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231
The scattered light is – as already noted - extremely weak compared to the
incident light (approx. I
0
x 10
-9
).
6.2.2. Scattering
from a
single particle
The relationship between the intensity of the scattered light (i) and the incident
light (I
0
) is for an isolated particle given by (for unpolarized light):
i
I
0
=
8
π
4
α
2
r
2
λ
0
4
(1
+
cos
2
θ
)
α
: polarizability
r: distance from scattering center to the observer (detector)
λ
0
: wavelength of light (in vacuo)
The scattering intensity reaches it’s maximum value at cos
2
θ
= 1, or
θ
= 0
°
, an
its minimum value at 90
°
. Modern instruments employ vertically polarized
light. In this case:
i
I
0
=
16
π
4
α
2
r
2
λ
0
4
(sin
2
φ
)
φ
: Angle relative to z-direction
The polarizability (
α
) is linked to the refractive index (n), which can be
determined experimentally. The excess (solvent subtracted) polarizability is
given by:
n
2
−
n
0
2
=
4
π
N
α
where N is the number of particles (macromolecules) per ml (cm
3
) in solution.
6.2.3. Scattering
from a
large number of
independent particles
Light waves scattered from a large number of particles will interfere, as waves
generally do. However, for a large number of particles moving independently
positive and negative interference cancel, and the total scattering intensity is
simply the sum of intensities from each particle. This situation changes when