92168.pdf

58 Optical properties

such a particle is, therefore, proportional to the number of individual

scatterers in the particle — i.e. to its volume and, hence, its mass; and

the total intensity of scattered light is proportional to the square of

the particle mass. Consequently, for a random dispersion containing

n particles of mass m, the total amount of light scattered is

proportional to nm^2 ; and as nm is proportional to the concentration c

of the dispersed phase ,

total light scattered cc cm

An alternative (but equivalent) approach is the so-called fluctuation

theory, in which light scattering is treated as a consequence of

random non-uniformities of concentration and, hence, refractive

index, arising from random molecular movement (see page 26).

Using this approach, the above relationship can be written in the

quantitative form derived by Debye^140 for dilute macromolecular

solutions:

He 1 „„

— = — + 2Bc

T M

i.e. Hc = !.. (3.4)

T M

time— »0

where r is the turbidity of the solution, Af is the molar mass of the
solute, B is the same as B 2 in equation (2.21) and H is a constant
given by

li ~~

3NA\^40 (dc

where n 0 is the refractive index of the solvent, n is the refractive index
of the solution and A 0 is the wavelength in vacua (i.e. A 0 = nX, where
A is the wavelength of the light in the solution). T is calculated from
the intensity of light scattered at a known angle (usually 90° or 0°).
Summation of the products, R d o>, over the solid angle 4ir leads to
the relationship