Page 69 - Introduction to Colloid and Surface Chemistry

Optical properties 59

where R (defined in equation 3.3) now refers to primary scattering
from unit volume of solution.
Therefore,
Kc 1
3 7
-^^ < - >
Urn c—»0
where
2

dn/dc is measured with a differential refractometer reading to the
sixth decimal place.
In contrast to osmotic pressure, light-scattering measurements
become easier as the particle size increases. For spherical particles
the upper limit of applicability of the Debye equation is a particle
diameter of c. A/20 (i.e. 20-25 nm for A 0 ~ 600 nm or A water ~ 450 nm;
or a relative molecular mass of the order of 10'). For asymmetric
particles this upper limit is lower. However, by modification of the
theory, much larger particles can also be studied by light scattering
methods. For polydispersed systems a mass-average relative molecular
mass is given.

Large particles

The theory of light scattering is more complicated when one or more
of the particle dimensions exceeds c. A/20. Such particles cannot be
considered as point sources of scattered light, and destructive
interference between scattered light waves originating from different
locations on the same particle must be taken into account. This
intraparticle destructive interference is zero for light scattered in a
forward direction (0 = 0°). Extinction will take place between waves
scattered backwards from the front and rear of a spherical particle of
diameter A/4 (i.e. the total path difference is A/2). The radiation
envelope for such a particle will, therefore, be unsymmetrical, more
light being scattered forwards than backwards.
When particles of refractive index significantly different from that
of the suspending medium contain a dimension greater than c. A/4,
extinction at intermediate angles is possible and maxima and minima
of scattering can be observed at different angles. The location of such
maxima and minima will depend on the wavelength, so that with