Mechanical and optical properties of colloidal solutions

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 SOLUTIONSThe main characteristic properties of colloidal solutions are:

Brownian motion The motion of

colloidal particle in dispersed medium

Direction of the particle

AverageBrownian displacement

;3 rN

RTx

a

Dtx 22 fN

RTtx

a

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:

dx

dCDS

dt

dm

• (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/sEinstein equation for spherical particles of the dispersed systems

D = kT/6πηrdiffusion 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 pressureof colloid solutions:

1. Osmotic pressure is very low:

aN

RT

V

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:

32

31

31

32

2

1

D

D

r

r

Hepp-Skatchard’s osmometr

mem

brane

solvent

man

ometer

Cap

illary w

ith tolu

ol

Co

lloid

al

so

lutio

n

M

C51053.2

where 2.53·105 – constant at 25ºС

π =[cm of water

shaft]

Sedimentation equilibrium

Sedimentation rate (Stock’s equation):

gr )(

9

2 02

Sedimentation analysisIt 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/Hwhere 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)

g

thHr

)(2

1/91

0

Sedimentation curves mono- and poly-disperced systems

gQ

mhr

)(2

9

0 Content of separated

fraction

Q

r

Distribution curve of the particles of the dispersed phase according to the size

Sedimentometers:а) Phygorovski’ b) Vagner’

h

Q

hm

, where m – mass settled down fraction, Q– general mass of powders

The scheme, which explains the color of the atmosphere

Observation point

Earth

Sky blue Sun

Sunset (Sunrise )

red

Rayleigh equation: 4

20

nVI

kI

The intensity of the transmitted light beam is defined according to Rayleigh equation:

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

22

02

1

20

21

4

23

0 )2n

n(24

n

nVII t

Optical propertiesOptical 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 1000times. 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 microscopeTo 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 technicaldifficulties of stabilising high-tension supplies and correcting lens aberrations.

The useful range of the transmission electron microscope forparticle size measurement is c. 1 nm-5 μm diameter.

The use of the electron microscope for studying colloidal systems islimited by the fact that electrons can only travel unhindered in highvacuum, so that any system having a significant vapour pressure mustbe thoroughly dried before it can be observed.A small amount of the material under investigation is deposited onan electron-transparent plastic or carbon film (10-20 nm thick)supported on a fine copper mesh grid. The sample scatters electronsout of the field of view, and the final image can be made visible on afluorescent 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

Lens LensDia

phra

gm

Light source

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 scatteringWhen 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-turbidityAll 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 lightAs 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

Flasks containing colloidal solution

Source of light

Plate

Limb Limb

photometer

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