Chemistry Reference
In-Depth Information
and
K
contains only quantities that are directly measurable, while
R
θ
has dimen-
sions of length
2
1
because it is defined per unit volume. When the viewing angle
is
π
/
2
,R
θ
becomes equal to the Rayleigh ratio:
r
2
R
90
5 I
0
θ
=I
0
(3-48)
, and
r
. If the scattering solute
molecules are small compared to the wavelength of light, it is only necessary to
measure
I
0
θ
Note that
R
θ
is apparently independent of
I
0
,
θ
as a function of enough values of
θ
to show that
R
θ
is indeed indepen-
dent of
/
2 is convenient) can be
used in the form of
Eq. (3-47)
to yield a plot of
Kc/R
θ
against
c
with intercept
1
/M
and limiting slope at low
c
equal to 2
A
2
. (This simple technique cannot be
used with polymeric solutes which have dimensions comparable to the wave-
length of light. Effects of large scatterers are summarized in
Section 3.2.3
.)
An alternative treatment of the experimental data involves consideration of the
fraction of light scattered from the primary beam in all directions per unit length
of path in the solution. A beam of initial intensity
I
0
decreases in intensity by an
amount
θ
. Then the data at a single scattering angle (
π
τ
I
0
dx
while traversing a path of length
dx
in a solution with turbidity
τ
.
The resulting beam has intensity
I
, and thus
I
I
0
e
2τx
5
(3-49)
or
τ 52
ln
ð
I
0
=
I
Þ=
x
(3-50)
The total scattering can be obtained by integrating
I
0
θ
(
Eq. 3-44
) over a sphere
of any radius
r
and it can then be shown that
16
3
π
τ 5
R
θ
(3-51)
It is customary also to define another optical constant
H
such that
2
3
n
0
ð
16
K
3
5
π
32
π
dn
=
dc
Þ
H
5
(3-52)
4
L
3
λ
and thus
Hc
τ
5
Kc
R
θ
5
1
M
1
3
A
3
c
2
2
A
2
c
1
1
?
(3-53)
3.2.2
Effect of Polydispersity
For a solution in the limit of infinite dilution,
Eq. (3-53)
becomes
τ 5
HcM
(3-54)
