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we observe large molecules (> ca.
λ
/20), where the intramolecular
interference must be accounted for.
Scattering from macromolecules in solution (R
G
<
λ
/20)
Molecules where R
G
is small compared to the wavelength of the light can be
considered as point scatterers (as a star in the night sky). The limit is in the
range of
λ
/20, so for
λ
= 500 nm we can consider molecules up to about 25
nm in the present context. This includes, for example, almost all globular
proteins and polysaccharides such as alginate or chitosan up to a molecular
weight of about 100.000 Da.
The main equation is:
Kc
R
θ
=
1
M
+
2
A
2
c
+
..
M
=
molecular weight (molar mass) (g/mol = Da)
A
2
=
second virial coefficient (thermodynamic parameter)
c
=
polymer concentration (g/ml)
The Rayleigh factor R
θ
reflects the scattering intensity (i
θ
) at a scattering angle
(
θ
) relative to the intensity of the incident light (I
0
), as well as the distance r
(instrument constant) through the equation:
R
θ
=
i
θ
I
0
r
2
1
+
cos
2
θ
⎛
⎝⎜
⎞
⎠⎟
K is an optical constant, which for vertically polarized light equals:
K
=
4
π
2
n
0
2
∂
n
∂
c
⎛
⎝⎜
⎞
⎠⎟
2
N
λ
0
4
N
: Avogadro'a number
n
0
: Refractive index of solvent (water and dilute salt solutions at 25C: n
0
=1.33)
The term (dn/dc) – the refractive index gradient – reflects as mentioned the
polarizability
α
(by slight rearrangements of the equation n
2
-n
0
2
= 4
π
N
α
, see