Chemistry Reference
In-Depth Information
shown in
Fig. 3.4b
. If any linear dimension of the scatterer is as great as about
λ/
20,
however, then the secondary radiations from dipoles in various regions of the
scatterer may vary in phase at a given viewing point. The resulting interference
will depend on the size and shape of the scatterer and on the observation angle.
The general effect can be illustrated with reference to
Fig. 3.4a
, in which a scat-
tering particle with dimensions near
is shown. Two scattering points,
P
1
and
P
2
, are shown. At plane
A
, all the incident light is in phase. Plane
B
is drawn per-
pendicular to the light which is scattered at angle
λ
θ
2
from the incident beam. The
distance
AP
1
B
AP
2
B
so that light that was in phase at
A
and was then scattered
at the two dipoles
P
1
and
P
2
will be out of phase at
B
.
Any phase difference at
B
will persist along the same viewing angle until the
scattered ray reaches the observer. The phase difference causes an interference and
reduction of intensity at the observation point. A beam is also shown scattered at a
smaller angle
,
θ
1
, with a corresponding normal plane
C
. The length difference
OP
1
C
2
OP
2
C
is less than
OP
2
B
2
OP
1
B
. (At the smaller angle
θ
1
,AP
2
.
AP
1
while
P
2
C
P
1
C
, so the differences in two legs of the paths between planes
A
and
C
tend
to compensate each other to some extent. At the larger angle
,
θ
2
, however,
AP
2
.
AP
1
and
P
2
B
P
1
B
.) The interference effect will therefore be greater the larger the
observation angle, and the radiation envelope will not be symmetrical. The scatter-
ing envelopes for large and small scatterers are compared schematically in
Fig. 3.4b
. Both envelopes are cylindrically symmetrical about the incident ray, but
that for the large scatterers is no longer symmetrical about a plane through the scat-
terer and normal to the incident direction. This effect is called
disymmetry
.
Interference effects diminish as the viewing angle approaches zero degrees to
the incident light. Laser light-scattering photometers are now commercially avail-
able in which scattering can be measured accurately at angles at least as low as 3
.
The optics of older commercial instruments which are in wide use are restricted to
angles greater than about 30
to the incident beam. Zero angle intensities are esti-
mated by extrapolation. It is always necessary to extrapolate the data to zero con-
centration, for reasons which are evident from
Eq. (3-44)
. Conventional treatment
of light-scattering data will also involve an extrapolation to zero viewing angle.
The double extrapolation to zero
.
and zero
c
is effectively done on the same
plot by the Zimm method. The rationale for this method follows from calculations
for random coil polymers which show that the ratio of the observed scattering
intensity at an angle
θ
to the intensity that would be observed if there were no
destructive inference is a function of the parameter sin
2
(
θ
θ
/
2). Zimm plots consist of
is plotted against sin
2
(
graphs in which
Kc/R
θ
bc
, where
b
is an arbitrary
scale factor chosen to give an open set of data points. (It is often convenient to
take
b
θ
/
2)
1
5
100.) In practice, intensities of scattered light are measured at a series of
concentrations, with several viewing angles at each concentration. The
Kc/R
θ
(or
Hc/
τ
) values are plotted as shown in
Fig. 3.5
. Extrapolated points at zero angle, for
example, are the intersections of the lines through the
Kc/R
θ
values for a fixed
c
and various
values with the ordinates at the corresponding
bc
values. Similarly,
the zero
c
line traverses the intersections of fixed
θ
θ
, variable
c
experimental points
