23
P
0
CELL
RALLS
LASER
(670 nm)
Figure 6: RALLS Diagram
Angular light scattering dissymmetry is not a factor for many important commercial
random-coil type polymers having molecular weight values in the order of 100,000 or less, like
most polycondensation, Nylon, or Dacron type polymers. For higher MW samples, a proper
account of LS dissymmetry is highly desirable to assure a better than 5% accuracy in the
molecular weight determination. In Viscotek’s software, the following algorithm is used to
account for LS dissymmetry automatically to guarantee accuracy:
1) Initially, the particle scattering function at 90°,
P
(90°)
, is assumed a value of 1.0 and
a molecular weight estimate
M
est
is calculated directly from the RALLS intensity
R
90
from Equation [A.2-10], that is:
[A.2-16]
KC
R
M
est
D
90
=
=
θ
where
K
is the optical constant defined earlier.
2) A Flory-Fox radius
R
FF
is then calculated from the above
M
est
and the experimental
intrinsic viscosity value [
η
]:
[A.2-17]
[ ]
R
M
FF est
est
,
=
1
6
1 2
1 3
η
Φ
where
Φ
is the Flory viscosity constant defined earlier in Equations [A.2-12] and [A.2-
13] that take into account the different degrees of solvent expansion factor for the
polymer molecules.
3) An improved 90° dissymmetry value of
P
(90°)
est
is then calculated from a specific
particle scattering function that fits either the rigid-rod, hard-sphere, or random coil
type; the following Debye
P
(
θ
)
function is chosen to update the
P
(90°)
est
value.
[A.2-18]
( )
(
)
(
)
P
X
e
X
est
X
90
2
1
2
o
=
− −
−
where,
[A.2-19]
X
n
R
FF est
=
4
0
0
π
λ
,
where
n
0
is the solvent refractive index, and
λ
0
is the wavelength of the incident light.