92168.pdf

60 Optical properties

Incident

beam

(b)

Constructive

interference

Destructive

interference

Figure 3.7 (a) Scattering from a relatively large particle, (b) Radiation envelope for

light scattered from a spherical particle (jt = 0.8, m — 1.25). See text and Figure 3.6 for

explanation

incident white light it is possible, with a suitable monodispersed
system, to observe spectral colour sequences (known as 'higher-order
Tyndall spectra').
Mie (1908) elaborated a general quantitative theory for light
scattering by spherical particles. The intensity of the light scattered at
various angles is related to m, the ratio of the refractive index of the
particles to that of the dispersion medium, and the parameter x =
2irr/A. Mie's theory has been extended by Gans to include certain
non-spherical shapes. The main features of Mie's theory were verified
by La Mer and Barnes^141 from measurements of the angular variation
of the light scattered by monodispersed sulphur sols containing
particles of radius 300-600 nm.
Since the light scattered forwards (0°) suffers no intraparticle
interference, its intensity is proportional to the square of the particle
mass. By measuring the light scattered by a colloidal solution or
dispersion as a function of both angle and concentration and
extrapolating to zero angle and zero concentration, the size of
relatively large particles can be calculated from the Debye equation.
This extrapolation (Zimm plot^142 ; Figure 3.8) is achieved by plotting
Kc/R 0 against sin^2 (0/2) + /cc, where k is an arbitrary constant
selected so as to give convenient spacing between the points on the
graph.

Kc I

(3-9)

RQ

limc-»0

M