Viscotek TDA 302, Instrument Manual, Page: 19 / 55

19
[A.2-1]
( )
KC
R M P
A C
w
θ
θ
= +
1
2
2
where
C
is the sample concentration,
M
w
is the weight average MW, and
A
2
is the second virial
coefficient. The term P (
θ
) is the particle scattering function
2,3
which describes the angular
dependence of light scattering intensity. The term P (
θ
) is a function of the geometry and size of
the polymer molecules with respect to wavelength of the incident light. The K term in Equation
[A.2-1] is an optical constant:
[A.2-2]
K
n
N
dn
dc
A
=








2
2
0
2
0
4
2
π
λ
where
n is the refractive index of the medium,
λ
0
is the wavelength of the incident beam, N
A
is
Avagadro’s number (6.023 x 10
23
), and dn/dc is the refractive index increment. The excess
Rayleigh ration R
θ
in Equation [A.3-1] gives the normalized scattering intensity with respect to
the scattered volume v , distance r , and incident intensity I
0
:
[A.2-3]
( )
R I I
r
I v
θ θ θ
= −






solution solvent
2
0
where
I
θ
solution
and
I
θ
solvent
represent the scattering intensity observed at the scattered angle
θ
, for
the polymer solution respectively.
Experimentally,
the P (
θ
) value can be determined as the ratio of scattering intensity at
the scattering angle
θ
, versus the scattering intensity at
θ
= 0°:
[A.2-4]
( )
P
I
I
θ θ
θ
=
=
solution
solution 0
o
Due to the dissymmetry and depending on the size of the polymer molecule, the
P (
θ
) function
can take on values that are equal to, or less than unity.
The angular dependence of light scattering intensity is the consequence of the
destructive interference of the scattered radiations.
4
When a scattering particle has its sizes
comparable to the wavelength of the incident beam, the scattering radiation from different parts
of the particle may get out of phase when they reach the detector. The extent of this phase
mismatch varies with the scattering angle. For example, due to the difference in the optical path
distances, the radiations from scattering point A and B would be more out of phase as they
reach detector 2 than detector 1. Because of this destructive radiation field interference, a lower
scattering intensity would be observed at the larger scattering angles, such as the case for
2
P. Kratochvil, “Classical Light Scattering from Polymer Solutions”, Elsevier, Amsterdam, 1987.
3
P. Kratochvil, in “Light Scattering of Polymer Solutions”, M. B. Huglin (Ed.), Academic Press, New York,
1967, Ch. 7.
4
B. H. Zimm, R. S. Stein, and P. Doty, Polymer Bulletin, 1 , 90, (1945).