the polarisation of the scattered
light (see Figure 3.5).
Doty nephelometr
photometer
Limb
Limb
Plate
Source
of light
Flasks containing
colloidal solution
Nephelometry is based on the measuring of the the intensity
of the scattered light beam by the dispersed system.
It,1/It,2 = c1/c2; It,1/It,2 = V1/V2;
It = k νV2I0 = kCVI0
where, k – constant, C = νV – volume concentration of the
dispersed phase
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