Chemistry Reference
In-Depth Information
treated as a single scattering source. The elements are large enough, however, to
contain very many solvent molecules and a few solute molecules. There will be
time fluctuations of solute concentration in a volume element. Because of local
variations in temperature and pressure, there will also be fluctuations in solvent
density and refractive index. These latter contribute to the scattering from the sol-
vent as well as from the solution, and solvent scattering is therefore subtracted
from the experimental solution scattering at any given angle. The work necessary
to establish a certain fluctuation in concentration is connected with the depen-
dence of osmotic pressure (
π
) on concentration, such that
the
M
term in
Eq. (3-41)
is effectively replaced by
RT/
(
d
π
/dc
).
For a monodisperse solute,
Eq. (3-24)
is
c
5
1
M
1
A
3
c
2
RT
A
2
c
1
1
?
(3-42)
(Recall that the
A
i
's are virial coefficients.) Then
d
dc
5RT
1
M
1
2
A
3
c
2
2
A
2
c1
1
?
(3-43)
and the equivalent of
Eq. (3-41)
for a solution of monodisperse polymer is
I
0
θ
2
n
0
cos
2
2
π
ð
dn
=
dc
Þ
ð
1
1
θÞ
c
I
0
5
(3-44)
4
r
2
L
ð
M
2
1
1
2
A
2
c
1
3
A
3
c
2
1
?
Þ
λ
3.2.1
Terminology
Some of the factors in the foregoing equation are instrument constants and are
determined independently of the actual light-scattering measurement. These
include
n
0
(refractive index of pure solvent at the experimental temperature and
wavelength);
L
(Avogadro's constant);
λ
, which is set by the experimenter; and
r
,
an instrument constant.
It is convenient to lump a number of these parameters into the reduced scatter-
ing intensity
R
θ
, which is defined for unit volume of a scattering solution as
I
0
θ
2
c
r
2
2
n
0
ð
2
π
dn
=
dc
Þ
R
θ
5
θÞ
5
(3-45)
cos
2
4
L
I
0
ð
1
1
λ
ð
M
2
1
1
2
A
2
c
1
3
A
3
c
2
1
?
Þ
and to define the optical constant
K
, such that
2
π
2
n
0
ð
dn
=
dc
Þ
2
K 5
(3-46)
4
L
λ
Thus,
3
A
3
c
2
Kc
=
R
θ
5
1
=
M
1
2
A
2
c
1
1
?
(3-47)
