Chemistry Reference
In-Depth Information
unpolarized incident light. The envelope is symmetrical about the plane corre-
sponding to
/
2. The scattered intensity in the forward direction equals that
in the reverse direction, and both are twice that scattered transversely because of
the term in (1
θ5π
cos
2
).
The scattered intensity is proportional to
1
θ
λ
2
4
. Thus, the shorter wavelengths
are scattered more intensely than longer wavelength light. (This is why the sky is
blue.) In light-scattering experiments, more intense signals can be obtained by
using light of shorter wavelength. If there are
N
independent scatterers in volume
V
, the combined intensity of scattering at distance
r
from the center of the (small)
volume and angle
to the incident beam will be simply (
N/V
) as great as that
recorded above for a single scatterer. This is because interference and enhance-
ment effects will cancel each other on the average if
θ
the scatterers are
independent.
If
c
is the weight of particles per unit volume, then the mass per particle is
Vc/N
and
Vc
=
N
5
M
=
L
(3-38)
where
M
is the molecular weight of the scattering material and
L
is Avogadro's
constant. Then, for
N/V
scatterers per unit volume,
8
I
0
θ
4
Lc
M
π
2
cos
2
I
0
5
4
r
2
α
ð
1
1
θÞ
(3-39)
λ
No average
M
is implied here, because we assume for the moment that all
scatterers are monodisperse in molecular weight.
The excess polarizability cannot be determined experimentally, but it can be
shown to be given by
n
0
M
2
dn
dc
α5
(3-40)
π
L
where
n
0
and
n
are the refractive indices of the suspending medium and suspen-
sion of scatterers, respectively. Substituting,
2
Mc
I
0
θ
I
0
5
2
cos
2
n
0
2
π
4
ð
1
1
θÞ
dn
dc
(3-41)
r
2
λ
L
The equations outlined so far are similar to those that apply to solutions of
monodisperse macromolecules, although the reasoning in the latter case is differ-
ent from the classical Rayleigh treatment that led to the preceding results. We can
nevertheless extend
Eq. (3-41)
to polymer solutions by the reasoning given below.
This makes for clarity of presentation but is not a rigorous development of the
final expressions used in light-scattering experiments.
It must be recognized that solutions are subject to fluctuations of solvent den-
sity and solute concentration. The liquid is considered to be made up of volume
elements. Each element is smaller than the wavelength of light so that it can be
