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234
According to the equation Kc/R
θ
= 1/M + 2A
2
c, Kc/R
θ
is a linear function of c,
with 1/M as intercept, and 2A
2
s slope. Thus, A
2
is found in addition to the
molecular weight M.
In the example above the intercept is 5
⋅
10
-6
⇒
M = 1/5
⋅
10
-6
= 200.000 g/mol
(Da). The slope is 6
⋅
10
-3
⇒
A
2
= 2
⋅
10
-3
(ml mol
-1
g
-1
).
This approach cannot be used for larger molecules, except when special
instruments operating at very low angles (5-7
°
) are used. Such instruments
exist, but have been generally been replaced by multi-angle instruments,
which can be used for all kinds of molecules (up to R
G
=
λ
/2, above which the
scattering behavior becomes much more complex (Mie scattering). In these
cases the scattering at zero angle, where the equation is 100% exact, is
obtained by extrapolation as discussed below.
6.2.4. Rayleigh-‐Gans
scattering
from
large particles
(R
G
<
λ
/2).
Large particles and molecules contain several scattering elements. These are
not independent as for small molecules, but
move in a correlated fashion. The
interference pattern from such particles
depends strongly on the scattering angle (
θ
),
and is always destructive (except at
θ
= 0
°
).
The size, shape and particle interactions all
influence the scattering behavior.
Fortunately, this situation can be accounted
for, and is integrated into the wonderful light
scattering equation:
Kc
R
θ
=
P
(
θ
)
−
1
1
M
+
2
A
2
c
+
.....
⎛
⎝⎜
⎞
⎠⎟
P
(
θ
)
=
1
N
2
i
=
1
n
∑
sin(
qR
i
,
j
)
qR
ij
j
=
1
n
∑
q
=
4
λ
sin
θ
2
⎛
⎝⎜
⎞
⎠⎟
(scattering vector)
R
i
,
j
=
distance between scattering centra of the molecule
The expression for P(
θ
) can be simplified by taking advantage of the
corresponding Taylor series:
Macromolecule divided into
small scattering centra, each
much smaller than
λ
/20.