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259
6.5.2.
Further analysis
The simplest analysis of [
η
]-M data from SMV is of course based on the Mark-
Houwink equation ([
η
] = KM
a
). The figure below is an overlay of data obtained
for two chitosans
49
covering different molecular weight ranges (M
w
= 240.000
and 38.000 Da, respectively).
The figure illustrates several aspects:
a)
The M-[
η
] range available for analysis can be increased by combining
results from several samples
b)
The combined line for chitosans shows curvature – it is not a straight
line! We find an exponent of about 1.14 for M < ca. 50.000. In this
range we observe short chains. They are not perfect random coils, but
approach the rigid rod range. At high M (M > 200.000) the slope
approaches 0.9, which is closer to the theoretical value for random
coils in good solvents (0.8).
6.2.6. Applying
the wormlike
coil model
The feature b) (above) is in fact well covered by the wormlike chain model,
which includes both the rod limit, the intermediate stiff coil region, and the true
random coil limit. The wormlike chain model considers the polymers as long,
curved cylinders, with constant, but randomly oriented curvature. General
expressions for both R
G
-M and [
η
]-M relations exist. We will here consider the
[
η
]-M relation. The mathematical model is quite complicated, but in a famous
article Bohdaneký
50
simplified it. According to the simplified model, (M
2
/[
η
])
1/3
becomes a linear function of M
1/2
:
49
MM-120-690 FA005.xls (2005)
50
Bohdanecký, M.
Macromolecules
1983
,
16
, 1483.
10
100
1,000
10,000
100,000
1,000,000
M
i
[
!
] (ml/g)