24
4) A new estimate of the molecular weight is calculated from:
[A.2-20]
( )
New
M
M
P
est
est
est
=
90
o
5) Steps of 2 and 4 are repeated using the new estimate of molecular weight until the
molecular weight and
R
FF
values no longer change. This usually takes three
iterations or less.
A similar algorithm, but with the different
P
(
θ
) functions is provided in the software as an
option for treating polymer samples of other conformational architectures. Either a rigid-rod or a
hard-sphere particle scattering function can be used besides the random coil model used as an
example to explain the basic features of the SEC-Viscometry-RALLS software package.
The accuracy of the MW determination by the SEC-Viscometry-RALLS triple detector
technique is illustrated by the results obtained on polybutadiene standards shown in
Table A.2-
1
shown below.
Nominal MW
[
η
]
Rg
P
(90°)
MW by SEC-
MW by
of Supplier
(dl/g)
(nm)
Visc-RALLS
UNICAL
1K
0.053
1.29
1.00
1.03K
1.36K
3
0.108
2.36
1.00
3.09
3.45
5
0.18
3.71
1.00
7.07
7.33
22
0.439
7.7
1.00
26.3
26.3
43
0.725
11.3
0.99
51.9
50.6
170
1.82
23.8
0.94
188
161
272
2.5
30.7
0.89
295
273
Table A.2-1 Accurate MW and Rg Determination by Triple Detector SEC
of Polybutadiene Standards in THF
The
P
(90°) values in the fourth column are the angular dissymmetry factor of the particle
scattering function measured at the 90° scattering angle. Remember that the
P
(90°) value
equals the ration of the scattering intensity at the 0° scattering angle. The
P
(90°) factor can be
1.00 or less. A
P
(90°) value of 1.00 is indicative of the fat that there is no angular dependence
of the scattering intensity, reflecting the presence of an isotropic scattering of small molecular
size. When
P
(90°) is close to 1.00, no angular dissymmetry correction of the 90° scattering
intensity is needed for the accurate MW determination.
The MW values from the triple detector measurement are shown in the fifth column of
Table A.2-1
. These values have been corrected for the angular dissymmetry factor of the
P
(90°) value. It is apparent from the
P
(90°) data that no correction is needed for the low MW
samples, and there is up to an 11% correction made for the 272K MW standard. It has been
shown that accurate MW determination is possible for samples up to several million MW by the
RALLS measurement with the dissymmetry correction. The RALLS dissymmetry correction is
automatically done in the triple detector software using the
R
g
values calculated from the
combined IV and MW information derived from the viscometer and LS detector signals.
